Relevant bibliographies by topics / Newton-Raphson iterations

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Newton-Raphson iterations'

Author: Grafiati
Published: 4 June 2021
Last updated: 11 February 2022

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Journal articles on the topic "Newton-Raphson iterations"

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RAMADHANI UTAMI, NANDA NINGTYAS, I. NYOMAN WIDANA, and NI MADE ASIH. "PERBANDINGAN SOLUSI SISTEM PERSAMAAN NONLINEAR MENGGUNAKAN METODE NEWTON-RAPHSON DAN METODE JACOBIAN." E-Jurnal Matematika 2, no. 2 (May 31, 2013): 11. http://dx.doi.org/10.24843/mtk.2013.v02.i02.p032.

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System of nonlinear equations is a collection of some nonlinear equations. The Newton-Raphson method and Jacobian method are methods used for solving systems of nonlinear equations. The Newton-Raphson methods uses first and second derivatives and indeed does perform better than the steepest descent method if the initial point is close to the minimizer. Jacobian method is a method of resolving equations through iteration process using simultaneous equations. If the Newton-Raphson methods and Jacobian methods are compared with the exact value, the Jacobian method is the closest to exact value but has more iterations. In this study the Newton-Raphson method gets the results faster than the Jacobian method (Newton-Raphson iteration method is 5 and 58 in the Jacobian iteration method). In this case, the Jacobian method gets results closer to the exact value.
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Kornerup, Peter, and Jean-Michel Muller. "Choosing starting values for certain Newton–Raphson iterations." Theoretical Computer Science 351, no. 1 (February 2006): 101–10. http://dx.doi.org/10.1016/j.tcs.2005.09.056.

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Shayya, W. H., R. H. Mohtar, and M. S. Baasiri. "A Computer Model for the Hydraulic Analysis of Open Channel Cross Sections." Journal of Agricultural and Marine Sciences [JAMS] 1 (January 1, 1996): 57. http://dx.doi.org/10.24200/jams.vol1iss0pp57-64.

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Irrigation and hydraulic engineers are often faced with the difficulty of tedious trial solutions of the Manning equation to determine the various geometric elements of open channels. This paper addresses the development of a computer model for the design of the most commonly used channel-sections. The developed model is intended as an educational tool. It may be applied to the hydraulic design of trapezoidal , rectangular, triangular, parabolic, round-concered rectangular, and circular cross sections. Two procedures were utilized for the solution of the encountered implicit equations; the Newton-Raphson and the Regula-Falsi methods. In order to initiate the solution process , these methods require one and two initial guesses, respectively. Tge result revealed that the Regula-Flasi method required more iterations to coverage to the solution compared to the Newton-Raphson method, irrespective of the nearness of the initial guess to the actual solution. The average number of iterations for the Regula-Falsi method was approximately three times that of the Newton-Raphson method.
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Souza, Luiz Antonio Farani de, Emerson Vitor Castelani, and Wesley Vagner Inês Shirabayashi. "Adaptation of the Newton-Raphson and Potra-Pták methods for the solution of nonlinear systems." Semina: Ciências Exatas e Tecnológicas 42, no. 1 (June 2, 2021): 63. http://dx.doi.org/10.5433/1679-0375.2021v42n1p63.

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In this paper we adapt the Newton-Raphson and Potra-Pták algorithms by combining them with the modified Newton-Raphson method by inserting a condition. Problems of systems of sparse nonlinear equations are solved the algorithms implemented in Matlab® environment. In addition, the methods are adapted and applied to space trusses problems with geometric nonlinear behavior. Structures are discretized by the Finite Element Positional Method, and nonlinear responses are obtained in an incremental and iterative process using the Linear Arc-Length path-following technique. For the studied problems, the proposed algorithms had good computational performance reaching the solution with shorter processing time and fewer iterations until convergence to a given tolerance, when compared to the standard algorithms of the Newton-Raphson and Potra-Pták methods.
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Mandailina, Vera, Syaharuddin Syaharuddin, Dewi Pramita, Malik Ibrahim, and Habib Ratu Perwira Negara. "Wilkinson Polynomials: Accuracy Analysis Based on Numerical Methods of the Taylor Series Derivative." Desimal: Jurnal Matematika 3, no. 2 (May 28, 2020): 155–60. http://dx.doi.org/10.24042/djm.v3i2.6134.

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Some of the numeric methods for solutions of non-linear equations are taken from a derivative of the Taylor series, one of which is the Newton-Raphson method. However, this is not the only method for solving cases of non-linear equations. The purpose of the study is to compare the accuracy of several derivative methods of the Taylor series of both single order and two-order derivatives, namely Newton-Raphson method, Halley method, Olver method, Euler method, Chebyshev method, and Newton Midpoint Halley method. This research includes qualitative comparison types, where the simulation results of each method are described based on the comparison results. These six methods are simulated with the Wilkinson equation which is a 20-degree polynomial. The accuracy parameters used are the number of iterations, the roots of the equation, the function value f (x), and the error. Results showed that the Newton Midpoint Halley method was the most accurate method. This result is derived from the test starting point value of 0.5 to the equation root x = 1, completed in 3 iterations with a maximum error of 0.0001. The computational design and simulation of this iterative method which is a derivative of the two-order Taylor series is rarely found in college studies as it still rests on the Newton-Raphson method, so the results of this study can be recommended in future learning.
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Sabziev, Elkhan Nariman. "Calculation of Flight Data Fusion Coefficients Using Newton–Raphson Iterations." Modeling, Control and Information Technologies, no. 4 (October 23, 2020): 100–103. http://dx.doi.org/10.31713/mcit.2020.20.

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The problem of plotting the flight path of an aircraft based on flight data containing numerous measurement errors is investigated. A theoretical (continuous) model of the flight data fusion problem is proposed in the form of a boundary value problem for a system of differential equations with unknown coefficients. The application of the Newton–Raphson iteration method for calculating the sought-for coefficients is described.
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Tong, Ming Yu, Di Jian Xu, Jin Liang Shi, and Yan Shi. "Application of the Newton-Raphson Method in a Voice Localization System." Applied Mechanics and Materials 513-517 (February 2014): 4435–38. http://dx.doi.org/10.4028/www.scientific.net/amm.513-517.4435.

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In a voice localization system, the nonlinear equation of voice sources coordinates were established according the accepted information, so the algorithm for solving nonlinear equations is the key problem to the voice source localization syetem. In this paper, the Newton - Raphson method (N-R) is applied to solve the nonlinear equations, by setting the initial solution of equations,then calculating the unbalance vector and Jacobian matrix (J) so as to attain corrected vetor, after modification and iteration the initial solution,until meet the precision numerical solution. Test results show that, application of N-R method in voice localization system have advantange of less number of iterations, saving chip resources and high precision, can meet the precision requirements of voice localization system.
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Raposo-Pulido, V., and J. Peláez. "An efficient code to solve the Kepler equation." Astronomy & Astrophysics 619 (November 2018): A129. http://dx.doi.org/10.1051/0004-6361/201833563.

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Context. This paper introduces a new approach for solving the Kepler equation for hyperbolic orbits. We provide here the Hyperbolic Kepler Equation–Space Dynamics Group (HKE–SDG), a code to solve the equation. Methods. Instead of looking for new algorithms, in this paper we have tried to substantially improve well-known classic schemes based on the excellent properties of the Newton–Raphson iterative methods. The key point is the seed from which the iteration of the Newton–Raphson methods begin. If this initial seed is close to the solution sought, the Newton–Raphson methods exhibit an excellent behavior. For each one of the resulting intervals of the discretized domain of the hyperbolic anomaly a fifth degree interpolating polynomial is introduced, with the exception of the last one where an asymptotic expansion is defined. This way the accuracy of initial seed is optimized. The polynomials have six coefficients which are obtained by imposing six conditions at both ends of the corresponding interval: the polynomial and the real function to be approximated have equal values at each of the two ends of the interval and identical relations are imposed for the two first derivatives. A different approach is used in the singular corner of the Kepler equation – |M| < 0.15 and 1 < e < 1.25 – where an asymptotic expansion is developed. Results. In all simulations carried out to check the algorithm, the seed generated leads to reach machine error accuracy with a maximum of three iterations (∼99.8% of cases with one or two iterations) when using different Newton–Raphson methods in double and quadruple precision. The final algorithm is very reliable and slightly faster in double precision (∼0.3 s). The numerical results confirm the use of only one asymptotic expansion in the whole domain of the singular corner as well as the reliability and stability of the HKE–SDG. In double and quadruple precision it provides the most precise solution compared with other methods.
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Yen, Jerome, Bangren Chen, KangZhang Wu, and Joseph Yen. "Fast generation of implied volatility surface: Optimize the traditional numerical analysis and machine learning." International Journal of Financial Engineering 08, no. 02 (June 2021): 2150037. http://dx.doi.org/10.1142/s2424786321500377.

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Machine learning has been used in financial markets in supporting many tasks, such as, asset movement forecasting and trading signal generation. Monte Carlo simulation and traditional numerical methods like Newton–Raphson have also been widely applied in financial markets, such as calculation for implied volatility (IV) and pricing of financial products. Is it possible to combine such approaches to more efficiently calculate the IVs to support the generation of IV surface, term structure, and smile? In this paper, we propose a framework that combines the traditional approaches and modern machine learning to support such calculation. In addition, we also propose an adaptive Newton–Raphson to reduce the number of iterations and the possibility of falling into local minimal over the traditional Newton–Raphson. Combining the superiorities of modern machine learning and adaptive Newton–Raphson, an improvement on computation efficiency over pure traditional numerical approaches was achieved. In addition, we also take into consideration of migrating such computation to hardware accelerators such as Graphics cards (GPU) and Field Programmable Gate Arrays (FPGA), to further speed up the computation. Therefore, polynomial regression has also been tested to generate the initial guess of IVs to pave the road of such migration.
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Zotos, Euaggelos E., Satyendra Kumar Satya, Rajiv Aggarwal, and Sanam Suraj. "Basins of Convergence in the Circular Sitnikov Four-Body Problem with Nonspherical Primaries." International Journal of Bifurcation and Chaos 28, no. 05 (May 2018): 1830016. http://dx.doi.org/10.1142/s0218127418300161.

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The Newton–Raphson basins of convergence, related to the equilibrium points, in the Sitnikov four-body problem with nonspherical primaries are numerically investigated. We monitor the parametric evolution of the positions of the roots, as a function of the oblateness coefficient. The classical Newton–Raphson optimal method is used for revealing the basins of convergence, by classifying dense grids of initial conditions in several types of two-dimensional planes. We perform a systematic and thorough analysis in an attempt to understand how the oblateness coefficient affects the geometry as well as the basin entropy of the convergence regions. The convergence areas are related with the required number of iterations and also with the corresponding probability distributions.
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Dissertations / Theses on the topic "Newton-Raphson iterations"

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Demir, Abdullah. "Form Finding And Structural Analysis Of Cables With Multiple Supports." Master's thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613609/index.pdf.

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Cables are highly nonlinear structural members under transverse loading. This nonlinearity is mainly due to the close relationship between the final geometry under transverse loads and the resulting stresses in its equilibrium state rather than the material properties. In practice, the cables are usually used as isolated single-segment elements fixed at the ends. Various studies and solution procedures suggested by researchers are available in the literature for such isolated cables. However, not much work is available for continuous cables with multiple supports. In this study, a multi-segment continuous cable is defined as a cable fixed at the ends and supported by a number of stationary roller supports in between. Total cable length is assumed constant and the intermediate supports are assumed to be frictionless. Therefore, the critical issue is to find the distribution of the cable length among its segments in the final equilibrium state. Since the solution of single-segment cables is available the additional condition to be satisfied for multi-segment continuous cables with multiple supports is to have stress continuity at intermediate support locations where successive cable segments meet. A predictive/corrective iteration procedure is proposed for this purpose. The solution starts with an initially assumed distribution of total cable length among the segments and each segment is analyzed as an independent isolated single-segment cable. In general, the stress continuity between the cable segments will not be satisfied unless the assumed distribution of cable length is the correct distribution corresponding to final equilibrium state. In the subsequent iterations the segment lengths are readjusted to eliminate the unbalanced tensions at segment junctions. The iterations are continued until the stress continuity is satisfied at all junctions. Two alternative approaches are proposed for the segment length adjustments: Direct stiffness method and tension distribution method. Both techniques have been implemented in a software program for the analysis of multi-segment continuous cables and some sample problems are analyzed for verification. The results are satisfactory and compares well with those obtained by the commercial finite element program ANSYS.
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Begiato, Rodolfo Gotardi 1980. "Métodos híbridos e livres de derivadas para resolução de sistemas não lineares." [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/305946.

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Orientadores: Márcia Aparecida Gomes Ruggiero, Sandra Augusta Santos
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
Made available in DSpace on 2018-08-21T10:21:10Z (GMT). No. of bitstreams: 1 Begiato_RodolfoGotardi_D.pdf: 3815627 bytes, checksum: 59584610cfd737a94e68dc5bf3735e25 (MD5) Previous issue date: 2012
Resumo: O objetivo desta tese é tratar da resolução de sistemas não lineares de grande porte, em que as funções são continuamente diferenciáveis, por meio de uma abordagem híbrida que utiliza um método iterativo com duas fases. A primeira fase consiste de versões sem derivadas do método do ponto fixo empregando parâmetros espectrais para determinar o tamanho do passo da direção residual. A segunda fase é constituída pelo método de Newton inexato em uma abordagem matrix-free, em que é acoplado o método GMRES para resolver o sistema linear que determina a nova direção de busca. O método híbrido combina ordenadamente as duas fases de forma que a segunda é acionada somente em caso de falha na primeira e, em ambas, uma condição de decréscimo não-monótono deve ser verificada para aceitação de novos pontos. Desenvolvemos ainda um segundo método, em que uma terceira fase de busca direta é acionada em situações em que o excesso de buscas lineares faz com que o tamanho de passo na direção do método de Newton inexato torne-se demasiadamente pequeno. São estabelecidos os resultados de convergência dos métodos propostos. O desempenho computacional é avaliado em uma série de testes numéricos com problemas tradicionalmente encontrados na literatura. Tanto a análise teórica quanto a numérica evidenciam a viabilidade das abordagens apresentadas neste trabalho
Abstract: This thesis handles large-scale nonlinear systems for which all the involved functions are continuously differentiable. They are solved by means of a hybrid approach based on an iterative method with two phases. The first phase is defined by derivative-free versions of a fixed-point method that employs spectral parameters to define the steplength along the residual direction. The second phase consists of a matrix-free inexact Newton method that employs the GMRES to solve the linear system that computes the search direction. The proposed hybrid method neatly combines the two phases in such a way that the second is called only in case the first one fails. To accept new points in both phases, a nonmonotone decrease condition upon a merit function has to be verified. A second method is developed as well, with a third phase based on direct search, that should act whenever too many line searches have excessively decreased the steplenght along the inexact- Newton direction. Convergence results for the proposed methods are established. The computational performance is assessed in a set of numerical experiments with problems from the literature. Both the theoretical and the experimental analysis corroborate the feasibility of the proposed strategies
Doutorado
Matematica Aplicada
Doutor em Matemática Aplicada
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Tong, Xiaolong. "A Constitutive Model for Crushable Polymer Foams Used in Sandwich Panels: Theory and FEA Application." University of Akron / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=akron1596806015399848.

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Books on the topic "Newton-Raphson iterations"

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Argyros, Ioannis K. Convergence and Applications of Newton-type Iterations. Springer, 2010.

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Convergence and Applications of Newton-type Iterations. Springer, 2008.

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Book chapters on the topic "Newton-Raphson iterations"

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Qin, Long, Fanwu Zhang, Lei Liu, Chunjiao Zhang, Jianbo Zheng, Xue Lei, Liuchun Yang, Fengmin Tian, and Fangxun Zhao. "Determination of Throttle Setpoint Control of Turbo-Charged GDI Engine Based on Newton Raphson Iteration." In Lecture Notes in Electrical Engineering, 1059–67. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-7945-5_78.

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Zhang, Yunong, Zhende Ke, Zhan Li, and Dongsheng Guo. "Comparison on Continuous-Time Zhang Dynamics and Newton-Raphson Iteration for Online Solution of Nonlinear Equations." In Advances in Neural Networks – ISNN 2011, 393–402. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21105-8_46.

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Rachdi, Mustapha, Ali Laksaci, Ali Hamié, Jacques Demongeot, and Idir Ouassou. "Curves Classification by Using a Local Likelihood Function and Its Practical Usefulness for Real Data." In Fuzzy Systems and Data Mining VI. IOS Press, 2020. http://dx.doi.org/10.3233/faia200691.

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We extend the classical approach in supervised classification based on the local likelihood estimation to the functional covariates case. The estimation procedure of the functional parameter (slope parameter) in the linear model when the covariate is of functional kind is investigated. We show, on simulated as well on real data, that classification error rates estimated using test samples, and the estimation procedure by local likelihood seem to lead to better estimators than the classical kernel estimation. In addition, this approach is no longer assuming that the linear predictors have a specific parametric form. However, this approach also has two drawbacks. Indeed, it was more expensive and slower than the kernel regression. Thus, as mentioned earlier, kernels other than the Gaussian kernel can lead to a divergence of the Newton-Raphson algorithm. In contrast, using a Gaussian kernel, 4 to 6 iterations are then sufficient to achieve convergence.
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"Newton–Raphson Iteration and Fractals." In Mathematical Explorations with MATLAB, 164–70. Cambridge University Press, 1999. http://dx.doi.org/10.1017/cbo9780511624117.014.

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Bethke, Craig M. "Solving for the Equilibrium State." In Geochemical Reaction Modeling. Oxford University Press, 1996. http://dx.doi.org/10.1093/oso/9780195094756.003.0009.

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In Chapter 3, we developed equations that govern the equilibrium state of an aqueous fluid and coexisting minerals. The principal unknowns in these equations are the mass of water nw, the concentrations mi of the basis species, and the mole numbers nk of the minerals. If the governing equations were linear in these unknowns, we could solve them directly using linear algebra. However, some of the unknowns in these equations appear raised to exponents and multiplied by each other, so the equations are nonlinear. Chemists have devised a number of numerical methods to solve such equations (e.g., van Zeggeren and Storey, 1970; Smith and Missen, 1982). All the techniques are iterative and, except for the simplest chemical systems, require a computer. The methods include optimization by steepest descent (White et al., 1958; Boynton, 1960) and gradient descent (White, 1967), back substitution (Kharaka and Barnes, 1973; Truesdell and Jones, 1974), and progressive narrowing of the range of the values allowed for each variable (the monotone sequence method; Wolery and Walters, 1975). Geochemists, however, seem to have reached a consensus (e.g., Karpov and Kaz’min, 1972; Morel and Morgan, 1972; Crerar, 1975; Reed, 1982; Wolery, 1983) that Newton-Raphson iteration is the most powerful and reliable approach, especially in systems where mass is distributed over minerals as well as dissolved species. In this chapter, we consider the special difficulties posed by the nonlinear forms of the governing equations and discuss how the Newton-Raphson method can be used in geochemical modeling to solve the equations rapidly and reliably. The governing equations are composed of two parts: mass balance equations that require mass to be conserved, and mass action equations that prescribe chemical equilibrium among species and minerals.
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Conference papers on the topic "Newton-Raphson iterations"

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Zhang, Wanjun, Feng Zhang, Jingxuan Zhang, Jingyi Zhang, and Jingyan Zhang. "Study on System Recognition Method for Newton-Raphson Iterations." In 2018 International Computers, Signals and Systems Conference (ICOMSSC). IEEE, 2018. http://dx.doi.org/10.1109/icomssc45026.2018.8941745.

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Papazafeiropoulos, George, Vagelis Plevris, and Manolis Papadrakakis. "NONLINEAR DYNAMIC RESPONSE OF HARDENING, SOFTENING AND ELASTOPLASTIC SDOF SYSTEMS USING GENERALIZED SINGLE STEP ALGORITHMS WITH NEWTON - RAPHSON ITERATIONS." In 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering Methods in Structural Dynamics and Earthquake Engineering. Athens: Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece, 2015. http://dx.doi.org/10.7712/120115.3582.3606.

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Nallathambi, Ashok Kumar, Eckehard Specht, and Albrecht Bertram. "Finite Element Technique for Phase-Change Heat Conduction Problem." In ASME 2009 Heat Transfer Summer Conference collocated with the InterPACK09 and 3rd Energy Sustainability Conferences. ASMEDC, 2009. http://dx.doi.org/10.1115/ht2009-88106.

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Liquid-solid phase transition is accompanied by a latent heat release, both in isothermal and non-isothermal phase transformations. The latent heat and the discontinuous phase change function increase the difficulty of obtaining a solution for the Fourier heat conduction equation. Celentano et al. [Int. J. Numer. Meth. Eng. 37(20), 1994] proposed a temperature-based finite element model for solving multidimensional transient heat conduction involving phase change. The present work addresses the computational aspects of the Celentano et al. model. The importance of a line search algorithm for improving the convergence of the Newton-Raphson iterations are explained in detail. While performing the iterations in this kind of fixed domain methods, the phase front moves back and forth fictitiously. The introduced phase change matrix handles the latent effect efficiently. The phase fractions are evaluated at the integration points instead of the nodal points. Several numerical examples are presented and the benefits and difficulties of the solution technique are elaborately discussed.
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Moreno, Carlos Luis. "Flow Analysis on Piping Networks Using the Finite Element Method." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-63553.

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The objective of this work is to apply the Finite Element Methodology (F.E.M.) to several piping systems, using an incompressible working fluid, in order to calculate the volumetric flow on each element and the piezometric load on each node of the network. To accomplish this goal a computational code was designed using Fortran Computational Language. Such a code consists of a main program and six subroutines. The input variables are general data of the network including the number of pipes, the number of nodes, the piezometric load values on nodes where they are constant (tanks for example), demanding flows in those nodes where the fluid is removed from the system, a connectivity table indicating the assumed flow direction in each pipe, and the number of pumps with respective parabolic curve coefficients. Program data also included both the maximum number of iterations and tolerance allowed. Fluid properties such as kinematic viscosity, density and pipe features such as length, diameter and absolute rugosity are also required. The output data include pipe volumetric flows and piezometric load on variable static pressure nodes. In this work, three different network systems were analyzed: 51-, 63- and 65-element networks. All were examples taken from the bibliography. The Finite Element Methodology results were first validated with real data, and then compared with the other results coming from the Hardy-Cross, Newton-Raphson and Linear Methods. The comparison was based on convergence speed and numerical stability. It is concluded that the methodology called Finite Element Methodology requires a smaller number of iterations than the Hardy-Cross, Linear and Newton-Raphson Methods. Another advantage of the Finite Element Methodology is that there is no need to assign the flow initial values that satisfy the Continuity Equation on each node of the piping network before running the program. Also, no loops establishing is needed. In addition, the designed code permits calculations for networks that present both booster and feed pumps. The importance of this work rests on the fact that nowadays it is necessary for piping network flow analysis to use computational simulation in order to design systems more efficiently and economically. Furthermore, this work is important for network construction as well as the satisfaction of consumer demand on a local community level, taking into account prevailing normative requirements. This paper, consequently, aims to contribute to progress in these areas.
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Li, Zhaokun, and Xianmin Zhang. "Multiobjective Topology Optimization of Compliant Microgripper With Geometrically Nonlinearity." In 2007 First International Conference on Integration and Commercialization of Micro and Nanosystems. ASMEDC, 2007. http://dx.doi.org/10.1115/mnc2007-21294.

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Since compliant mechanism is usually required to perform in more than one environment, the ability to consider multiple objectives has to be included within the framework of topology optimization. And the topology optimization of micro-compliant mechanisms is actually a geometrically nonlinear problem. This paper deals with multiobjective topology optimization of micro-compliant mechanisms undergoing large deformation. The objective function is defined by the minimum compliance and maximum geometric advantage to design a mechanism which meets both stiffness and flexibility requirements. The weighted sum of conflicting objectives resulting from the norm method is used to generate the optimal compromise solutions, and the decision function is set to select the preferred solution. Geometrically nonlinear structural response is calculated using a Total-Lagrange finite element formulation and the equilibrium is found using an incremental scheme combined with Newton-Raphson iterations. The solid isotropic material with penalization approach is used in design of compliant mechanisms. The sensitivities of the objective functions are found with the adjoint method and the optimization problem is solved using the Method of Moving Asymptotes. These methods are further investigated and realized with the numerical example of compliant microgripper, which is simulated to show the availability of this approach proposed in this paper.
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Kumar, Prabhat, Roger A. Sauer, and Anupam Saxena. "On Synthesis of Contact Aided Compliant Mechanisms Using the Material Mask Overlay Method." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-47064.

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Contact Aided Compliant Mechanisms (CCMs) are synthesized via the Material Mask Overlay Strategy (MMOS) to trace a desired non-smooth path. MMOS employs hexagonal cells to discretize the design region and engages negative circular masks to designate material states. To synthesize CCMs, the modified MMOS presented herein involves systematic mutation of five mask parameters through a hill climber search to evolve not only the continuum topology (slave surfaces), but also, to introduce the desired rigid, interacting surfaces within some masks. Various geometric singularities are subdued via hexagonal cells though numerous V-notches get retained at the continuum boundaries. To facilitate contact analysis, boundary smoothing is performed by shifting boundary nodes of the evolving continuum systematically. Numerous hexagonal cells get morphed into concave sub-regions as a consequence. Large deformation finite element formulation with Mean Value Coordinates (MVC) based shape functions is used to cater to the generic hexagonal shapes. Contact analysis is accomplished via the Newton-Raphson iterations with load increment in conjunction with the penalty method and active set constraints. An objective function based on Fourier Shape Descriptors is minimized subject to suitable design constraints. An example of a path generating CCM is included to establish the efficacy of the proposed synthesis method.
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Kurzke, Joachim. "About Simplifications in Gas Turbine Performance Calculations." In ASME Turbo Expo 2007: Power for Land, Sea, and Air. ASMEDC, 2007. http://dx.doi.org/10.1115/gt2007-27620.

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Any gas turbine performance simulation tool employs simplifications, some more, some less. It depends on the intent of the simulation which simplifications are appropriate. For beginners, many are necessary for teaching how the gas turbine works from principle. For practical applications — because of the accuracy requirements — many simplifications introduced in textbooks are not appropriate. This paper comments on the simplifications that are typically made. Simplified gas property models are quite acceptable for ideal cycle analysis. For the examination of real cycles, however, especially the model of the burner should be better than those described in most textbooks. This is because these models yield the best cycle efficiency at stoichiometric fuel-air-ratio while a realistic burner model leads to the conclusion that the best thermal efficiency happens to be at significantly lower fuel-air-ratios respectively temperatures. For off-design simulations many simplifications have the aim to avoid iterative solutions or restricting the algorithms to one-dimensional iterations. If more than one iteration variable shows up — which is the case with multi-spool engine simulations — then the problem is solved with fitting several one-dimensional iterations into each other. This methodology is described in most textbooks, but it is nearly never used in industry because the logic is more complex than necessary and difficult to adapt to special needs. The seeming simplification is actually a complication when applied to real world problems. Universities should teach as a standard the multidimensional Newton Raphson iteration technique which allows writing gas turbine cycle codes with nearly no restriction to the methods of formulating the laws of physics. The consequence of simplified mathematics is often an off-design simulation which does not employ compressor and turbine maps. Such a methodology yields accurate values for thermal efficiency respectively specific fuel consumption only within a narrow range of operating conditions; the accuracy of the results is not sufficient for real world applications. Of course also in programs for industrial use the reality is modeled with many compromises. Some simplifications which have not so obvious consequences are discussed. For example, there is an influence of the speed-flow characteristics in the booster map on its operating line if an often used type of fan performance representation is employed. Another example is that an oversimplified description of what happens in the compressor interduct can lead to wrong conclusions when the effects of inlet flow distortion on the stability of compressors in series are sought.
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8

Xin, Jin, Xiaohan Liu, and Xiaoyan Wei. "A New Numerical Method for Fuel Temperature Calculation." In 2017 25th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/icone25-66248.

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For most fuel rod codes, the time independent heat conduction equation, which is a steady heat conduction equation, is applied in fuel temperature calculation. However, it can affect the fuel temperature prediction in II condition, which the linear power has much change in some seconds. For improving the fuel temperature prediction in II condition, this paper gives a new numerical method, which combines classical thermal conduction integration method and the difference applied in time partial derivative. For guaranteeing the numerical method’s stability and convergence rate, the multi-dimension Newton-Raphson procedure are applied in fuel temperature calculation. This paper describes the theoretical deduction of the numerical method, and Halden fuel thermal conductivity model applied in fuel temperature calculation. In order to verify new numerical method’s correctness, stability and convergence rate, the comparison between numerical solution and analytic solution is performed in 4 hypothetical conditions that the power transient duration is respectively 3s, 15s, 30s and 120s, the linear power changes from 15kW/m to 45 kW/m, and the fuel pellet surface temperature changes from 400 degree to 750 degree. And fuel density, specific heat and thermal conductivity are assumed as constants so that there exists analytic solution in this condition. The 4 hypothetical conditions have covered the worst II condition. According to the results in 4 hypothetical conditions, the fuel centerline temperature relative difference between numerical solution and theoretical solution is less than 0.6%, and the iterations are less than 5. So the numerical method possesses excellent correctness, stability and convergence, and this method has much potential in application in fuel rod code.
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9

Kraffer, F., and J. J. Loiseau. "Spectral factorization via Lyapunov equation based Newton-Raphson iteration." In Proceedings of 2002 American Control Conference. IEEE, 2002. http://dx.doi.org/10.1109/acc.2002.1025480.

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Chen, Chang-New. "The Global Secant Relaxation-Based Accelerated Iteration Procedure for Solution of Nonlinear Finite Element Equation Systems of Offshore Structural Mechanics Problems." In ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2011. http://dx.doi.org/10.1115/omae2011-50170.

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A global secant relaxation (GSR)-based accelerated iteration scheme can be used to carry out the incremental/iterative solution of various nonlinear finite element systems of offshore structural mechanics problems. This computation procedure can overcome the possible deficiency of numerical instability caused by local failure existing in the iterative computation. Moreover, this method can efficiently accelerate the convergency of the iterative computation. This incremental/iterative analysis can consistently be carried out to update the response history up to a near ultimate load stage, which is important for investigating the global failure behaviour of a structure under certain external cause, if the constant stiffness is used. Consequently, this method can widely be used to solve general nonlinear problems. Mathematical procedures of Newton-Raphson techniques in finite element methods for nonlinear finite element problems are summarized. These techniques are the Newton-Raphson method, quasi-Newton methods, modified Newton-Raphson methods and accelerated modified Newton-Raphson methods. Numerical results obtained by using various accelerated modified Newton-Raphson methods are used to study the convergency performances of these techniques for material nonlinearity problems and deformation nonlinearity problems, separately.
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