To see the other types of publications on this topic, follow the link: Second-order method.
Dissertations / Theses on the topic 'Second-order method'
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 50 dissertations / theses for your research on the topic 'Second-order method.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
1
Auffredic, Jérémy. "A second order Runge–Kutta method for the Gatheral model." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-49170.
Full textAbstract:
In this thesis, our research focus on a weak second order stochastic Runge–Kutta method applied to a system of stochastic differential equations known as the Gatheral Model. We approximate numerical solutions to this system and investigate the rate of convergence of our method. Both call and put options are priced using Monte-Carlo simulation to investigate the order of convergence. The numerical results show that our method is consistent with the theoretical order of convergence of the Monte-Carlo simulation. However, in terms of the Runge-Kutta method, we cannot accept the consistency of our method with the theoretical order of convergence without further research.
2
Mashalaba, Qaphela. "Implementation of numerical Fourier method for second order Taylor schemes." Master's thesis, Faculty of Commerce, 2019. http://hdl.handle.net/11427/30978.
Full textAbstract:
The problem of pricing contingent claims in a complete market has received a significant amount of attention in literature since the seminal work of Black, Fischer and Scholes, Myron (1973). It was also in 1973 that the theory of backward stochastic differential equations (BSDEs) was developed by Bismut, Jean-Michel (1973), but it was much later in the literature that BSDEs developed links to contingent claim pricing. This dissertation is a thorough exposition of the survey paper Ruijter, Marjon J and Oosterlee, Cornelis W (2016) in which a highly accurate and efficient Fourier pricing technique compatible with BSDEs is developed and implemented. We prove our understanding of this technique by reproducing some of the numerical experiments and results in Ruijter, Marjon J and Oosterlee, Cornelis W (2016), and outlining some key implementationl considerations.
3
Ben, Romdhane Mohamed. "Higher-Degree Immersed Finite Elements for Second-Order Elliptic Interface Problems." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/39258.
Full textAbstract:
A wide range of applications involve interface problems. In most of the cases, mathematical modeling of these interface problems leads to partial differential equations with non-smooth or discontinuous inputs and solutions, especially across material interfaces. Different numerical methods have been developed to solve these kinds of problems and handle the non-smooth behavior of the input data and/or the solution across the interface. The main focus of our work is the immersed finite element method to obtain optimal numerical solutions for interface problems.
In this thesis, we present piecewise quadratic immersed finite element (IFE) spaces that are used with an immersed finite element (IFE) method with interior penalty (IP) for solving two-dimensional second-order elliptic interface problems without requiring the mesh to be aligned with the material interfaces. An analysis of the constructed IFE spaces and their dimensions is presented. Shape functions of Lagrange and hierarchical types are constructed for these spaces, and a proof for the existence is established. The interpolation errors in the proposed piecewise quadratic spaces yield optimal O(h³) and O(h²) convergence rates, respectively, in the L² and broken H¹ norms under mesh refinement. Furthermore, numerical results are presented to validate our theory and show the optimality of our quadratic IFE method.
Our approach in this thesis is, first, to establish a theory for the simplified case of a linear interface. After that, we extend the framework to quadratic interfaces. We, then, describe a general procedure for handling arbitrary interfaces occurring in real physical practical applications and present computational examples showing the optimality of the proposed method. Furthermore, we investigate a general procedure for extending our quadratic IFE spaces to p-th degree and construct hierarchical shape functions for p=3.Ph. D.
4
Beamis, Christopher Paul 1960. "Solution of second order differential equations using the Godunov integration method." Thesis, The University of Arizona, 1990. http://hdl.handle.net/10150/277319.
Full textAbstract:
This MS Thesis proposes the use of an integration technique due to Godunov for the direct numerical solution of systems of second order differential equations. This method is to be used instead of the conventional technique of separating each second order equation into two first order equations and then solving the resulting system with one of the many methods available for systems of first order differential equations. Stability domains and expressions for the truncation error will be developed for this method when it is used to solve the wave equation, a passive mechanical system, and a passive electrical circuit. It will be shown both analytically and experimentally that the Godunov method compares favorably with the Adams-Bashforth third order method when used to solve both the wave equation and the mechanical system, but that there are potential problems when this method is used to simulate electrical circuits which result in integro-differential equations.
5
Dzacka, Charles Nunya. "A Variation of the Carleman Embedding Method for Second Order Systems." Digital Commons @ East Tennessee State University, 2009. https://dc.etsu.edu/etd/1877.
Full textAbstract:
The Carleman Embedding is a method that allows us to embed a finite dimensional system of nonlinear differential equations into a system of infinite dimensional linear differential equations. This technique works well when dealing with first-order nonlinear differential equations. However, for higher order nonlinear ordinary differential equations, it is difficult to use the Carleman Embedding method. This project will examine the Carleman Embedding and a variation of the method which is very convenient in applying to second order systems of nonlinear equations.
6
Vie, Jean-Léopold. "Second-order derivatives for shape optimization with a level-set method." Thesis, Paris Est, 2016. http://www.theses.fr/2016PESC1072/document.
Full textAbstract:
Le but de cette thèse est de définir une méthode d'optimisation de formes qui conjugue l'utilisation de la dérivée seconde de forme et la méthode des lignes de niveaux pour la représentation d'une forme.On considèrera d'abord deux cas plus simples : un cas d'optimisation paramétrique et un cas d'optimisation discrète.Ce travail est divisé en quatre parties.La première contient le matériel nécessaire à la compréhension de l'ensemble de la thèse.Le premier chapitre rappelle des résultats généraux d'optimisation, et notamment le fait que les méthodes d'ordre deux ont une convergence quadratique sous certaines hypothèses.Le deuxième chapitre répertorie différentes modélisations pour l'optimisation de formes, et le troisième se concentre sur l'optimisation paramétrique puis l'optimisation géométrique.Les quatrième et cinquième chapitres introduisent respectivement la méthode des lignes de niveaux (level-set) et la méthode des éléments-finis.La deuxième partie commence par les chapitres 6 et 7 qui détaillent des calculs de dérivée seconde dans le cas de l'optimisation paramétrique puis géométrique.Ces chapitres précisent aussi la structure et certaines propriétés de la dérivée seconde de forme.Le huitième chapitre traite du cas de l'optimisation discrète.Dans le neuvième chapitre on introduit différentes méthodes pour un calcul approché de la dérivée seconde, puis on définit un algorithme de second ordre dans un cadre général.Cela donne la possibilité de faire quelques premières simulations numériques dans le cas de l'optimisation paramétrique (Chapitre 6) et dans le cas de l'optimisation discrète (Chapitre 7).La troisième partie est consacrée à l'optimisation géométrique.Le dixième chapitre définit une nouvelle notion de dérivée de forme qui prend en compte le fait que l'évolution des formes par la méthode des lignes de niveaux, grâce à la résolution d'une équation eikonale, se fait toujours selon la normale.Cela permet de définir aussi une méthode d'ordre deux pour l'optimisation.Le onzième chapitre détaille l'approximation d'intégrales de surface et le douzième chapitre est consacré à des exemples numériques.La dernière partie concerne l'analyse numérique d'algorithmes d'optimisation de formes par la méthode des lignes de niveaux.Le Chapitre 13 détaille la version discrète d'un algorithme d'optimisation de formes.Le Chapitre 14 analyse les schémas numériques relatifs à la méthodes des lignes de niveaux.Enfin le dernier chapitre fait l'analyse numérique complète d'un exemple d'optimisation de formes en dimension un, avec une étude des vitesses de convergenceThe main purpose of this thesis is the definition of a shape optimization method which combines second-order differentiationwith the representation of a shape by a level-set function. A second-order method is first designed for simple shape optimization problems : a thickness parametrization and a discrete optimization problem. This work is divided in four parts.The first one is bibliographical and contains different necessary backgrounds for the rest of the work. Chapter 1 presents the classical results for general optimization and notably the quadratic rate of convergence of second-order methods in well-suited cases. Chapter 2 is a review of the different modelings for shape optimization while Chapter 3 details two particular modelings : the thickness parametrization and the geometric modeling. The level-set method is presented in Chapter 4 and Chapter 5 recalls the basics of the finite element method.The second part opens with Chapter 6 and Chapter 7 which detail the calculation of second-order derivatives for the thickness parametrization and the geometric shape modeling. These chapters also focus on the particular structures of the second-order derivative. Then Chapter 8 is concerned with the computation of discrete derivatives for shape optimization. Finally Chapter 9 deals with different methods for approximating a second-order derivative and the definition of a second-order algorithm in a general modeling. It is also the occasion to make a few numerical experiments for the thickness (defined in Chapter 6) and the discrete (defined in Chapter 8) modelings.Then, the third part is devoted to the geometric modeling for shape optimization. It starts with the definition of a new framework for shape differentiation in Chapter 10 and a resulting second-order method. This new framework for shape derivatives deals with normal evolutions of a shape given by an eikonal equation like in the level-set method. Chapter 11 is dedicated to the numerical computation of shape derivatives and Chapter 12 contains different numerical experiments.Finally the last part of this work is about the numerical analysis of shape optimization algorithms based on the level-set method. Chapter 13 is concerned with a complete discretization of a shape optimization algorithm. Chapter 14 then analyses the numerical schemes for the level-set method, and the numerical error they may introduce. Finally Chapter 15 details completely a one-dimensional shape optimization example, with an error analysis on the rates of convergence
7
Andrade, Prashant William. "Implementation of second-order absorbing boundary conditions in frequency-domain computations /." Digital version accessible at:, 1999. http://wwwlib.umi.com/cr/utexas/main.
Full text
8
Zhang, Chun Yang. "A second order ADI method for 2D parabolic equations with mixed derivative." Thesis, University of Macau, 2012. http://umaclib3.umac.mo/record=b2592940.
Full text
9
Dunn, Kyle George. "An Integral Equation Method for Solving Second-Order Viscoelastic Cell Motility Models." Digital WPI, 2014. https://digitalcommons.wpi.edu/etd-theses/578.
Full textAbstract:
For years, researchers have studied the movement of cells and mathematicians have attempted to model the movement of the cell using various methods. This work is an extension of the work done by Zheltukhin and Lui (2011), Mathematical Biosciences 229:30-40, who simulated the stress and displacement of a one-dimensional cell using a model based on viscoelastic theory. The report is divided into three main parts. The first part considers viscoelastic models with a first-order constitutive equation and uses the standard linear model as an example. The second part extends the results of the first to models with second-order constitutive equations. In this part, the two examples studied are Burger model and a Kelvin-Voigt element connected with a dashpot in series. In the third part, the effects of substrate with variable stiffness are explored. Here, the effective adhesion coefficient is changed from a constant to a spatially-dependent function. Numerical results are generated using two different functions for the adhesion coefficient. Results of this thesis show that stress on the cell varies greatly across each part of the cell depending on the constitute equation we use, while the position and velocity of the cell remain essentially unchanged from a large-scale point of view.
10
Chibi, Ahmed-Salah. "Defect correction and Galerkin's method for second-order elliptic boundary value problems." Thesis, Imperial College London, 1989. http://hdl.handle.net/10044/1/47378.
Full text
11
Kim, Taejong. "Mesh independent convergence of modified inexact Newton methods for second order nonlinear problems." Texas A&M University, 2003. http://hdl.handle.net/1969.1/3870.
Full textAbstract:
In this dissertation, we consider modified inexact Newton methods applied to
second order nonlinear problems. In the implementation of Newton's method applied
to problems with a large number of degrees of freedom, it is often necessary to solve
the linear Jacobian system iteratively. Although a general theory for the convergence
of modified inexact Newton's methods has been developed, its application to nonlinear
problems from nonlinear PDE's is far from complete. The case where the nonlinear
operator is a zeroth order perturbation of a fixed linear operator was considered in
the paper written by Brown et al..
The goal of this dissertation is to show that one can develop modified inexact
Newton's methods which converge at a rate independent of the number of unknowns
for problems with higher order nonlinearities. To do this, we are required to first, set
up the problem on a scale of Hilbert spaces, and second, to devise a special iterative
technique which converges in a higher order Sobolev norm, i.e., H1+alpha(omega) \ H1
0(omega)
with 0 < alpha < 1/2. We show that the linear system solved in Newton's method can
be replaced with one iterative step provided that the initial iterate is close enough.
The closeness criteria can be taken independent of the mesh size.
In addition, we have the same convergence rates of the method in the norm of
H1 0(omega) using the discrete Sobolev inequalities.
12
Booth, Andrew S. "Collocation methods for a class of second order initial value problems with oscillatory solutions." Thesis, Durham University, 1993. http://etheses.dur.ac.uk/5664/.
Full textAbstract:
We derive and analyse two families of multistep collocation methods for periodic initial-value problems of the form y" = f(x, y); y((^x)o) = yo, y(^1)(xo) = zo involving ordinary differential equations of second order in which the first derivative does not appear explicitly. A survey of recent results and proposed numerical methods is given in chapter 2. Chapter 3 is devoted to the analysis of a family of implicit Chebyshev methods proposed by Panovsky k Richardson. We show that for each non-negative integer r, there are two methods of order 2r from this family which possess non-vanishing intervals of periodicity. The equivalence of these methods with one-step collocation methods is also established, and these methods are shown to be neither P-stable nor symplectic. In chapters 4 and 5, two families of multistep collocation methods are derived, and their order and stability properties are investigated. A detailed analysis of the two-step symmetric methods from each class is also given. The multistep Runge-Kutta-Nystrom methods of chapter 4 are found to be difficult to analyse, and the specific examples considered are found to perform poorly in the areas of both accuracy and stability. By contrast, the two-step symmetric hybrid methods of chapter 5 are shown to have excellent stability properties, in particular we show that all two-step 27V-point methods of this type possess non-vanishing intervals of periodicity, and we give conditions under which these methods are almost P-stable. P-stable and efficient methods from this family are obtained and demonstrated in numerical experiments. A simple, cheap and effective error estimator for these methods is also given.
13
Comas, Lou Enric. "Application of the generalized rank annihilation method (GRAM) to second-order liquid chromatographic data." Doctoral thesis, Universitat Rovira i Virgili, 2005. http://hdl.handle.net/10803/8995.
Full textAbstract:
Les mesures analítiques i els instruments que les generen poden classificar-se en funció del numero de dades que s'obtenen al mesurar una mostra. Si s'obté una matriu de respostes, s'anomenen dades d'ordre dos.En aquesta tesi es van utilitzar els dades d'ordre dos, obtingudes mitjançant un cromatògraf líquid d'alta resolució amb un detector de diodes en fila (DAD).
L'instrument HPLC-DAD és força comú. Tot i això, normalment, per determinar la concentració dels analits d'interès no s'utilitzen totes les dades enregistrades per l'instrument. El mode espectral només s'utilitza per identificar els analits o per verificar la puresa dels pics, mentre que l'àrea o l'alçada del pic s'utilitza per quantificar mitjançant calibratge univariant. Aquesta manera de treballar és molt útil sempre i quan la resposta mesurada sigui selectiva per l'analit d'interès.
En analitzar contaminants ambientals en mostres complexes, com poden ser mostres d'aigua de riu, no és senzill obtenir mesures selectives. Quan les respostes no son selectives, els mètodes de calibratge de segon ordre (els que utilitzen dades de segon ordre) es poden utlitzar per a quantificar l'analit d'interès.
La present tesi es basa en l'estudi de les propietats del mètode de calibratge de segon ordre Generalized Rank Annihilation Method (GRAM). Aquest mètode fou desenvolupat a mitjans de la dècada dels 80, i té unes propietats molt atractives:
1) Per a determinar la concentració de l'analit d'interès en una mostra test només cal una mostra de calibratge o estàndard.
2) No calen mesures selectives, amb la qual cosa el temps de la separació es pot reduir de manera considerable.
Tot i això, el GRAM té una sèrie de limitacions que fan que no s'apliqui de manera rutinària. L'objectiu de la tesi és estudiar els avantatges i les limitacions del GRAM i millorar els aspectes necessaris per a què és pugui aplicar de manera rutinària.
Per emprar GRAM les dades experimentals han de complir una sèrie de requisits matemàtics: (i) la resposta mesurada ha de ser suma de respostes corresponents als diferents analits i (ii) la resposta d'un analit ha de ser proporcional en les diferents mostres: l'analit ha d'eluir exactament al mateix temps de retenció tant en l'estàndard com en la mostra test. Si aquest requisit no es compleix, les prediccions del GRAM son esbiaixades.
S'han desenvolupat fórmules de superar aquestes dificultats. S'ha desenvolupat un mètode per alienar pics cromatogràfics, basat en un mètode de resolució de corbes (Iterative Target Transformation Factor Analysis, ITTFA). En sistemes HPLC-DAD, és força habitual que els pics de l'analit d'interès elueixin a diferents temps de retenció.
Les diferencies no son gaire grans (pocs segons) però poden ser suficients per fer que els resultats del GRAM siguin incorrectes.
El GRAM és un mètode basat en factors, i cal introduir aquest paràmetre per a calcular un model. S'ha desenvolupat un mètode gràfic per a triar el nombre de factors que s'utilitzen per calcular el model GRAM. Està basat en un paràmetre de l'algorisme GRAM (á).
Finalment s'ha desenvolupat un criteri per a determinar mostres discrepants (outliers).
El criteri desenvolupat per detectar outliers està basat en el Senyal Analític Net (NAS).
Tot l'esmentat anteriorment, s'ha aplicat a casos reals, en concret a l'anàlisi de naftalensulfonats i de contaminats polars presents en mostres d'aigua, tant de riu com de depuradora. Així s'ha pogut demostrar la utilitat del GRAM a la cromatografia, i comparar el GRAM amb altres mètodes de calibratge de segon ordre com el PARAFAC i MCR-ALS. Es va trobar que tots tres mètodes produïen resultats comparables.
Analytical measurements and the instruments that generate them can be classified regarding the number of data that are obtained when a sample is measured. When a matrix of response is obtained, it is known as second-order data.
In this thesis, second-order data were used, obtained from a high performance liquid chromatography (HPLC) couple with a diode array detector (DAD). This instrument is quite common in the analytical laboratories. However, the concentration of the analytes of interest is normally found without using all the measured data. The spectral model only is used to identify the analytes of for verifying the peak purity, whereas the area or the height of the peak is used to quantify using univariate calibration. This is a very useful strategy. However, the measured response must be selective to the analyte of interest.
When environmental pollutants were analyzed, like water samples, it is no so easy to get selective measurements. When the responses are not selective, the analyte on interest can still be quantified by using second-order calibration methods, which are the methods that use second-order data.
This thesis is based on the study of the properties of the second-order calibration method Generalized Rank Annihilation Method (GRAM).
This method was developed in the mid eighties and has very attractive properties:
1) To determine the concentration of the analyte of interest in a test sample, it is only necessary one calibration sample or standard.
2) Selective measurements are not necessary, implying the reduce of the separation time.
Despite these advantages, GRAM has some limitations which make that it is not applied routinely. The objectives of the thesis are to study the advantages and limitations of GRAM and improve the negative points in order to apply GRAM routinely.
To use GRAM the experimental data must accomplish some mathematical requirements: (i) the measured response must be result of the addition due to the different analytes in the peak and (ii) the response of the analyte must be proportional in the different samples: the analyte of interest must elute at the same retention time both in the calibration and in the test sample. When these conditions are not met, the GRAM predictions are biased.
Mathematical algorithms have been developed to overcome such difficulties. An algorithm to align chromatographic peaks has been developed, based on curve resolution method (Iterative Target Transformation Factor Analysis, ITTFA). In HPLCDAD systems is quite often that the peaks of the analyte of interest elute at different retention time in the calibration and in the test sample. Even the differences are not big (few seconds), they can be enough to make the GRAM results incorrect.
GRAM is a factor based calibration method, and the number of factors has to be introduced as an input to build a GRAM method. A graphical criterion has been selected to determine the number the number of factors, which is base on the use of a parameter of the GRAM algorithm (á).
Finally, a criterion to detect outlying samples has been developed, which is based on the Net Analyte Signal (NAS).
All the above commented were applied to real cases. Specifically to the analysis of aromatic sulfonates and polar pollutants in water form river samples and waste water plants. We were able to show the applicability of GRAM and to compare GRAM with other second-order calibration methods, such as PARAFAC i MCR-ALS. We found that the three methods provided comparable results.
14
Clack, Jhules. "Theoretical Analysis for Moving Least Square Method with Second Order Pseudo-Derivatives and Stabilization." University of Cincinnati / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1418910272.
Full text
15
Iaccarino, Gianni Luca. "Analytical Solution of two Traction-Value Problems in Second-Order Elasticity with Live Loads." Thesis, Virginia Tech, 2006. http://hdl.handle.net/10919/35137.
Full textAbstract:
We present a generalization of Signorini's method to the case of live loads which allows us to derive approximate solutions to some pure traction-value problems in finite elastostatics. The boundary-value problems and the corresponding compatibility conditions are formulated in order to determine the displacement of the system up to the second-order of approximation. In particular, we consider the case of homogeneous and isotropic elastic bodies and we solve the following two traction-value problems with live loads:(i) a sphere subjected to the action of a uniform pressure field;(ii)a hollow circular cylinder whose inner and outer surfaces are subjected to uniform pressures. Then, starting from these solutions, we suggest experiments to determine the second-order constitutive constants of the elastic body. Expressions of the second-order material constants in terms of displacements and Lame' coefficients are determined.Master of Science
16
Ritter, Baird S. "Solution strategies for second order, nonlinear, one dimensional, two point boundary value problems by FEM analysis." Thesis, Monterey, California : Naval Postgraduate School, 1990. http://handle.dtic.mil/100.2/ADA246063.
Full textAbstract:
Thesis (M.S. in Mechanical Engineering)--Naval Postgraduate School, December 1990.Thesis Advisor: Salinas, D. "December 1990." Description based on title screen as viewed on April 1, 2010. DTIC Identifier(s): Boundary value problems, finite element analysis, differential equations, problem solving, theses, interpolation, iterations, one dimensional, computer programs, approximation/mathematics, linearity. Author(s) subject terms: Galerkin FEM, nonlinear, quasilinearization, linearization, interpolation, iteration, differential equation, convergence. Includes bibliographical references (p. 164). Also available in print.
17
Luo, BiYong. "Shooting method-based algorithms for solving control problems associated with second-order hyperbolic partial differential equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ66358.pdf.
Full text
18
Sulemana, Hisham. "Comparison of mortality rate forecasting using the Second Order Lee–Carter method with different mortality models." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-43563.
Full textAbstract:
Mortality information is very important for national planning and health of a country. Mortality rate forecasting is a basic contribution for the projection of financial improvement of pension plans, well-being and social strategy planning. In the first part of the thesis, we fit the selected mortality rate models, namely the Power-exponential function based model, the ModifiedPerks model and the Heligman and Pollard (HP4) model to the data obtained from the HumanMortality Database [22] for the male population ages 1–70 of the USA, Japan and Australia. We observe that the Heligman and Pollard (HP4) model performs well and better fit the data as compared to the Power-exponential function based model and the Modified Perks model. The second part is to systematically compare the quality of the mortality rate forecasting using the second order Lee–Carter method with the selected mortality rate models. The results indicate that Power-exponential function based model and the Heligman and Pollard (HP4) model gives a more reliable forecast depending on individual countries.
19
Cisternino, Marco. "A parallel second order Cartesian method for elliptic interface problems and its application to tumor growth model." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2012. http://tel.archives-ouvertes.fr/tel-00690743.
Full textAbstract:
Cette thèse porte sur une méthode cartésienne parallèle pour résoudre des problèmes elliptiques avec interfaces complexes et sur son application aux problèmes elliptiques en domaine irrégulier dans le cadre d'un modèle de croissance tumorale. La méthode est basée sur un schéma aux différences fi nies et sa précision est d'ordre deux sur tout le domaine. L'originalité de la méthode consiste en l'utilisation d'inconnues additionnelles situées sur l'interface et qui permettent d'exprimer les conditions de transmission à l'interface. La méthode est décrite et les détails sur la parallélisation, réalisée avec la bibliothèque PETSc, sont donnés. La méthode est validée et les résultats sont comparés avec ceux d'autres méthodes du même type disponibles dans la littérature. Une étude numérique de la méthode parallélisée est fournie. La méthode est appliquée aux problèmes elliptiques dans un domaine irrégulier apparaissant dans un modèle continue et tridimensionnel de croissance tumorale, le modèle à deux espèces du type Darcy . L'approche utilisée dans cette application est basée sur la pénalisation des conditions de transmission a l'interface, afin de imposer des conditions de Neumann homogènes sur le bord d'un domaine irrégulier. Les simulations du modèle sont fournies et montrent la capacité de la méthode à imposer une bonne approximation de conditions au bord considérées.
20
Jeschke, Anja [Verfasser], and Jörn [Akademischer Betreuer] Behrens. "Second Order Convergent Discontinuous Galerkin Projection Method for Dispersive Shallow Water Flows / Anja Jeschke ; Betreuer: Jörn Behrens." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2018. http://d-nb.info/1172880662/34.
Full text
21
Jeschke, Anja Verfasser], and Jörn [Akademischer Betreuer] [Behrens. "Second Order Convergent Discontinuous Galerkin Projection Method for Dispersive Shallow Water Flows / Anja Jeschke ; Betreuer: Jörn Behrens." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2018. http://nbn-resolving.de/urn:nbn:de:gbv:18-94463.
Full text
22
Haque, Md Z. "An adaptive finite element method for systems of second-order hyperbolic partial differential equations in one space dimension." Ann Arbor, Mich. : ProQuest, 2008. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3316356.
Full textAbstract:
Thesis (Ph.D. in Computational and Applied Mathematics)--S.M.U.Title from PDF title page (viewed Mar. 16, 2009). Source: Dissertation Abstracts International, Volume: 69-08, Section: B Adviser: Peter K. Moore. Includes bibliographical references.
23
Rawat, Vineet. "Finite Element Domain Decomposition with Second Order Transmission Conditions for Time-Harmonic Electromagnetic Problems." The Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=osu1243360543.
Full text
24
Kadrnka, Libor [Verfasser], and Armin [Akademischer Betreuer] Iske. "The Finite Volume Particle Method : a Meshfree Method of Second Order for the Numerical Solution of Hyperbolic Conservation Laws / Libor Kadrnka. Betreuer: Armin Iske." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2015. http://d-nb.info/107194827X/34.
Full text
25
Hazda, Jakub. "Analýza Stirlingova oběhu." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2015. http://www.nusl.cz/ntk/nusl-231710.
Full textAbstract:
This paper deals with the thermodynamic cycle of Striling engine. Analysis of the ideal cycle, Schmidt analysis and second-order method with loss correction by PROSA 2.4 software is applied. The results are compared with experimental data of two model engines.
26
Tran, Dai Quang. "Toward improved flange bracing requirements for metal building frame systems." Thesis, Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/33908.
Full textAbstract:
This research investigates the application of the AISC Direct Analysis Method for stability bracing design of columns, beams, beam-columns and frames. Emphasis is placed on out-of-plane flange bracing design in metal building frame systems. Potential improvements and extensions to the 2005 AISC Appendix 6 stability bracing provisions are studied and evaluated. The structural attributes considered include various general conditions encountered in practical metal building design: unequal brace spacing, unequal brace stiffness, nonprismatic member geometry, variable axial load or bending moment along the member length, cross-section double or single symmetry, combined bending and axial load, combined torsional and lateral bracing from girts/purlins with or without diagonal braces from these components to the inside flanges, load height, cross-section distortion, and non-rigid end boundary conditions. The research addresses both the simplification to basic bracing design rules as well as direct computation for more complex cases. The primary goal is improved assessment of the demands on flange bracing systems in metal building frames.
27
Knisley, Jeff, L. Lee Glenn, Karl Joplin, and Patricia Carey. "Eigenslope Method for Second-Order Parabolic Partial Differential Equations and the Special Case of Cylindrical Cellular Structures With Spatial Gradients in Membrane Capacitance." Digital Commons @ East Tennessee State University, 2007. https://dc.etsu.edu/etsu-works/7521.
Full textAbstract:
Boundary value problems in PDEs usually require determination of the eigenvalues and Fourier coefficients for a series, the latter of which are often intractable. A method was found that simplified both analytic and numeric solutions for Fourier coefficients based on the slope of the eigenvalue function at each eigenvalue (eigenslope). Analytic solutions by the eigenslope method resulted in the same solutions, albeit in different form, as other methods. Numerical solutions obtained by calculating the slope of the eigenvalue function at each root (hand graphing, Euler's, Runge-Kutta, and others) also matched. The method applied to all classes of separable PDEs (parabolic, hyperbolic, and elliptical), orthogonal (Sturm-Liouville) or non orthogonal expansions, and to complex eigenvalues. As an example, the widespread assumption of uniform capacitance was tested. An analytic model of cylindrical brain cell structures with an exponential distribution of membrane capacitance was developed with the eigenslope method. The stimulus-response properties of the models were compared under different configurations and shown to fit to experimental data from dendritic neurons. The long-standing question was addressed of whether the amount of variation of membrane capacitance measured in experimental studies is sufficient to markedly alter the vital neuron characteristic of passive signal propagation. We concluded that the degree of membrane capacitance variation measured in cells does not alter electrical responses at levels that are physiologically significant. The widespread assumption of uniform membrane capacitance is likely to be a valid approximation.
28
Endres, Lanson Adam. "Computation modeling of drill bits a new method for reproducing bottom hole geometry and a second-order explicit integrator via composition for coupled rotating rigid bodies /." Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2007. http://wwwlib.umi.com/cr/ucsd/fullcit?p3283920.
Full textAbstract:
Thesis (Ph. D.)--University of California, San Diego, 2007.Title from first page of PDF file (viewed December 3, 2007). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 154-160).
29
Ruggeri, Felipe. "A higher order time domain panel method for linear and weakly non linear seakeeping problems." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/3/3135/tde-09122016-074844/.
Full textAbstract:
This thesis addresses the development of a weakly non-linear Higher Order Time Domain Rankine Panel Method (TDRPM) for the linear and weakly non-linear seakeeping analysis of floating offshore structures, including wave-current interaction effects. A higher order boundary elements method is adopted based on the body geometry description using Non-uniform Rational B-splines (NURBS) formulation, which can be generated by many standard Computed Aided Design (CAD) softwares widely available, and the several computed quantities (velocity potential, free surface elevation and others) are described using a B-spline formulation of arbitrary degree. The problem is formulated considering wave-current-body interactions up to second order effects, these ones considering the terms obtained by interaction of zero/first order quantities. In order to provide numerical stability, the Initial Boundary Value Problem (IBVP) is formulated in terms of the velocity potential and the local acceleration potential, the later used to predict the hydrodynamic pressure accurately. The zeroth order problem is solved using the double-body linearization instead of the Neumman-Kelvin one in order to allow bluff bodies simulation, leading to very complex expressions regarding the m-terms computation. The method adopts the Rankine sources as Green\'s function, which are integrated using Gauss quadrature in the entire domain, but for the self-influence terms that are integrated using a desingularized procedure. The numerical method is verified initially considering simplified geometries (sphere and circular cylinder) for both, first and second-order computations, with and without current effects. The derivatives of the velocity potential are verified by comparing the numerical m-terms to the analytical solutions for a hemisphere under uniform flow. The mean and double frequency drift forces are computed for fixed and floating structures and the quantities involved in these computations (wave runup, velocity field) are also compared to literature results, including the free floating response of a sphere under current effects. Two practical cases are also studied, namely the wave-induced second order responses of a semi-submersible platform and the wavedrift-damping effect evaluated through the equilibrium angle of a turret moored FPSO. For the former, some specific model tests were designed and conducted in a wave-basin.Essa tese aborda o desenvolvimento de um método de Rankine de ordem alta no domínio do tempo (TDRPM) para o estudo de problemas lineares e fracamente não lineares, incluindo o efeito de corrente, envolvendo sistemas flutuantes. O método de ordem alta desenvolvido considera a geometria do corpo como descrita pelo padrão Non-uniform Rational Basis Spline (NURBS), que está disponível em diverso0s softwares de Computed Aided Design (CAD) disponíveis, sendo as diversas funções (potencial de velocidades, elevação da superfície-livre e outros) descritos usando B-splines de grau arbitrário. O problema é formulado considerando interações onda-corrente-estrutura para efeitos de até segunda ordem, os de ordem superior sendo calculados considerando as interações somente dos termos de ordem inferior. Para garantir a estabilidade numérica, o problema de contorno com valor inicial é formulado0 com relação ao potencial de velocidade e de parcela local do potencial de acelerações, este para garantir cálculos precisos da pressão dinâmica. O problema de ordem zero é resolvido usando a linearização de corpo-duplo ao invés da linearização de Neumman-Kelvin para permitir a análise de corpos rombudos, o que requer o cálculo de termos-m de grande complexidade. O método adota fontes de Rankine como funções de Green, que são integradas através de quadratura de Gauss-Legendre no domínio todo, exceto com relação aos termos de auto-influência que adotasm um procedimento de dessingularização. O método numérico é inicialmente verificado considerando corpos de geometria simplificada (esfera e cilindro), considerando efeitos de primeira e segunda ordens, com e sem corrente. As derivadas do potencial de velocidade são verificadas comparando os termos-m obtidos numericamente com soluções analíticas disponíveis para a esfera em fluído infinito. As forças de deriva média e dupla-frequência são calculadas para estruturas fixas e flutuantes, sendo as funções calculadas (elevação da superfície, campo de velocidade) comparadas com resultados disponíveis na literatura, incluindo o movimento da esfera flutuante sob a ação de corrente e ondas. São também estudados dois casos de aplicação prática, a resposta de segunda ordem de uma plataforma semi-submersível e o efeito de wave-drift damping para o ângulo de equilíbrio de uma plataforma FPSO ancorada através de sistema turred. No caso da semi-submersível, os ensaios foram projetados e realizados em tanque de provas.
30
Li, Boning. "Extending the scaled boundary finite-element method to wave diffraction problems." University of Western Australia. School of Civil and Resource Engineering, 2007. http://theses.library.uwa.edu.au/adt-WU2007.0173.
Full textAbstract:
[Truncated abstract] The study reported in this thesis extends the scaled boundary finite-element method to firstorder and second-order wave diffraction problems. The scaled boundary finite-element method is a newly developed semi-analytical technique to solve systems of partial differential equations. It works by employing a special local coordinate system, called scaled boundary coordinate system, to define the computational field, and then weakening the partial differential equation in the circumferential direction with the standard finite elements whilst keeping the equation strong in the radial direction, finally analytically solving the resulting system of equations, termed the scaled boundary finite-element equation. This unique feature of the scaled boundary finite-element method enables it to combine many of advantages of the finite-element method and the boundaryelement method with the features of its own. ... In this thesis, both first-order and second-order solutions of wave diffraction problems are presented in the context of scaled boundary finite-element analysis. In the first-order wave diffraction analysis, the boundary-value problems governed by the Laplace equation or by the Helmholtz equation are considered. The solution methods for bounded domains and unbounded domains are described in detail. The solution process is implemented and validated by practical numerical examples. The numerical examples examined include well benchmarked problems such as wave reflection and transmission by a single horizontal structure and by two structures with a small gap, wave radiation induced by oscillating bodies in heave, sway and roll motions, wave diffraction by vertical structures with circular, elliptical, rectangular cross sections and harbour oscillation problems. The numerical results are compared with the available analytical solutions, numerical solutions with other conventional numerical methods and experimental results to demonstrate the accuracy and efficiency of the scaled boundary finite-element method. The computed results show that the scaled boundary finite-element method is able to accurately model the singularity of velocity field near sharp corners and to satisfy the radiation condition with ease. It is worth nothing that the scaled boundary finite-element method is completely free of irregular frequency problem that the Green's function methods often suffer from. For the second-order wave diffraction problem, this thesis develops solution schemes for both monochromatic wave and bichromatic wave cases, based on the analytical expression of first-order solution in the radial direction. It is found that the scaled boundary finiteelement method can produce accurate results of second-order wave loads, due to its high accuracy in calculating the first-order velocity field.
31
Costa, Henrique de Britto. "Elementos finitos (via resíduos ponderados) na resolução do problema de segunda ordem das placas." Universidade de São Paulo, 1986. http://www.teses.usp.br/teses/disponiveis/3/3144/tde-03072017-165248/.
Full textAbstract:
Este trabalho aborda os conceitos básicos da teoria de segunda ordem das placas elásticas delgadas, utilizando o Método dos Elementos Finitos (introduzido através do Método dos Resíduos Ponderados, na variante de Galerkin). São deduzidas as matrizes de rigidez geométrica, de rigidez secante e de rigidez tangente, relativas ao problema em consideração. É proposta ainda uma conduta notavelmente simplificada, que facilita sobremaneira a construção da matriz de rigidez tangente.This paper delas with the basic concepts of the secondf order theory of thin elastic plates, through the use of the Finite Element Method 9introcuced through the Weighted Residual Method, in Galerkin\'s approach). The matrices of geometric stiffness, secant stiffness, and tangent stiffness for the problem under consideration are deduced. It is also proposed an outstandingly simplified conduct, which will greatly easen the construction of the tangent stiffness matrix.
32
Karlgaard, Christopher David. "Second-Order Relative Motion Equations." Thesis, Virginia Tech, 2001. http://hdl.handle.net/10919/34025.
Full textAbstract:
This thesis presents an approximate solution of second order
relative motion equations. The equations of motion for a Keplerian
orbit in spherical coordinates are expanded in Taylor series form
using reference conditions consistent with that of a circular
orbit. Only terms that are linear or quadratic in state variables
are kept in the expansion. A perturbation method is employed to
obtain an approximate solution of the resulting nonlinear
differential equations. This new solution is compared with the
previously known solution of the linear case to show improvement,
and with numerical integration of the quadratic differential
equation to understand the error incurred by the approximation. In
all cases, the comparison is made by computing the difference of
the approximate state (analytical or numerical) from numerical
integration of the full nonlinear Keplerian equations of motion.Master of Science
33
El-Sharif, Najla Saleh Ahmed. "Second-order methods for some nonlinear second-order initial-value problems with forcing." Thesis, Brunel University, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.309501.
Full text
34
Trần, Thanh Ngọc. "Limit and shakedown analysis of plates and shells including uncertainties." Doctoral thesis, Universitätsbibliothek Chemnitz, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200800256.
Full textAbstract:
The reliability analysis of plates and shells with respect to plastic collapse or to inadaptation is formulated on the basis of limit and shakedown theorems. The loading, the material strength and the shell thickness are considered as random variables. Based on a direct definition of the limit state function, the nonlinear problems may be efficiently solved by using the First and Second Order Reliability Methods (FORM/SORM). The sensitivity analyses in FORM/SORM can be based on the sensitivities of the deterministic shakedown problem. The problem of reliability of structural systems is also handled by the application of a special barrier technique which permits to find all the design points corresponding to all the failure modes. The direct plasticity approach reduces considerably the necessary knowledge of uncertain input data, computing costs and the numerical errorDie Zuverlässigkeitsanalyse von Platten und Schalen in Bezug auf plastischen Kollaps oder Nicht-Anpassung wird mit den Traglast- und Einspielsätzen formuliert. Die Lasten, die Werkstofffestigkeit und die Schalendicke werden als Zufallsvariablen betrachtet. Auf der Grundlage einer direkten Definition der Grenzzustandsfunktion kann die Berechnung der Versagenswahrscheinlichkeit effektiv mit den Zuverlässigkeitsmethoden erster und zweiter Ordnung (FROM/SORM) gelöst werden. Die Sensitivitätsanalysen in FORM/SORM lassen sich auf der Basis der Sensitivitäten des deterministischen Einspielproblems berechnen. Die Schwierigkeiten bei der Ermittlung der Zuverlässigkeit von strukturellen Systemen werden durch Anwendung einer speziellen Barrieremethode behoben, die es erlaubt, alle Auslegungspunkte zu allen Versagensmoden zu finden. Die Anwendung direkter Plastizitätsmethoden führt zu einer beträchtlichen Verringerung der notwendigen Kenntnis der unsicheren Eingangsdaten, des Berechnungsaufwandes und der numerischen Fehler
35
Coskun, Korhan. "Three Dimensional Laminar Compressible Navier Stokes Solver For Internal Rocket Flow Applications." Master's thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/12609086/index.pdf.
Full textAbstract:
A three dimensional, Navier-Stokes finite volume flow solver which uses Roe&rsquos upwind flux differencing scheme for spatial and Runge-Kutta explicit multi-stage time stepping scheme and implicit Lower-Upper Symmetric Gauss Seidel (LU-SGS) iteration scheme for temporal discretization on unstructured and hybrid meshes is developed for steady rocket internal viscous flow applications. The spatial accuracy of the solver can be selected as first or second order. Second order accuracy is achieved by piecewise linear reconstruction. Gradients of flow variables required for piecewise linear reconstruction are calculated with both Green-Gauss and Least-Squares approaches. The solver developed is first verified against the three-dimensional viscous laminar flow over flat plate. Then the implicit time stepping algorithms are compared against two rocket motor internal flow problems. Although the solver is intended for internal flows, a test case involving flow over an airfoil is also given. As the last test case, supersonic vortex flow between concentric circular arcs is selected.
36
Rodríguez, Cuesta Mª José. "Limit of detection for second-order calibration methods." Doctoral thesis, Universitat Rovira i Virgili, 2006. http://hdl.handle.net/10803/9013.
Full textAbstract:
Analytical chemistry can be split into two main types, qualitative and quantitative. Most modern analytical chemistry is quantitative. Popular sensitivity to health issues is aroused by the mountains of government regulations that use science to, for instance, provide public health information to prevent disease caused by harmful exposure to toxic substances. The concept of the minimum amount of an analyte or compound that can be detected or analysed appears in many of these regulations (for example, to discard the presence of traces of toxic substances in foodstuffs) generally as a part of method validation aimed at reliably evaluating the validity of the measurements.The lowest quantity of a substance that can be distinguished from the absence of that substance (a blank value) is called the detection limit or limit of detection (LOD). Traditionally, in the context of simple measurements where the instrumental signal only depends on the amount of analyte, a multiple of the blank value is taken to calculate the LOD (traditionally, the blank value plus three times the standard deviation of the measurement). However, the increasing complexity of the data that analytical instruments can provide for incoming samples leads to situations in which the LOD cannot be calculated as reliably as before.
Measurements, instruments and mathematical models can be classified according to the type of data they use. Tensorial theory provides a unified language that is useful for describing the chemical measurements, analytical instruments and calibration methods. Instruments that generate two-dimensional arrays of data are second-order instruments. A typical example is a spectrofluorometer, which provides a set of emission spectra obtained at different excitation wavelengths.
The calibration methods used with each type of data have different features and complexity. In this thesis, the most commonly used calibration methods are reviewed, from zero-order (or univariate) to second-order (or multi-linears) calibration models. Second-order calibration models are treated in details since they have been applied in the thesis.
Concretely, the following methods are described:
- PARAFAC (Parallel Factor Analysis)
- ITTFA (Iterative Target Transformation Analysis)
- MCR-ALS (Multivariate Curve Resolution-Alternating Least Squares)
- N-PLS (Multi-linear Partial Least Squares)
Analytical methods should be validated. The validation process typically starts by defining the scope of the analytical procedure, which includes the matrix, target analyte(s), analytical technique and intended purpose. The next step is to identify the performance characteristics that must be validated, which may depend on the purpose of the procedure, and the experiments for determining them. Finally, validation results should be documented, reviewed and maintained (if not, the procedure should be revalidated) as long as the procedure is applied in routine work.
The figures of merit of a chemical analytical process are 'those quantifiable terms which may indicate the extent of quality of the process. They include those terms that are closely related to the method and to the analyte (sensitivity, selectivity, limit of detection, limit of quantification, ...) and those which are concerned with the final results (traceability, uncertainty and representativity) (Inczédy et al., 1998). The aim of this thesis is to develop theoretical and practical strategies for calculating the limit of detection for complex analytical situations. Specifically, I focus on second-order calibration methods, i.e. when a matrix of data is available for each sample.
The methods most often used for making detection decisions are based on statistical hypothesis testing and involve a choice between two hypotheses about the sample. The first hypothesis is the "null hypothesis": the sample is analyte-free. The second hypothesis is the "alternative hypothesis": the sample is not analyte-free. In the hypothesis test there are two possible types of decision errors. An error of the first type occurs when the signal for an analyte-free sample exceeds the critical value, leading one to conclude incorrectly that the sample contains a positive amount of the analyte. This type of error is sometimes called a "false positive". An error of the second type occurs if one concludes that a sample does not contain the analyte when it actually does and it is known as a "false negative". In zero-order calibration, this hypothesis test is applied to the confidence intervals of the calibration model to estimate the LOD as proposed by Hubaux and Vos (A. Hubaux, G. Vos, Anal. Chem. 42: 849-855, 1970).
One strategy for estimating multivariate limits of detection is to transform the multivariate model into a univariate one. This strategy has been applied in this thesis in three practical applications:
1. LOD for PARAFAC (Parallel Factor Analysis).
2. LOD for ITTFA (Iterative Target Transformation Factor Analysis).
3. LOD for MCR-ALS (Multivariate Curve Resolution - Alternating Least Squares)
In addition, the thesis includes a theoretical contribution with the proposal of a sample-dependent LOD in the context of multivariate (PLS) and multi-linear (N-PLS) Partial Least Squares.
La Química Analítica es pot dividir en dos tipus d'anàlisis, l'anàlisi quantitativa i l'anàlisi qualitativa. La gran part de la química analítica moderna és quantitativa i fins i tot els govern fan ús d'aquesta ciència per establir regulacions que controlen, per exemple, nivells d'exposició a substàncies tòxiques que poden afectar la salut pública. El concepte de mínima quantitat d'un analit o component que es pot detectar apareix en moltes d'aquestes regulacions, en general com una part de la validació dels mètodes per tal de garantir la qualitat i la validesa dels resultats.
La mínima quantitat d'una substància que pot ser diferenciada de l'absència d'aquesta substància (el que es coneix com un blanc) s'anomena límit de detecció (limit of detection, LOD). En procediments on es treballa amb mesures analítiques que són degudes només a la quantitat d'analit present a la mostra (situació d'ordre zero) el LOD es pot calcular com un múltiple de la mesura del blanc (tradicionalment, 3 vegades la desviació d'aquesta mesura). Tanmateix, l'evolució dels instruments analítics i la complexitat creixent de les dades que generen, porta a situacions en les que el LOD no es pot calcular fiablement d'una forma tan senzilla. Les mesures, els instruments i els models de calibratge es poden classificar en funció del tipus de dades que utilitzen. La Teoria Tensorial s'ha utilitzat en aquesta tesi per fer aquesta classificació amb un llenguatge útil i unificat. Els instruments que generen dades en dues dimensions s'anomenen instruments de segon ordre i un exemple típic és l'espectrofluorímetre d'excitació-emissió, que proporciona un conjunt d'espectres d'emissió obtinguts a diferents longituds d'ona d'excitació.
Els mètodes de calibratge emprats amb cada tipus de dades tenen diferents característiques i complexitat. En aquesta tesi, es fa una revisió dels models de calibratge més habituals d'ordre zero (univariants), de primer ordre (multivariants) i de segon ordre (multilinears). Els mètodes de segon ordre estan tractats amb més detall donat que són els que s'han emprat en les aplicacions pràctiques portades a terme.
Concretament es descriuen:
- PARAFAC (Parallel Factor Analysis)
- ITTFA (Iterative Target Transformation Analysis)
- MCR-ALS (Multivariate Curve Resolution-Alternating Least Squares)
- N-PLS (Multi-linear Partial Least Squares)
Com s'ha avançat al principi, els mètodes analítics s'han de validar. El procés de validació inclou la definició dels límits d'aplicació del procediment analític (des del tipus de mostres o matrius fins l'analit o components d'interès, la tècnica analítica i l'objectiu del procediment). La següent etapa consisteix en identificar i estimar els paràmetres de qualitat (figures of merit, FOM) que s'han de validar per, finalment, documentar els resultats de la validació i mantenir-los mentre sigui aplicable el procediment descrit.
Algunes FOM dels processos químics de mesura són: sensibilitat, selectivitat, límit de detecció, exactitud, precisió, etc. L'objectiu principal d'aquesta tesi és desenvolupar estratègies teòriques i pràctiques per calcular el límit de detecció per problemes analítics complexos. Concretament, està centrat en els mètodes de calibratge que treballen amb dades de segon ordre.
Els mètodes més emprats per definir criteris de detecció estan basats en proves d'hipòtesis i impliquen una elecció entre dues hipòtesis sobre la mostra. La primera hipòtesi és la hipòtesi nul·la: a la mostra no hi ha analit. La segona hipòtesis és la hipòtesis alternativa: a la mostra hi ha analit. En aquest context, hi ha dos tipus d'errors en la decisió. L'error de primer tipus té lloc quan es determina que la mostra conté analit quan no en té i la probabilitat de cometre l'error de primer tipus s'anomena fals positiu. L'error de segon tipus té lloc quan es determina que la mostra no conté analit quan en realitat si en conté i la probabilitat d'aquest error s'anomena fals negatiu. En calibratges d'ordre zero, aquesta prova d'hipòtesi s'aplica als intervals de confiança de la recta de calibratge per calcular el LOD mitjançant les fórmules d'Hubaux i Vos (A. Hubaux, G. Vos, Anal. Chem. 42: 849-855, 1970)
Una estratègia per a calcular límits de detecció quan es treballa amb dades de segon ordre es transformar el model multivariant en un model univariant. Aquesta estratègia s'ha fet servir en la tesi en tres aplicacions diferents::
1. LOD per PARAFAC (Parallel Factor Analysis).
2. LOD per ITTFA (Iterative Target Transformation Factor Analysis).
3. LOD per MCR-ALS (Multivariate Curve Resolution - Alternating Least Squares)
A més, la tesi inclou una contribució teòrica amb la proposta d'un LOD que és específic per cada mostra, en el context del mètode multivariant PLS i del multilinear N-PLS.
37
Snyman, H. "Second order analyses methods for stirling engine design." Thesis, Stellenbosch : University of Stellenbosch, 2007. http://hdl.handle.net/10019.1/16102.
Full textAbstract:
Thesis (MScIng( Mechanical Engineering)--University of Stellenbosch, 2007.121 Leaves printed single pages, preliminary pages a-l and numbered pages 1-81.
ENGLISH ABSTRACT:In the midst of the current non-renewable energy crises specifically with regard to fossil fuel, various research institutions across the world have turned their focus to renewable and sustainable development. Using our available non.renewable resources as efficiently as possible has been a focal point the past decades and will certainly be as long as these resources exist Various means to utilize the world's abundant and freely available renewable energy has been studied and some even introduced and installed as sustainable energy sources, Electricity generation by means of wind powered turbines, photo-voltaic cells, and tidal and wave energy are but a few examples. Modern photo-voltaic cells are known to have a solar to electricity conversion efficiency of 12% (Van Heerden, 2003) while wind turbines have an approximate wind to electricity conversion efficiency of 50% (Twele et aI., 2002). This low solar to electricity conversion efficiency together with the fact that renewable energy research is a relatively modern development, lead to the investigation into methods capable of higher solar to electricity conversion efficiencies. One such method could be to use the relatively old technology of the Stirling cycle developed in the early 1800's (solar to electricity conversion efficiency in the range of 20.24 % according Van Heerden, 2003). The Stirling cycle provides a method for converting thermal energy to mechanical power which can be used to generate electricity, One of the main advantages of Stirling machines is that they are capable of using any form of heat source ranging from solar to biomass and waste heat. This document provides a discussion of some of the available methods for the analysis of Stirling machines. The six (6) different methods considered include: the method of Beale, West, mean-pressurepower- formula (MPPF), Schmidt, idea! adiabatic and the simple analysis methods. The first three (3) are known to be good back-of-the-envelope methods specifically for application as synthesis tools during initialisation of design procedures, while the latter three (3) are analysis tools finding application during Stirling engine design and analysis procedures. These analysis methods are based on the work done by Berchowitz and Urieli (1984) and form the centre of this document. Sections to follow provide a discussion of the mathematical model as well as the MATlAB implementation thereof. Experimental tests were conducted on the Heinrici engine to provide verification of the simulated resutls. Shortcomings of these analyses methods are also discussed in the sections to follow. Recommendations regarding improvements of the simulation program, possible fields of application for Stirling technology, as well as future fields of study are made in the final chapter of this document. A review of relevanl literature regarding modern applications of Stirling technology and listings of companies currently manufacturing and developing Stirling machines and findings of research done at various other institutions are provided.
AFRIKAANSE OPSOMMING:Die tempo van uitputling van die wereld se nie-hernubare energiebronne die afgelope jare het aanleiding gegee daartoe dal daar loenemend fokus toegespits word op die ontwikkeling van hernubare alternatiewe. Meer doeltreffende benutting van die wereld se nie-hernubare energie is reeds 'n fokus punt, vir navorsers reg oor die wereld, vir die afgelope dekades. Die aarde se oorvloedryke hernubare energie bronne word reeds met verskeie metodes ontgin. Die omskakeling van wind-, son- en gety energie na elektrisieteids is net 'n paar voorbeelde. Die effektiwiteid van sonkrag na elektrisietyds omskakeling van moderne fotovo!la'iese selle is in die orde van 12% (Van Heerden, 2003) terwyl die doeltreffendeid van wind energie na elektrisiteit omskakelling in die orde van 50% (Twele et at, 2002) is. Hierdie relatief lae omskelings doeltreffendeid van sonkrag na elektrisietyd, tesame met die feit dat die hernubare industrie nag relatief jonk is, lei lot die soeke na ander meer doellreffende moontlikhede Die Stirling siklus is nie 'n mod erne beginsel nie, maar die toepassing daarvan veral in die hernubare energie industrie is wei 'n relatiewe nuwe beg rip, veral in teme van die omskakeling van sonkrag na elektriese energie (gemiddelde sonkrag na lektriese energie omskakelings doellreffendeid in die orde van 20-24% is gevind deur Van Heerden, 2003). Die omskakeling van lermiese energie na meganiese energie is sekerlik die hoof uitkomsle van die Stirling siklus, alhoewel dit ook toepassing vind in die verkoefingsindustrie. Die feit dat die Stirling siklus van enige vorm van termiese energie (bv. son. biomassa, asook hilte geproduseer as byproduk tydens sekere prosesse) gebruik kan maak. is een van die redes wat die tegnologie 56 aanloklik maak, spesifiek !.o,v. die hernubare energie sektor. Ses (6) metodes vir die analise van die Stirling siklus word in hierdie dokument bespreek. Dit slui! die volgnde in: Beale-, West-, die gemiddelde-druk-krag-metode (GDKM), Schmidt-, adiabatiese- en die eenvoudige analise melodes. Die eerste drie (3) metodes is handige berekenings metodes Iydens die aanvangs en sinlesefase van Stirling enjin ontwerp, lerwyl die laaste drie (3) meer loegespils is op die volledige ontwerps- en analisefases gedurende die Stirling eniin ontwerps proses. Die drie (3) analise melodes is gebaseer op die werk wat deur Berchowitz en Urieli (1984) gedoen is en maak die kern van die dokument uit. Die wiskundige model, implimentering daarvan in MATlAB, sowel as die eksperimentele verifieering van die resultate word bespreek. Tekortkominge van die analise metodes word ook aangespreek in elke hoofsluk. Moontlikke verbeterings len opsigte van die verskeie aannames word in die finale hoofsluk van die dokumenl aangespreek. Verskeie voorgestelde riglings vir toekomslige navorsings projekle word ook in die finale hoofstuk van die dokument genoem. 'n Kort oorsig van die relevanle lileraluur in verband mel huidige loepassings van die Stirling legnologie, asook die name van maatskappye wal tans hierdie tegnologiee ontwikkel en vervaardig, word genoem.
38
Trần, Thanh Ngọc. "Limit and shakedown analysis of plates and shells including uncertainties." Doctoral thesis, Bericht ; 2/2008, 2007. https://monarch.qucosa.de/id/qucosa%3A18876.
Full textAbstract:
The reliability analysis of plates and shells with respect to plastic collapse or to inadaptation is formulated on the basis of limit and shakedown theorems. The loading, the material strength and the shell thickness are considered as random variables. Based on a direct definition of the limit state function, the nonlinear problems may be efficiently solved by using the First and Second Order Reliability Methods (FORM/SORM). The sensitivity analyses in FORM/SORM can be based on the sensitivities of the deterministic shakedown problem. The problem of reliability of structural systems is also handled by the application of a special barrier technique which permits to find all the design points corresponding to all the failure modes. The direct plasticity approach reduces considerably the necessary knowledge of uncertain input data, computing costs and the numerical error.Die Zuverlässigkeitsanalyse von Platten und Schalen in Bezug auf plastischen Kollaps oder Nicht-Anpassung wird mit den Traglast- und Einspielsätzen formuliert. Die Lasten, die Werkstofffestigkeit und die Schalendicke werden als Zufallsvariablen betrachtet. Auf der Grundlage einer direkten Definition der Grenzzustandsfunktion kann die Berechnung der Versagenswahrscheinlichkeit effektiv mit den Zuverlässigkeitsmethoden erster und zweiter Ordnung (FROM/SORM) gelöst werden. Die Sensitivitätsanalysen in FORM/SORM lassen sich auf der Basis der Sensitivitäten des deterministischen Einspielproblems berechnen. Die Schwierigkeiten bei der Ermittlung der Zuverlässigkeit von strukturellen Systemen werden durch Anwendung einer speziellen Barrieremethode behoben, die es erlaubt, alle Auslegungspunkte zu allen Versagensmoden zu finden. Die Anwendung direkter Plastizitätsmethoden führt zu einer beträchtlichen Verringerung der notwendigen Kenntnis der unsicheren Eingangsdaten, des Berechnungsaufwandes und der numerischen Fehler.
39
Fadlelmula, Fadlelseed Mohamed Mohieldin. "Probabilistic Modeling Of Failure In Rock Slopes." Master's thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/12608549/index.pdf.
Full textAbstract:
This study presents the results of probabilistic modeling of plane and wedge types of slope failures, based on the &rdquoAdvance First Order Second Moment (AFOSM)&rdquo
reliability method. In both of those failure types, two different failure criteria namely, Coulomb linear and Barton Bandis non-linear failure criteria are utilized in the development of the probabilistic models. Due to the iterative nature of the AFOSM method, analyzing spreadsheets have been developed in order to carry out the computations. The developed spreadsheets are called &ldquo
Plane Slope Analyzer (PSA)&rdquo
and &ldquo
Wedge Slope Analyzer (WSA)&rdquo
. The developed probabilistic models and their spreadsheets are verified by investigating the affect of rock and slope parameters such as, ground water level, slope height, cohesion, friction angle, and joint wall compressive strength (JCS) and their distribution types on the reliability index (&
#946
), and probability of slope failure (PF). In this study, different probability distributions are used and the inverse transformation formulas of their non-normal variates to their equivalent normal ones are developed as well. In addition, the wedge failure case is also modeled by using system reliability approach and then the results of conventional probability of failure and the system reliability approach are compared.
40
Dobrev, Veselin Asenov. "Preconditioning of discontinuous Galerkin methods for second order elliptic problems." [College Station, Tex. : Texas A&M University, 2007. http://hdl.handle.net/1969.1/ETD-TAMU-2531.
Full text
41
Crews, Hugh Bates. "Fast FSR Methods for Second-Order Linear Regression Models." NCSU, 2008. http://www.lib.ncsu.edu/theses/available/etd-04282008-151809/.
Full textAbstract:
Many variable selection techniques have been developed that focus on first-order linear regression models. In some applications, such as modeling response surfaces, fitting second-order terms can improve predictive accuracy. However, the number of spurious interactions can be large leading to poor results with many methods. We focus on forward selection, describing algorithms that use the natural hierarchy existing in second-order linear regression models to limit spurious interactions. We then develop stopping rules by extending False Selection Rate methodology to these algorithms. In addition, we describe alternative estimation methods for fitting regression models including the LASSO, CART, and MARS. We also propose a general method for controlling multiple-group false selection rates, which we apply to second-order linear regression models. By estimating a separate entry level for first-order and second-order terms, we obtain equal contributions to the false selection rate from each group. We compare the methods via Monte Carlo simulation and apply them to optimizing response surface experimental designs.
42
Brabazon, Keeran J. "Multigrid methods for nonlinear second order partial differential operators." Thesis, University of Leeds, 2014. http://etheses.whiterose.ac.uk/8481/.
Full textAbstract:
This thesis is concerned with the efficient numerical solution of nonlinear partial differential equations (PDEs) of elliptic and parabolic type. Such PDEs arise frequently in models used to describe many physical phenomena, from the diffusion of a toxin in soil to the flow of viscous fluids. The main focus of this research is to better understand the implementation and performance of nonlinear multigrid methods for the solution of elliptic and parabolic PDEs, following their discretisation. For the most part finite element discretisations are considered, but other techniques are also discussed. Following discretisation of a PDE the two most frequently used nonlinear multigrid methods are Newton-Multigrid and the Full Approximation Scheme (FAS). These are both very efficient algorithms, and have the advantage that when they are applied to practical problems, their execution times scale linearly with the size of the problem being solved. Even though this has yet to be proved in theory for most problems, these methods have been widely adopted in practice in order to solve highly complex nonlinear (systems of) PDEs. Many research groups use either Newton-MG or FAS without much consideration as to which should be preferred, since both algorithms perform satisfactorily. In this thesis we address the question as to which method is likely to be more computationally efficient in practice. As part of this investigation the implementation of the algorithms is considered in a framework which allows the direct comparison of the computational effort of the two iterations. As well as this, the convergence properties of the methods are considered, applied to a variety of model problems. Extensive results are presented in the comparison, which are explained by available theory whenever possible. The strength and range of results presented allows us to confidently conclude that for a practical problem, discretised using a finite element discretisation, an improved efficiency and stability of a Newton-MG iteration, compared to an FAS iteration, is likely to be observed. The relative advantage of a Newton-MG method is likely to be larger the more complex the problem being solved becomes.
43
Mustafa, Akdemir. "Development Of An Axisymmetric, Turbulent And Unstructured Navier-stokes Solver." Master's thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12611904/index.pdf.
Full textAbstract:
An axisymmetric, Navier-Stokes finite volume flow solver, which uses Harten, Lax and van Leer (HLL) and Harten, Lax and van Leer&ndashContact (HLLC) upwind flux differencing scheme for spatial and uses Runge-Kutta explicit multi-stage time stepping scheme for temporal discretization on unstructured meshe is developed. Developed solver can solve the compressible axisymmetric flow. The spatial accuracy of the solver can be first or second order accurate. Second order accuracy is achieved by piecewise linear reconstruction. Gradients of flow variables required for piecewise linear reconstruction are calculated by Green-Gauss theorem. Baldwin-Lomax turbulent model is used to compute the turbulent viscosity. Approximate Riemann solver of HLL and HLLC implemented in solver are validated by solving a cylindrical explosion case. Also the solver&rsquo
s capability of solving unstructured, multi-zone domain is investigated by this problem. First and second order results of solver are compared by solving the flow over a circular bump. Axisymmetric flow in solid propellant rocket motor is solved in order to validate the axisymmetric feature of solver. Laminar flow over flat plate is solved for viscous terms validation. Turbulent model is studied in the flow over flat plate and flow with mass injection test cases.
44
Yildirim, Ufuk. "Assessment Of Second-order Analysis Methods Presented In Design Codes." Master's thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/12610498/index.pdf.
Full textAbstract:
The main objective of the thesis is evaluating and comparing Second-Order Elastic Analysis
Methods defined in two different specifications, AISC 2005 and TS648 (1980). There are
many theoretical approaches that can provide exact solution for the problem. However,
approximate methods are still needed for design purposes. Simple formulations for code
applications were developed, and they are valid as acceptable results can be obtained within
admissible error limits. Within the content of the thesis, firstly background information
related to second-order effects will be presented. The emphasis will be on the definition of
geometric non-linearity, also called as P-δ
and P-&
#916
effects. In addition, the approximate methods defined in AISC 2005 (B1 &ndash
B2 Method), and TS648 (1980) will be discussed in detail. Then, example problems will be solved for the demonstration of theoretical formulations for members with and without end translation cases. Also, the results obtained from the structural analysis software, SAP2000, will be compared with the results acquired from the exact and the approximate methods. Finally, conclusions related to the study will be stated.
45
Abuazoum, Latifa Abdalla. "Advanced model updating methods for generally damped second order systems." Thesis, University of Nottingham, 2011. http://eprints.nottingham.ac.uk/12063/.
Full textAbstract:
This thesis is mostly about the analysis of second order linear vibrating systems. The main purpose of this study is to extend methods which have previously been developed for either undamped or proportionally damped or classically damped systems to the general case. These methods are commonly used in aerospace industries. Ground vibration testing of aircraft is performed to identify the dynamic behaviour of the structure. New aircraft materials and joining methods - composite materials and/or novel adhesive bonding approaches in place of riveted or welded joints - cause higher levels of damping that have not been seen before in aircraft structure. Any change occurring in an original structure causes associated changes of the dynamic behaviour of the structure. Analytical finite element analyses and experimental modal testing have become essential tools for engineers. These techniques are used to determine the dynamic characteristics of mechanical structures. In Chapters 3 and 4, structural analysis and modal testing have been carried out an aircraft-like structure. Modal analysis techniques are used to extract modal data which are identified from a single column of the frequency response matrix. The proposed method is presented for fitting modal peaks one by one. This technique overcomes the difficulty due to the conventional methods which require a series of measured FRFs at different points of excitation. New methods presented in this thesis are developed and implemented initially for undamped systems in all cases. These ideas are subsequently extended for generally damped linear systems. The equations of motion of second order damped systems are represented in state space. These methods have been developed based on Lancaster Augmented Matrices (LAMs) and diagonalising structure preserving equivalences (DSPEs). In Chapter 5, new methods are developed for computing the derivatives of the non-zeros of the diagonalised system and the derivatives of the diagonalising SPEs with respect to modifications in the system matrices. These methods have provided a new approach to the evaluation and the understanding of eigenvalue and eigenvector derivatives. This approach resolves the quandary where eigenvalue and eigenvector derivatives become undefined when a pair of complex eigenvalues turns into a pair of real eigenvalues or vice-versa. They also have resolved when any one or more of the system matrices is singular. Numerical examples have illustrated the new methods and they have shown that the method results overcome certain difficulties of conventional methods. In Chapter 6, Möbius transformations are used to address a problem where the mass matrix is singular. Two new transformations are investigated called system spectral transformation SSTNQ and diagonalising spectral/similarity transformation DSTOQ. The transformation SSTNQ maps between matrices of two systems having the same short eigenvectors and their diagonalised system matrices. The transformation DSTOQ maps between two diagonalising SPE‟s having identical eigenvalues. Modal correlation methods are implemented to evaluate and quantify the differences between the output results from these techniques. Different cross orthogonality measures represent a class of methods which are recently performed as modal correlation for damped systems. In Chapter 7, cross orthogonality measures and mutual orthogonality measures are developed for undamped systems. These measures are defined in terms of real matrices - the diagonalising structure preserving equivalences (DSPEs). New methods are well developed for ill-conditioned system such that they work for all occasions and not only for cases where mass matrix is non-singular. Also a measure of the residuals is introduced which does not demand invertibility of diagonalised system matrices. Model updating methods are used in order to update models of systems by matching the output results from analytical system models with the experimentally obtained values. In Chapter 8, both cross-orthogonality measures and mutual-orthogonality measures are developed and used in the model updating of generally damped linear systems. Model updating based on the mutual orthogonality measures exhibits monotonic convergence from every starting position. That is to say, the ball of convergence has an infinite radius whereas updating procedures based on comparing eigenvectors exhibit a finite ball of convergence. Craig Bampton transformations are one of component methods which are used to reduce and decouple large structure systems. In Chapter 9 Craig Bampton transformations are developed for undamped systems and extended for damped second order systems in state space. Craig Bampton transformations are generalised and presented in SPEs forms. The two parts of the Craig Bampton transformations are extended in the full sizes of the substructure. The extended Craig Bampton transformations are modified to format each block of transformed substructure matrices as LAMs matrices format. This thesis generalises and develops the methods mentioned above and illustrates these concepts with an experimental modal test and some examples. The thesis also contains brief information about basic vibration properties of general linear structures and literature review relevant to this project.
46
Fleming, Cliona Mary. "Second order chemometric methods and the analysis of complex data /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/8552.
Full text
47
Mansour, Rami. "Reliability Assessment and Probabilistic Optimization in Structural Design." Doctoral thesis, KTH, Hållfasthetslära (Avd.), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-183572.
Full textAbstract:
Research in the field of reliability based design is mainly focused on two sub-areas: The computation of the probability of failure and its integration in the reliability based design optimization (RBDO) loop. Four papers are presented in this work, representing a contribution to both sub-areas. In the first paper, a new Second Order Reliability Method (SORM) is presented. As opposed to the most commonly used SORMs, the presented approach is not limited to hyper-parabolic approximation of the performance function at the Most Probable Point (MPP) of failure. Instead, a full quadratic fit is used leading to a better approximation of the real performance function and therefore more accurate values of the probability of failure. The second paper focuses on the integration of the expression for the probability of failure for general quadratic function, presented in the first paper, in RBDO. One important feature of the proposed approach is that it does not involve locating the MPP. In the third paper, the expressions for the probability of failure based on general quadratic limit-state functions presented in the first paper are applied for the special case of a hyper-parabola. The expression is reformulated and simplified so that the probability of failure is only a function of three statistical measures: the Cornell reliability index, the skewness and the kurtosis of the hyper-parabola. These statistical measures are functions of the First-Order Reliability Index and the curvatures at the MPP. In the last paper, an approximate and efficient reliability method is proposed. Focus is on computational efficiency as well as intuitiveness for practicing engineers, especially regarding probabilistic fatigue problems where volume methods are used. The number of function evaluations to compute the probability of failure of the design under different types of uncertainties is a priori known to be 3n+2 in the proposed method, where n is the number of stochastic design variables.QC 20160317
48
Qvarngård, Daniel. "Modeling Optical Parametric Generation in Inhomogeneous Media." Thesis, Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-74256.
Full text
49
Davis, Benjamin J. "A study into discontinuous Galerkin methods for the second order wave equation." Thesis, Monterey, California: Naval Postgraduate School, 2015. http://hdl.handle.net/10945/45836.
Full textAbstract:
Approved for public release; distribution is unlimitedThere are numerous numerical methods for solving different types of partial differential equations (PDEs) that describe the physical dynamics of the world. For instance, PDEs are used to understand fluid flow for aerodynamics, wave dynamics for seismic exploration, and orbital mechanics. The goal of these numerical methods is to approximate the solution to a continuous PDE with an accurate discrete representation. The focus of this thesis is to explore a new Discontinuous Galerkin (DG) method for approximating the second order wave equation in complex geometries with curved elements. We begin by briefly highlighting some of the numerical methods used to solve PDEs and discuss the necessary concepts to understand DG methods. These concepts are used to develop a one- and two-dimensional DG method with an upwind flux, boundary conditions, and curved elements. We demonstrate convergence numerically and prove discrete stability of the method through an energy analysis.
50
Chronopoulos, Dimitrios. "Prediction of the vibroacoustic response of aerospace composite structures in a broadband frequency range." Phd thesis, Ecole Centrale de Lyon, 2012. http://tel.archives-ouvertes.fr/tel-00787864.
Full textAbstract:
During its mission, a launch vehicle is subject to broadband, severe, aeroacoustic and structure-borne excitations of various provenances, which can endanger the survivability of the payload and the vehicles electronic equipment, and consequently the success of the mission. Aerospace structures are generally characterized by the use of exotic composite materials of various configurations and thicknesses, as well as by their extensively complex geometries and connections between different subsystems. It is therefore of crucial importance for the modern aerospace industry, the development of analytical and numerical tools that can accurately predict the vibroacoustic response of large, composite structures of various geometries and subject to a combination of aeroacoustic excitations. Recently, a lot of research has been conducted on the modelling of wave propagation characteristics within composite structures. In this study, the Wave Finite Element Method (WFEM) is used in order to predict the wave dispersion characteristics within orthotropic composite structures of various geometries, namely flat panels, singly curved panels, doubly curved panels and cylindrical shells. These characteristics are initially used for predicting the modal density and the coupling loss factor of the structures connected to the acoustic medium. Subsequently the broad-band Transmission Loss (TL) of the modelled structures within a Statistical Energy Analysis (SEA) wave-context approach is calculated. Mainly due to the extensive geometric complexity of structures, the use of Finite Element(FE) modelling within the aerospace industry is frequently inevitable. The use of such models is limited mainly because of the large computation time demanded even for calculations in the low frequency range. During the last years, a lot of researchers focus on the model reduction of large FE models, in order to make their application feasible. In this study, the Second Order ARnoldi (SOAR) reduction approach is adopted, in order to minimize the computation time for a fully coupled composite structural-acoustic system, while at the same time retaining a satisfactory accuracy of the prediction in a broadband sense. The system is modelled under various aeroacoustic excitations, namely a diffused acoustic field and a Turbulent Boundary Layer (TBL) excitation. Experimental validation of the developed tools is conducted on a set of orthotropic sandwich composite structures. Initially, the wave propagation characteristics of a flat panel are measured and the experimental results are compared to the WFEM predictions. The later are used in order to formulate an Equivalent Single Layer (ESL) approach for the modelling of the spatial response of the panel within a dynamic stiffness matrix approach. The effect of the temperature of the structure as well as of the acoustic medium on the vibroacoustic response of the system is examined and analyzed. Subsequently, a model of the SYLDA structure, also made of an orthotropic sandwich material, is tested mainly in order to investigate the coupling nature between its various subsystems. The developed ESL modelling is used for an efficient calculation of the response of the structure in the lower frequency range, while for higher frequencies a hybrid WFEM/FEM formulation for modelling discontinuous structures is used.