Dissertations / Theses on the topic 'Numerical integration. Integrals'

This thesis is concerned with the evaluation of rapidly oscillatory integrals, that is integrals in which the integrand has numerous local maxima and minima over the range of integration. Three numerical integration rules are presented. The first is suitable for computing rapidly oscillatory integrals with trigonometric oscillations of the form f(x) exp(irq(x)). The method is demonstrated, empirically, to be convergent and numerically stable as the order of the formula is increased. For other forms of oscillatory behaviour, a second approach based on Lagrange's identity is presented. The technique is suitable for any oscillatory weight function, provided that it satisfies an ordinary linear differential equation of order m :2:: 1. The method is shown to encompass Bessel oscillations, trigonometric oscillations and Fresnel oscillations, and products of these terms. Examples are included which illustrate the efficiency of the method in practical applications. Finally, integrals where the integrand is singular and oscillatory are considered. An extended Clenshaw-Curtis formula is developed for Fourier integrals which exhibit algebraic and logarithmic singularities. An efficient algorithm is presented for the practical implementation of the method.

High-dimensional integrals arise in a variety of areas, including quantum physics, the physics and chemistry of molecules, statistical mechanics and more recently, in financial applications. In order to approximate multidimensional integrals, one may use Monte Carlo methods in which the quadrature points are generated randomly or quasi-Monte Carlo methods, in which points are generated deterministically. One particular class of quasi-Monte Carlo methods for multivariate integration is represented by lattice rules. Lattice rules constructed throughout this thesis allow good approximations to integrals of functions belonging to certain weighted function spaces. These function spaces were proposed as an explanation as to why integrals in many variables appear to be successfully approximated although the standard theory indicates that the number of quadrature points required for reasonable accuracy would be astronomical because of the large number of variables. The purpose of this thesis is to contribute to theoretical results regarding the construction of lattice rules for multiple integration. We consider both lattice rules for integrals over the unit cube and lattice rules suitable for integrals over Euclidean space. The research reported throughout the thesis is devoted to finding the generating vector required to produce lattice rules that have what is termed a low weighted discrepancy . In simple terms, the discrepancy is a measure of the uniformity of the distribution of the quadrature points or in other settings, a worst-case error. One of the assumptions used in these weighted function spaces is that variables are arranged in the decreasing order of their importance and the assignment of weights in this situation results in so-called product weights . In other applications it is rather the importance of group of variables that matters. This situation is modelled by using function spaces in which the weights are general . In the weighted settings mentioned above, the quality of the lattice rules is assessed by the weighted discrepancy mentioned earlier. Under appropriate conditions on the weights, the lattice rules constructed here produce a convergence rate of the error that ranges from O(n−1/2) to the (believed) optimal O(n−1+δ) for any δ gt 0, with the involved constant independent of the dimension.

Der Strahlungstransport stellt eine von drei Arten des Wärmetransports zwischen Gebieten unterschiedlicher Temperatur dar. Eine der einfachsten Formen bildet der Strahlungstransport im Vakuum, ein Vorgang, der im kosmischen Umfeld, beispielsweise bei der Energieübertragung von einem Stern auf seine Planeten, beobachtbar ist. Hierbei ist es hinreichend, sich auf die Betrachtung von Oberflächen zu beschränken. Strahlungstransport kann jedoch auch in semitransparenten Medien, wie biologischem Gewebe oder Glas, beobachtet werden. Das Medium, in dem der Strahlungstransport erfolgt, wirkt sich durch Vorgänge wie Absorption, Emission, Reflexion oder Streuung auf den Strahlungstransport aus. Für die Modellierung des Strahlungstransports in einem solchen Umfeld können verschiedene Modelle, darunter das Strahlenmodell, genutzt werden. Dieses Modell beschreibt den Wärmetransport anhand einer skalaren Größe, die Strahlungsintensität genannt wird. Betrachtet wird die Strahlungsintensität in diesem Modell entlang eines Strahls in eine vorgegebene Richtung. Die mathematische Darstellung des Strahlenmodells des Strahlungstransports in partizipierenden Medien führt auf eine richtungsabhängige Integro-Differentialgleichung. Ist die Richtungsabhängigkeit nicht von Interesse, so kann der Übergang zu einer winkelintegrierten Form erfolgen. Dieser Übergang führt schließlich auf ein System schwach singulärer fredholmscher Integralgleichungen zweiter Art. Dieses charakterisiert nun nicht mehr die erwähnte Strahlungsintensität, sondern beschreibt die sogenannte Einstrahlung sowie den Strahlungsfluss. Das System singulärer Integralgleichungen kann mittels eines Galerkin-Ansatzes numerisch gelöst werden. Geht man von einer hinreichenden Glattheit des Randes aus, kann die Kompaktheit des Operators der Integralgleichungen gezeigt werden. Dies wiederum erlaubt Rückschlüsse auf die Existenz und Eindeutigkeit einer Lösung. Ein Augenmerk bei der Ermittlung der Galerkin-Näherung ist auf die Bestimmung der singulären Integrale der Galerkin-Diskretisierung zu richten. Für die Bestimmung multidimensionaler, singulärer Integrale stellt die Arbeit das Verfahren der hierarchischen Integration vor. Basierend auf einer Zerlegung des Integrationsgebietes, erfolgt die Beschreibung singulärer Integrale durch ein Gleichungssystem, dessen rechte Seite nur von regulären Integralen abhängig ist. Können diese regulären Integrale sowie die Lösung des Gleichungssystems exakt bestimmt werden, so sind auch die singulären Integrale exakt bestimmt. Bei einer numerischen Bestimmung der regulären Integrale ist die Fehlerordnung ausschlaggebend für den Fehler der singulären Integrale. Als Integrationsgebiete werden Hyperwürfel beliebiger Dimension sowie Simplizes bis einschließlich Dimension 3 als Integrationsgebiete betrachtet. Als Voraussetzungen an den Kern des Doppelintegrals sind nur die Eigenschaften der Translationsinvarianz sowie der Homogenität zu richten. Kann ein nicht translationsinvarianter oder nicht homogener Kern eines Integrals in Summanden zerlegt werden, die selbst translationsinvariant und homogen sind, ist auch die Bestimmung solcher Integrale möglich. Darüber hinaus stellt die Arbeit Verbindungen zu dem Begriff des Hadamard partie finie her. Auf diese Weise lässt sich das Verfahren der hierarchischen Integration für beliebige Dimensionen und beliebige Singularitätsordnungen anwenden. Die Strahlungstransportgleichung ist im Allgemeinen mittels eines Galerkin-Ansatzes lösbar, führt jedoch auf eine voll besetzte Systemmatrix. Numerische Beispiele beleuchten daher Methoden der Matrixkompression mittels hierarchischer Matrizen sowie der direkten Erzeugung schwach besetzter Matrizen über regulären Gittern und Gittern mit hängenden Knoten und skizziert Ansätze zur Parallelisierung auf entsprechenden Computersystemen.

This PhD thesis consists of a summary and seven papers, where various applications of auto-validated computations are studied. In the first paper we describe a rigorous method to determine unknown parameters in a system of ordinary differential equations from measured data with known bounds on the noise of the measurements. Papers II, III, IV, and V are concerned with Abelian integrals. In Paper II, we construct an auto-validated algorithm to compute Abelian integrals. In Paper III we investigate, via an example, how one can use this algorithm to determine the possible configurations of limit cycles that can bifurcate from a given Hamiltonian vector field. In Paper IV we construct an example of a perturbation of degree five of a Hamiltonian vector field of degree five, with 27 limit cycles, and in Paper V we construct an example of a perturbation of degree seven of a Hamiltonian vector field of degree seven, with 53 limit cycles. These are new lower bounds for the maximum number of limit cycles that can bifurcate from a Hamiltonian vector field for those degrees. In Papers VI, and VII, we study a certain kind of normal form for real hyperbolic saddles, which is numerically robust. In Paper VI we describe an algorithm how to automatically compute these normal forms in the planar case. In Paper VII we use the properties of the normal form to compute local invariant manifolds in a neighbourhood of the saddle.

El Método de los Momentos (MoM) ha sido ampliamente utilizado en las últimas décadas para la discretización y la solución de las formulaciones de ecuación integral que aparecen en muchos problemas electromagnéticos de antenas y dispersión. Las más utilizadas de dichas formulaciones son la Ecuación Integral de Campo Eléctrico (EFIE), la Ecuación Integral de Campo Magnético (MFIE) y la Ecuación Integral de Campo Combinada (CFIE), que no es más que una combinación lineal de las dos anteriores.
Las formulaciones MFIE y CFIE son válidas únicamente para objetos cerrados y necesitan tratar la integración de núcleos con singularidades de orden superior al de la EFIE. La falta de técnicas eficientes y precisas para el cálculo de dichas integrales singulares a llevado a imprecisiones en los resultados. Consecuentemente, su uso se ha visto restringido a propósitos puramente académicos, incluso cuando tienen una velocidad de convergencia muy superior cuando son resuelto iterativamente, debido a su excelente número de condicionamiento.
En general, la principal desventaja del MoM es el alto coste de su construcción, almacenamiento y solución teniendo en cuenta que es inevitablemente un sistema denso, que crece con el tamaño eléctrico del objeto a analizar. Por tanto, un gran número de métodos han sido desarrollados para su compresión y solución. Sin embargo, muchos de ellos son absolutamente dependientes del núcleo de la ecuación integral, necesitando de una reformulación completa para cada núcleo, en caso de que sea posible.
Esta tesis presenta nuevos enfoques o métodos para acelerar y incrementar la precisión de ecuaciones integrales discretizadas con el Método de los Momentos (MoM) en electromagnetismo computacional.
En primer lugar, un nuevo método iterativo rápido, el Multilevel Adaptive Cross Approximation (MLACA), ha sido desarrollado para acelerar la solución del sistema lineal del MoM. En la búsqueda por un esquema de propósito general, el MLACA es un método independiente del núcleo de la ecuación integral y es puramente algebraico. Mejora simultáneamente la eficiencia y la compresión con respecto a su versión mono-nivel, el ACA, ya existente. Por tanto, representa una excelente alternativa para la solución del sistema del MoM de problemas electromagnéticos de gran escala.
En segundo lugar, el Direct Evaluation Method, que ha provado ser la referencia principal en términos de eficiencia y precisión, es extendido para superar el cálculo del desafío que suponen las integrales hiper-singulares 4-D que aparecen en la formulación de Ecuación Integral de Campo Magnético (MFIE) así como en la de Ecuación Integral de Campo Combinada (CFIE). La máxima precisión asequible -precisión de máquina se obtiene en un tiempo más que razonable, sobrepasando a cualquier otra técnica existente en la bibliografía.
En tercer lugar, las integrales hiper-singulares mencionadas anteriormente se convierten en casi-singulares cuando los elementos discretizados están muy próximo pero sin llegar a tocarse. Se muestra como las reglas de integración tradicionales tampoco convergen adecuadamente en este caso y se propone una posible solución, basada en reglas de integración más sofisticadas, como la Double Exponential y la Gauss-Laguerre.
Finalmente, un esfuerzo en facilitar el uso de cualquier programa de simulación de antenas basado en el MoM ha llevado al desarrollo de un modelo matemático general de un puerto de excitación en el espacio discretizado. Con este nuevo modelo, ya no es necesaria la adaptación de los lados del mallado al puerto en cuestión.
The Method of Moments (MoM) has been widely used during the last decades for the discretization and the solution of integral equation formulations appearing in several electromagnetic antenna and scattering problems. The most utilized of these formulations are the Electric Field Integral Equation (EFIE), the Magnetic Field Integral Equation (MFIE) and the Combined Field Integral Equation (CFIE), which is a linear combination of the other two.
The MFIE and CFIE formulations are only valid for closed objects and need to deal with the integration of singular kernels with singularities of higher order than the EFIE. The lack of efficient and accurate techniques for the computation of these singular integrals has led to inaccuracies in the results. Consequently, their use has been mainly restricted to academic purposes, even having a much better convergence rate when solved iteratively, due to their excellent conditioning number.
In general, the main drawback of the MoM is the costly construction, storage and solution considering the unavoidable dense linear system, which grows with the electrical size of the object to analyze. Consequently, a wide range of fast methods have been developed for its compression and solution. Most of them, though, are absolutely dependent on the kernel of the integral equation, claiming for a complete re-formulation, if possible, for each new kernel.
This thesis dissertation presents new approaches to accelerate or increase the accuracy of integral equations discretized by the Method of Moments (MoM) in computational electromagnetics.
Firstly, a novel fast iterative solver, the Multilevel Adaptive Cross Approximation (MLACA), has been developed for accelerating the solution of the MoM linear system. In the quest for a general-purpose scheme, the MLACA is a method independent of the kernel of the integral equation and is purely algebraic. It improves both efficiency and compression rate with respect to the previously existing single-level version, the ACA. Therefore, it represents an excellent alternative for the solution of the MoM system of large-scale electromagnetic problems.
Secondly, the direct evaluation method, which has proved to be the main reference in terms of efficiency and accuracy, is extended to overcome the computation of the challenging 4-D hyper-singular integrals arising in the Magnetic Field Integral Equation (MFIE) and Combined Field Integral Equation (CFIE) formulations. The maximum affordable accuracy --machine precision-- is obtained in a more than reasonable computation time, surpassing any other existing technique in the literature.
Thirdly, the aforementioned hyper-singular integrals become near-singular when the discretized elements are very closely placed but not touching. It is shown how traditional integration rules fail to converge also in this case, and a possible solution based on more sophisticated integration rules, like the Double Exponential and the Gauss-Laguerre, is proposed.
Finally, an effort to facilitate the usability of any antenna simulation software based on the MoM has led to the development of a general mathematical model of an excitation port in the discretized space. With this new model, it is no longer necessary to adapt the mesh edges to the port.

This thesis deals with continuous system simulation. The systems can be described by system of differential equations or block diagram. Differential equations are usually solved by numerical methods that are integrated into simulation software such as Matlab, Maple or TKSL. Taylor series method has been used for numerical solutions of differential equations. The presented method has been proved to be both very accurate and fast and also procesed in parallel systems. The aim of the thesis is to design, implement and compare a few versions of the parallel system.

This thesis deals with discrete integrable systems theory and modified Hamiltonian equations in the field of geometric numerical integration. Modified Hamiltonians are used to show that symplectic schemes for Hamiltonian systems are accurate over long times. However, for nonlinear systems the series defining the modified Hamiltonian equation usually diverges. The first part of the thesis demonstrates that there are nonlinear systems where the modified Hamiltonian has a closed-form expression and hence converges. These systems arise from the theory of discrete integrable systems. Specifically, they arise as reductions of a lattice version of the Korteweg-de Vries (KdV) partial differential equation. We present cases of one and two degrees of freedom symplectic mappings, for which the modified Hamiltonian equations can be computed as a closed form expression using techniques of action-angle variables, separation of variables and finite-gap integration. These modified Hamiltonians are also given as power series in the time step by Yoshida's method based on the Baker-Campbell-Hausdorff series. Another example is a system of an implicit dependence on the time step, which is obtained by dimensional reduction of a lattice version of the modified KdV equation. The second part of the thesis contains a different class of discrete-time system, namely the Boussinesq type, which can be considered as a higher-order counterpart of the KdV type. The development and analysis of this class by means of the B{\"a}cklund transformation, staircase reductions and Dubrovin equations forms one of the major parts of the thesis. First, we present a new derivation of the main equation, which is a nine-point lattice Boussinesq equation, from the B{\"a}cklund transformation for the continuous Boussinesq equation. Second, we focus on periodic reductions of the lattice equation and derive all necessary ingredients of the corresponding finite-dimensional models. Using the corresponding monodromy matrix and applying techniques from Lax pair and $r$-matrix structure analysis to the Boussinesq mappings, we study the dynamics in terms of the so-called Dubrovin equations for the separated variables.

The application of the finite integral of multiple variable functions is penetrating into more and more industries and science disciplines. The demands placed on solutions to these problems (such as high accuracy or high speed) are often quite contradictory. Therefore, it is not always possible to apply analytical approaches to these problems; numerical methods provide a suitable alternative. However, the ever-growing complexity of these problems places too high a demand on many of these numerical methods, and so neither of these methods are useful for solving such problems. The goal of this thesis is to design and implement a new numerical method that provides highly accurate and very fast computation of finite integrals of multiple variable functions. This new method combines pre-existing approaches in the field of numerical mathematics.

This thesis deals with the design system for multiple integrals for diferential expression with space variables. Today, integration is one of engineering problems. Reader is acquainted with different method of integration, then with numerican integration and Taylor series. The practical aim of this work is to design software and hardware system of numerican integration multiple integrals.

The boundary element method (BEM) has become a powerful method for the numerical solution of boundary-value problems (BVPs), due to its ability (at least for problems with constant coefficients) of reducing a BVP for a linear partial differential equation (PDE) defined in a domain to an integral equation defined on the boundary, leading to a simplified discretisation process with boundary elements only. On the other hand, the coefficients in the mathematical model of a physical problem typically correspond to the material parameters of the problem. In many physical problems, the governing equation is likely to involve variable coefficients. The application of the BEM to these equations is hampered by the difficulty of finding a fundamental solution. The first part of this thesis will focus on the derivation of the boundary integral equation (BIE) for the Laplace equation, and numerical results are presented for some examples using constant elements. Then, the formulations of the boundary-domain integral or integro-differential equation (BDIE or BDIDE) for heat conduction problems with variable coefficients are presented using a parametrix (Levi function), which is usually available. The second part of this thesis deals with the extension of the BDIE and BDIDE formulations to the treatment of the two-dimensional Helmholtz equation with variable coefficients. Four possible cases are investigated, first of all when both material parameters and wave number are constant, in which case the zero-order Bessel function of the second kind is used as fundamental solution. Moreover, when the material parameters are variable (with constant or variable wave number), a parametrix is adopted to reduce the Helmholtz equation to a BDIE or a BDIDE. Finally, when material parameters are constant (with variable wave number), the standard fundamental solution for the Laplace equation is used in the formulation. In the third part, the radial integration method (RIM) is introduced and discussed in detail. Modifications are introduced to the RIM, particularly the fact that the radial integral is calculated by using a pure boundary-only integral which relaxes the “star-shaped” requirement of the RIM. Then, the RIM is used to convert the domain integrals appearing in both BDIE and BDIDE for heat conduction and Helmholtz equations to equivalent boundary integrals. For domain integrals consisting of known functions the transformation is straightforward, while for domain integrals that include unknown variables the transformation is accomplished with the use of augmented radial basis functions (RBFs). The most attractive feature of the method is that the transformations are very simple and have similar forms for both 2D and 3D problems. Finally, the application of the RIM is discussed for the diffusion equation, in which the parabolic PDE is initially reformulated as a BDIE or a BDIDE and the RIM is used to convert the resulting domain integrals to equivalent boundary integrals. Three cases have been investigated, for homogenous, non-homogeneous and variable coefficient diffusion problems.

Lo scopo della presente tesi è quello di illustrare alcuni dei principali strumenti messi a disposizione dai controlli automatici a servizio dell’ingegneria, in particolare analizzando la struttura generale di una fabbrica automatica e descrivendone i principali sistemi di controllo. L’elaborato è suddiviso in tre macro parti: la prima ha l’obiettivo di inquadrare quella che è la fabbrica automatica, partendo dal precedente concetto di fabbrica tradizionale fino ad arrivare alla fabbrica moderna, caratterizzata da una spinta flessibilità produttiva determinata da una politica di produzione per lotti con elevati livelli di caratterizzazione. Della fabbrica automatica viene poi approfondita l’integrazione con i calcolatori attraverso il sistema concettuale del CIM, Computer Integrated Manufacturing, e l’impiego di celle di fabbricazione flessibili, ovvero le FMS, Flexible Manufacturing System. La seconda parte è incentrata sull’analisi delle logiche di controllo impiegate all’interno di tutto il processo di progettazione e di produzione, suddivise in tre gruppi: il primo focalizzato sui sistemi per la produzione automatica, NC e DNC; il secondo sui sistemi di simulazione e testing del prodotto, CAD, CAM e CAT; il terzo sui sistemi di controllo e sviluppo dati, SCADA, MES e DCS. La terza ed ultima parte è circoscritta all’approfondimento di un particolare sistema di controllo per la gestione dei processi, ovvero sull’uso del PLC, il Controllore Logico Programmabile. Vengono analizzate le componenti fisiche che lo costituiscono, il funzionamento base, i tempi di esecuzione delle istruzioni, i criteri di scelta e di dimensionamento ed altri aspetti rilevanti. Infine è presente un esempio applicativo di alcuni aspetti sovra citati con il caso dell’azienda bolognese G.D, leader del settore delle macchine automatiche a controllo numerico per la fabbricazione e l’impacchettamento delle sigarette.

This work provides an overview of methods for the numerical solution of differential equations. Options of their parallelization, a division of computational operations on multiple microprocessors, are provided with emphasis placed on the Taylor series. The next part of the work is devoted to the description of a specialized parallel system, which was design to fast solving of these equations. Differential equations are appropriate to describe electrical circuits. An important characteristic of each circuit is its behavior in the frequency domain. The aim of this thesis was to design and implement a program which investigate frequency characteristics of AC circuits. A method for analyzing a circuit and automatically assembling corresponding equations is presented. These differential equations are then solved in TKSL. At the end of this work a time consumption is evaluated and compared with Matlab.

L’obbiettivo che si pone questo lavoro è quello di combinare in un unico impianto due tecnologie utilizzate per scopi differenti (impianto integrato): un impianto di climatizzazione geotermico a bassa entalpia di tipo open-loop ed un impianto di bonifica delle acque di falda di tipo Pump&Treat. Il sito selezionato per lo studio è ubicato in via Lombardia, nell’area industriale di Ozzano dell’Emilia (BO), ed è definito “Ex stabilimento Ot-Gal”: si tratta di una galvanotecnica con trattamento di metalli, dismessa alla fine degli anni ’90. Durante una precedente fase di caratterizzazione del sito condotta dalla ditta Geo-Net Srl, sono stati rilevati in falda dei superamenti delle CSC previste dal D.lgs. 152/2006 di alcuni contaminanti, in particolare Tricloroetilene (TCE) e 1.1-Dicloroetilene (1.1-DCE). Successivamente, nel 2010-2011, Geo-net Srl ha eseguito una parziale bonifica delle acque di falda attraverso l’utilizzo di un impianto Pump and Treat. Grazie a tutti i dati pregressi riguardanti i monitoraggi, le prove e i sondaggi, messi a disposizione per questo studio da Geo-Net Srl, è stato possibile eseguire una sperimentazione teorica, in forma di modellazione numerica di flusso e trasporto, dell’impianto integrato oggetto di studio. La sperimentazione è stata effettuata attraverso l’utilizzo di modelli numerici basati sul codice di calcolo MODFLOW e su codici ad esso comunemente associati, quali MODPATH e MT3DMS. L’analisi dei risultati ottenuti ha permesso di valutare in modo accurato l’integrazione di queste due tecnologie combinate in unico impianto. In particolare, la bonifica all’interno del sito avviene dopo 15 dalla messa in attività. Sono stati anche confrontati i costi da sostenere per la realizzazione e l’esercizio dell’impianto integrato rispetto a quelli di un impianto tradizionale. Tale confronto ha mostrato che l’ammortamento dell’impianto integrato avviene in 13 anni e che i restanti 7 anni di esercizio producono un risparmio economico.

This thesis deals with the concepts of numerical integrator using floating point arithmetic for solving partial differential equations. The integrator uses Euler method and Taylor series. Thesis shows parallel and serial approach to computing with exponents and significands. There is also a comparison between modern parallel systems and the proposed concepts.

This work deals with the automatic control of calculations of specialized system. The reader is acquainted with the numerical solution of differential equations by Taylor series method and numerical integrators. The practical aim of this work is to analyze parallel characteristics of Taylor series method, specification of parallel math operations and design of control of this operations.

This thesis focuses on the methodology of controlling dynamic systems in real time. It contents a review of the control theory basis and the elementary base of regulators construction. Then the list of matemathic formulaes follows as well as the math basis for the system simulations using a difeerential count and the problem of difeerential equations solving. Furthermore, there is a systematic approach to the design of general regulator enclosed, using modern simulation techniques. After the results confirmation in the Matlab system, the problematics of transport delay & quantization modelling follow.

Studi recenti evidenziano una stretta correlazione esistente tra gli eventi di precipitazione estrema e la presenza di atmospheric river (AR). Si tratta di estese strutture filamentose di concentrazione anomala di vapore acqueo collocate nei primi 3 km della troposfera e legate alla formazione di un intenso low-level jet posizionato davanti al fronte freddo di un ciclone extra-tropicale. Gli effetti degli AR sulle precipitazioni sono stati ampiamente descritti in letteratura limitatamente alla West Coast americana, alle regioni lungo le coste atlantiche europee e recentemente al Giappone e all'India. Nel seguente lavoro di tesi viene individuata per la prima volta nel bacino del Mediterraneo la presenza di un AR che ha condizionato in modo determinante l'intenso evento meteorologico del 27-30 ottobre 2018 in Italia. Le simulazioni numeriche effettuate con il modello numerico meteorologico BOLAM e l'utilizzo di specifici algoritmi hanno permesso di individuare l'AR, il quale trasporta vapore acqueo dall'Atlantico sub-tropicale, attraverso il continente africano, transitando sull'Algeria fino al Mediterraneo centrale lungo una traiettoria di circa 3000 km. Inoltre, l'utilizzo di una specifica diagnostica per il calcolo del budget di acqua in atmosfera ha consentito una caratterizzazione quantitativa del ruolo dell'AR e degli altri contributi di umidità presenti sul Mediterraneo. A questo proposito, è stato valutato l'impatto dell'evaporazione dal mare sulle piogge sul Nord e Centro Italia, attraverso un confronto con i contributi di umidità trasportati da sorgenti remote. Questa analisi è stata approfondita mediante l'utilizzo di esperimenti numerici di sensibilità. Infine, è stato evidenziato il possibile impatto dell'AR sulla ciclogenesi esplosiva osservata sul Mediterraneo, che ha caratterizzato la seconda fase dell'evento.

碩士
國立臺灣海洋大學
資訊工程學系
94
In this thesis, we study the numerical methods for integrating the Fourier-type integrals, defined by $\int_0^{\infty}f(x)\sin{\omega x}\,dx$ or $\int_0^{\infty}f(x)\cos{\omega x}\,dx$. We focus on the two of most efficient schemes, namely the accelerated trapezoidal-type rules and the Fourier-type double exponential formulas. We propose an algorithm for selecting the two parameters, namely $h$(the step size) and $N$(the number of function calculations), to be approximately optimal for the new Fourier-type double exponential formula. This algorithm significantly reduces the number of function evaluations and definitely improves the drawback of Ooura and Mori's approach. For the problem what Ooura and Mori left of the special integrals, $\int_0^{\infty}\frac{\cos{\omega x}}{(x-2)^2+1}\,dx$, we also present a hybrid scheme of combining the Gauss-type rule with the double exponential formula. This approach resolves the inefficiency of the new Fourier-type double exponential formula. The comparison of the accelerated trapezoidal-type rules and double exponential formula and their tests were also done. %In this thesis, we study the two of most efficient schemes, namely the accelerated trapezoidal rule and the double-exponential.

The aim of this work is to provide new results of global existence for dif- ferent evolution equations of fluid mechanics. We are in general interested in finding weak solutions without restrictions on the size of initial data. The proofs of existence are based on several different approaches including en- ergy methods, convergence analysis of finite numerical methods and convex integration. All these techniques significantly exploit results of mathematical analysis and other branches of mathematics. 1