Dissertations / Theses on the topic 'Hamiltonian Boundary Value Method'
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Heredia, N. Fernando. "A new method for boundary value problems." Thesis, Monterey, California. Naval Postgraduate School, 1985. http://hdl.handle.net/10945/21467.
Full textRockstroh, Parousia. "Boundary value problems for the Laplace equation on convex domains with analytic boundary." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/273939.
Full textUgail, Hassan. "Method of boundary based smooth shape design." ACTA Press, 2005. http://hdl.handle.net/10454/2685.
Full textChan, Kwok Cheung. "Shooting method for singularly perturbed two-point boundary value problems." HKBU Institutional Repository, 1998. http://repository.hkbu.edu.hk/etd_ra/274.
Full textBozkaya, Canan. "Boundary Element Method Solution Of Initial And Boundary Value Problems In Fluid Dynamics And Magnetohydrodynamics." Phd thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/12609552/index.pdf.
Full textAlsaedy, Ammar, and Nikolai Tarkhanov. "The method of Fischer-Riesz equations for elliptic boundary value problems." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/6179/.
Full textMokhtarzadeh, M. R. "A general global approximation method for the solution of boundary value problems." Thesis, Loughborough University, 1998. https://dspace.lboro.ac.uk/2134/14478.
Full textChibi, 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 textYang, Zhiyun. "A Cartesian grid method for elliptic boundary value problems in irregular regions /." Thesis, Connect to this title online; UW restricted, 1996. http://hdl.handle.net/1773/6759.
Full textPoullikkas, Andreas. "The Method of Fundamental Solutions for the solution of elliptic boundary value problems." Thesis, Loughborough University, 1997. https://dspace.lboro.ac.uk/2134/27141.
Full textWomble, David Eugene. "The convergence of the method of lines for time dependent free boundary problems." Diss., Georgia Institute of Technology, 1986. http://hdl.handle.net/1853/29154.
Full textJin, Kang Meir Amnon J. "On the Lattice Boltzmann method implementation and applications /." Auburn, Ala, 2008. http://repo.lib.auburn.edu/EtdRoot/2008/FALL/Mathematics_and_Statistics/Dissertation/Jin_Kang_9.pdf.
Full textMcFall, Kevin Stanley. "An artificial neural network method for solving boundary value problems with arbitrary irregular boundaries." Diss., Available online, Georgia Institute of Technology, 2006, 2006. http://etd.gatech.edu/theses/available/etd-04052006-154934/.
Full textGeorge Vachtsevanos, Committee Member ; Nader Sadegh, Committee Member ; J. Robert Mahan, Committee Chair ; Ali Siadat, Committee Member ; Zhuomin Zhang, Committee Member.
Chien, Chyou-Chi. "On the evaluation of hyper-singular integrals arising in the boundary element method for elasticity and acoustic problems." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/21264.
Full textMudavanhu, Blessing. "A new renormalization method for the asymptotic solution of multiple scale singular perturbation problems /." Thesis, Connect to this title online; UW restricted, 2002. http://hdl.handle.net/1773/6794.
Full textRitter, 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 textThesis 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.
VARGAS, JOSE VIRIATO COELHO. "INITIAL VALUE METHOD FOR THE SOLUTION OF NON-SIMILAR BOUNDARY LAYERS APPLIED TO A WEDGE IN MEXED CONVECTION." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1992. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=19598@1.
Full textO presente trabalho apresenta o método de varredura de valores iniciais para a solução de problemas não-similares de camada limite, aplicado a uma cunha em convecção mista. É feita uma análise dos efeitos da força de empuxo nas características de transferência de calor e atrito, na superfície da cunha submetida a um escoamento laminar em convecção forçada. Os casos analisados referem-se a temperatura uniforme na superfície e a fluxo de calor uniforme através da superfície. Apresentam-se resultados numéricos para a placa vertical e a cunha em 120 graus celsius (problema similar), os quais foram comparados com os disponíveis na literatura, apresentando-se excelente concordância. Ainda são apresentados resultados para a cunha em 90 graus celsius e em 180 graus Celsius. Os resultados foram obtidos para o número de Prandtl 0,7 em uma larga faixa do parâmetro de não-similaridade (0 a 100 para temperatura uniforme e 0 a 5 para fluxo de calor uniforme). Em geral, verifica-se que para ambos os casos estudados de condições da superfície, o coeficiente de atrito local e o número de Nusselt local aumentam com o aumento da força de empuxo para o escoamento ajudado e diminuem com o aumento da força de empuxo para o escoamento ajudado e diminuem com o aumento da força de empuxo para o escoamento oposto. Verifica-se também que os efeitos de convecção natural diminuem com o aumento do ângulo da cunha. Compara-se, por fim os resultados de transferência de calor entre os dois casos estudados. O método possibilita a obtenção de resultados com o uso de um microcomputador PC AT-286 com o co-processador matemático, sem o uso de dupla precisão. As tolerâncias utilizadas para a convergência são as mesmas dos resultados disponíveis na literatura. Adicionalmente, o tempo computacional necessário para a obtenção das soluções foi bastante reduzido. Para toda a faixa de variação do parâmetro de não-similaridade, o equacionamento utilizado foi o mesmo, baseado em parâmetros de correlação para convecção forçada em uma superfície plana com injeção de massa, com ótima concordância com resultados disponíveis na literatura.
The present work introduces a method for searching initial values, to solve non-similar Boundary Layer problems. The new method has been applied to the problem of mixed convection on a Wedge. An analysis is performed to study the effects of buoyancy force on the heat transfer and friction characteristics of laminar forced convection flow which is either maintained at a uniform temperature or subjected to a uniform temperature or subjected to a uniform heat flux. Numerical results are presented for Prandtl number of 7,0 over a wide range of values of the buoyancy force parameters (0 to 100 for uniform temperature and 0 to 5 for uniform heat flux). The results for the vertical plate and for the similar wedge (120 graus celsius) Have been compared with solutions availabein the literature, showing an excellent agreement. In addition, solutions for the 90 degree celsius wedge and for the flat wall (180 degree celsius are also obtained. In general, it is found that for both surface heating conditions, the local friction factor and the local Nusselt number increase with increasing bouyancy force for assisting flow and decrease with inscreasing bouyancy force for opposing flow. Further, the effects of the buoyancy force on these two quantities are found to diminish as the angle of the wedge increases. A comparison is also made of the results beteween the case of uniform wall temperature and the case of uniform surface heat flux. The method turns possible to obtain results with the use of a microcomputer PC AT-286 with a Math co-processor, discarding the use of double precision. The tolerances for convergence are the same as the results available in the literature. The necessary computacional time to get the solution was greatly reduced. For the entire range of the buoyancy force parameter, the governing equations are the same, based upon forced convection parameters. To illustrate the flexibility of the method, the surface mass trasnfer problem of uniform injection (blowing) in a flat plate under forced cnvection, has been solved and the results compared with the available ones in the literature.
Nyamayaro, Takura T. A. "On the design and implementation of a hybrid numerical method for singularly perturbed two-point boundary value problems." University of the Western Cape, 2014. http://hdl.handle.net/11394/4326.
Full textWith the development of technology seen in the last few decades, numerous solvers have been developed to provide adequate solutions to the problems that model different aspects of science and engineering. Quite often, these solvers are tailor-made for specific classes of problems. Therefore, more of such must be developed to accompany the growing need for mathematical models that help in the understanding of the contemporary world. This thesis treats two point boundary value singularly perturbed problems. The solution to this type of problem undergoes steep changes in narrow regions (called boundary or internal layer regions) thus rendering the classical numerical procedures inappropriate. To this end, robust numerical methods such as finite difference methods, in particular fitted mesh and fitted operator methods have extensively been used. While the former consists of transforming the continuous problem into a discrete one on a non-uniform mesh, the latter involves a special discretisation of the problem on a uniform mesh and are known to be more accurate. Both classes of methods are suitably designed to accommodate the rapid change(s) in the solution. Quite often, finite difference methods on piece-wise uniform meshes (of Shishkin-type) are adopted. However, methods based on such non-uniform meshes, though layer-resolving, are not easily extendable to higher dimensions. This work aims at investigating the possibility of capitalising on the advantages of both fitted mesh and fitted operator methods. Theoretical results are confirmed by extensive numerical simulations.
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 textJin, Jicheng. "Finite element methods for some elliptic problems with singularity and problems on unbounded domains." HKBU Institutional Repository, 2004. http://repository.hkbu.edu.hk/etd_ra/597.
Full textKuhn, Wolfgang. "Rigorous and reasonable error bounds for the numerical solution of dynamical systems." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/28941.
Full textStarkloff, Hans-Jörg. "Stochastic finite element method with simple random elements." Universitätsbibliothek Chemnitz, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200800596.
Full textRattana, Amornrat, and Christine Böckmann. "Matrix methods for computing Eigenvalues of Sturm-Liouville problems of order four." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/5927/.
Full textUgail, Hassan, M. I. G. Bloor, and M. J. Wilson. "Implementing automatic design optimisation in an interactive environment." American Institute of Aeronautics and Astronautics, 2000. http://hdl.handle.net/10454/2942.
Full textAoyama, Taiki, Shota Fukumoto, and Hideyuki Azegami. "Shape optimization of continua using NURBS as basis functions." Springer, 2013. http://hdl.handle.net/2237/21124.
Full textYoerger, Edward J. Jr. "Vertical Acoustic Propagation in the Non-Homogeneous Layered Atmosphere for a Time-Harmonic, Compact Source." ScholarWorks@UNO, 2019. https://scholarworks.uno.edu/td/2709.
Full text畔上, 秀幸, and Hideyuki Azegami. "領域最適化問題の一解法." 日本機械学会, 1994. http://hdl.handle.net/2237/7238.
Full textWeichselbaum, Andreas. "Nanoscale Quantum Dynamics and Electrostatic Coupling." Ohio University / OhioLINK, 2004. http://www.ohiolink.edu/etd/view.cgi?ohiou1091115085.
Full textOzdemir, Nilufer A. "The method of moments solution of a nonconformal volume integral equation via the IE-FFT algorithm for electromagnetic scattering from penetrable objects." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1182258230.
Full textDesiderio, Luca. "H-matrix based Solver for 3D Elastodynamics Boundary Integral Equations." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLY002/document.
Full textThis thesis focuses on the theoretical and numerical study of fast methods to solve the equations of 3D elastodynamics in frequency-domain. We use the Boundary Element Method (BEM) as discretization technique, in association with the hierarchical matrices (H-matrices) technique for the fast solution of the resulting linear system. The BEM is based on a boundary integral formulation which requires the discretization of the only domain boundaries. Thus, this method is well suited to treat seismic wave propagation problems. A major drawback of classical BEM is that it results in dense matrices, which leads to high memory requirement (O (N 2 ), if N is the number of degrees of freedom) and computational costs.Therefore, the simulation of realistic problems is limited by the number of degrees of freedom. Several fast BEMs have been developed to improve the computational efficiency. We propose a fast H-matrix based direct BEM solver
Kulkarni, Mandar S. "Multi-coefficient Dirichlet Neumann type elliptic inverse problems with application to reflection seismology." Birmingham, Ala. : University of Alabama at Birmingham, 2009. https://www.mhsl.uab.edu/dt/2010r/kulkarni.pdf.
Full textTitle from PDF t.p. (viewed July 21, 2010). Additional advisors: Thomas Jannett, Tsun-Zee Mai, S. S. Ravindran, Günter Stolz, Gilbert Weinstein. Includes bibliographical references (p. 59-64).
El, Bouzid Hassan. "Méthodes d'éléments finis raffinés pour quelques problèmes aux limites dans des domaines non-réguliers." Valenciennes, 1996. https://ged.uphf.fr/nuxeo/site/esupversions/78c75dce-f930-4497-9077-c57356a9fac0.
Full textЯчменьов, Володимир Олександрович, Владимир Александрович Ячменев, Volodymyr Oleksandrovych Yachmenov, and С. А. Терновский. "Решение начально-краевых задач для уравнений с дробными производными." Thesis, Сумский государственный университет, 2014. http://essuir.sumdu.edu.ua/handle/123456789/39366.
Full textLadecký, Martin. "Isogeometrická analýza a její použití v mechanice kontinua." Master's thesis, Vysoké učení technické v Brně. Fakulta stavební, 2018. http://www.nusl.cz/ntk/nusl-371938.
Full textJoubert, Dominique. "Numerical methods for pricing American put options under stochastic volatility / Dominique Joubert." Thesis, North-West University, 2013. http://hdl.handle.net/10394/10202.
Full textMSc (Applied Mathematics), North-West University, Potchefstroom Campus, 2013
Acikgoz, Nazmiye. "Adaptive and Dynamic Meshing Methods for Numerical Simulations." Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/14521.
Full textBrideson, Michael. "Electromagnetic induction tomography : a feasibility study." Thesis, Queensland University of Technology, 2000.
Find full textROSSI, ELENA. "Balance Laws: Non Local Mixed Systems and IBVPs." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2016. http://hdl.handle.net/10281/103090.
Full textAxelsson, Andreas, and kax74@yahoo se. "Transmission problems for Dirac's and Maxwell's equations with Lipschitz interfaces." The Australian National University. School of Mathematical Sciences, 2002. http://thesis.anu.edu.au./public/adt-ANU20050106.093019.
Full textVogt, Andreas. "Analytische und numerische Untersuchung von direkten und inversen Randwertproblemen in Gebieten mit Ecken mittels Integralgleichungsmethoden." [S.l.] : [s.n.], 2001. http://webdoc.sub.gwdg.de/diss/2002/vogt/vogt.pdf.
Full textNouisri, Amine. "Identification paramétrique en dynamique transitoire : traitement d’un problème couplé aux deux bouts." Thesis, Université Paris-Saclay (ComUE), 2015. http://www.theses.fr/2015SACLN005/document.
Full textThis thesis deals with parameters identification in transient dynamic in case of highly noisy experimental data. One long-term goal is the derivation of a non-intrusive method dedicated to the implementation in a commercial finite element code.In this work, the modified error in the constitutive relation framework is used to treat the identification of material parameters. The minimization of the cost function under constraints leads, in the case of transient dynamics, to a « two points boundary value problem » in which the differential space-time problem involves both initial and final time conditions. This results in a problem coupling the direct and adjoint fields, whose treatment is difficult.In the first part, methods such as those based on the « Riccati equations » and the « shooting methods » have been studied. It is shown that the identification is robust even in the case of highly corrupted measures, but these methods are limited either by the implementation intrusiveness, conditioning problems or the numerical cost.In the second part, an iterative over-relaxation approach is developed and compared to the aforementioned approaches on academic problems in order to validate the interest of the method. Finally, comparisons are carried out between this approach and a « discretized » variation of the formulation introduced by Bonnet and Aquino [Inverse Problems, vol. 31, 2015]
Silva, Clovis Antonio da. "Um novo algoritmo, naturalmente paralelizável, para o cálculo de permeabilidades equivalentes em reservatórios." Universidade do Estado do Rio de Janeiro, 2008. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=1252.
Full textNeste trabalho é apresentado um novo procedimento numérico para o upscaling de permeabilidade utilizando condições de contorno periódicas. Este procedimento combina decomposição de domínio com elementos finitos mistos na discretização do problema local de pressão-velocidade necessário para se encontrar as permeabilidades equivalentes.
A new numerical method is proposed for the permeabilities upscaling take into consideration periodic boundary conditions. This method combines domain decomposition with mixed finite elements in discretization of the local problem of pressure-velocity necessary to meet the equivalent permeabilities.
Docherty, Paul J. "Developing literary Glasgow : towards a strategy for a reading, writing and publishing city." Thesis, University of Stirling, 2018. http://hdl.handle.net/1893/28083.
Full textNguyen, Thi Nhu Thao. "Modélisation mathématique et simulation de la dynamique spatiale de populations de campagnols dans l’est de la France." Thesis, Bourgogne Franche-Comté, 2020. http://www.theses.fr/2020UBFCD031.
Full textThe main objective of the thesis is to propose and analyze mathematical models based on partial differential equations (PDE) to describe the spatial dynamics of two species of voles (Microtus arvalis and Arvicola terrestris), which are particularly monitored in Eastern France. The models that we have proposed are based on PDE which describe the evolution of the density of the population of voles as a function of time, age and position in space. We have two complementary approaches to represent the dynamics. In the first approach, we propose a first model that consists of a scalar PDE depending on time, age, and space supplemented with a non-local boundary condition. The flux is linear with constant coefficient in the direction of age but contains a non-local term in the directions of space. Moreover, the equation contains a second order term in the spatial variables only. We have demonstrated the existence and stability of weak entropy solutions for the model by using, respectively, the Panov's theorem of the multidimensional compensated and a doubling of the variables type argument. In the second approach we were inspired by a Multi Agent model proposed by Marilleau-Lang-Giraudoux, where the spatial dynamics of juveniles is decoupled from local evolution in each plot. To apply this model, we have introduced a directed graph whose nodes are the plots. In each node, the evolution of the colony is described by a transport equation with two variables, time and age, and the movements of dispersion, in space, are represented by the passages from one node to the other. We have proposed a discretization of the model, by finite volume methods, and noticed that this approach manages to reproduce the qualitative characteristics of the spatial dynamics observed in nature. We also proposed to consider a predator-prey system consisting of a hyperbolic equation for predators and a parabolic-hyperbolic equation for preys, where the prey's equation is analogous to the first model of the vole populations. The drift term in the predators' equation depends nonlocally on the density of prey and the two equations are also coupled via classical source terms of Lotka-Volterra type. We establish existence of solutions by applying the vanishing viscosity method, and we prove stability by a doubling of variables type argument. Moreover, concerning the numerical simulation of the first model in one-dimensional space, we obtain a finite volume discretization by using the upwind scheme and then validate the numerical scheme.The last part of my thesis work is a project in which I participated during a Summer school CEMRACS. The project was on a subject of biomathematics different from that of the thesis (an epidemiological model for salmonellosis). A new generic multi-scale modeling framework for heterogeneous transmission of pathogens in an animal population is suggested. At the intra-host level, the model describes the interaction between the commensal microbiota, the pathogen and the inflammatory response. Random fluctuations in the ecological dynamics of the individual microbiota and transmission at the inter-host scale are added to obtain a PDE model of drift-diffusion of pathogen distribution at the population level. The model is also extended to represent transmission between several populations. Asymptotic behavior as well as the impact of control strategies, including cleaning and administration of antimicrobials, are studied by numerical simulation
Hartmann, Marcelo. "Métodos de Monte Carlo Hamiltoniano na inferência Bayesiana não-paramétrica de valores extremos." Universidade Federal de São Carlos, 2015. https://repositorio.ufscar.br/handle/ufscar/4601.
Full textIn this work we propose a Bayesian nonparametric approach for modeling extreme value data. We treat the location parameter _ of the generalized extreme value distribution as a random function following a Gaussian process model (Rasmussem & Williams 2006). This configuration leads to no closed-form expressions for the highdimensional posterior distribution. To tackle this problem we use the Riemannian Manifold Hamiltonian Monte Carlo algorithm which allows samples from the posterior distribution with complex form and non-usual correlation structure (Calderhead & Girolami 2011). Moreover, we propose an autoregressive time series model assuming the generalized extreme value distribution for the noise and obtained its Fisher information matrix. Throughout this work we employ some computational simulation studies to assess the performance of the algorithm in its variants and show many examples with simulated and real data-sets.
Neste trabalho propomos uma abordagem Bayesiana não-paramétrica para a modelagem de dados com comportamento extremo. Tratamos o parâmetro de locação _ da distribuição generalizada de valor extremo como uma função aleatória e assumimos um processo Gaussiano para tal função (Rasmussem & Williams 2006). Esta situação leva à intratabilidade analítica da distribuição a posteriori de alta dimensão. Para lidar com este problema fazemos uso do método Hamiltoniano de Monte Carlo em variedade Riemanniana que permite a simulação de valores da distribuição a posteriori com forma complexa e estrutura de correlação incomum (Calderhead & Girolami 2011). Além disso, propomos um modelo de série temporal autoregressivo de ordem p, assumindo a distribuição generalizada de valor extremo para o ruído e determinamos a respectiva matriz de informação de Fisher. No decorrer de todo o trabalho, estudamos a qualidade do algoritmo em suas variantes através de simulações computacionais e apresentamos vários exemplos com dados reais e simulados.
Franceschi, Sandro. "Approche analytique pour le mouvement brownien réfléchi dans des cônes." Thesis, Tours, 2017. http://www.theses.fr/2017TOUR4046/document.
Full textObliquely reflected Brownian motion in the quadrant, introduced by Harrison, Reiman, Varadhan and Williams in the eighties, has been studied a lot in the probabilistic literature. This thesis, which presents the complete study of the invariant measure of this process in all the cones of the plan, has for overall aim to extend to the continuous framework an analytic method initially developped for random walks in the quarter plane by Fayolle, Iasnogorodski and Malyshev in the seventies. This approach is based on functional equations which link generating functions in the discrete case and Laplace transform in the continuous case. These equations allow to determine and to solve boundary value problems satisfied by these generating functions. In the recurrent case, it permits to compute explicitly the invariant measure of the process with orthogonal reflexions, in the chapter 2, and with any reflexions, in the chapter 3. The Laplace transform of the invariant measure is analytically extended to a Riemann surface induced by the kernel of the functional equation. The study of singularities and the use of saddle point methods on this surface allows to determine the full asymptotics of the invariant measure along every directions in the chapter 4
FRASCA, CACCIA GIANLUCA. "A new efficient implementation for HBVMs and their application to the semilinear wave equation." Doctoral thesis, 2015. http://hdl.handle.net/2158/992629.
Full text(5930024), Kshitij Mall. "Advancing Optimal Control Theory Using Trigonometry For Solving Complex Aerospace Problems." Thesis, 2019.
Find full textChen, Chien-Chou, and 陳建州. "Semi-Analytic Method for Boundary Value Problems of ODEs." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/97394865236013850652.
Full text國立中山大學
應用數學系研究所
93
In this thesis, we demonstrate the capability of power series, combined with numerical methods, to solve boundary value problems and Sturm-Liouville eigenvalue problems of ordinary differential equations. This kind of schemes is usually called the numerical-symbolic, numerical-analytic or semi-analytic method. In the first chapter, we develop an adaptive algorithm, which automatically decides the terms of power series to reach desired accuracy. The expansion point of power series can be chosen freely. It is also possible to combine several power series piecewisely. We test it on several models, including the second and higher order linear or nonlinear differential equations. For nonlinear problems, the same procedure works similarly to linear problems. The only differences are the nonlinear recurrence of the coefficients and a nonlinear equation, instead of linear, to be solved. In the second chapter, we use our semi-analytic method to solve singularly perturbed problems. These problems arise frequently in fluid mechanics and other branches of applied mathematics. Due to the existence of boundary or interior layers, its solution is very steep at certain point. So the terms of series need to be large in order to reach the desired accuracy. To improve its efficiency, we have a strategy to select only a few required basis from the whole polynomial family. Our method is shown to be a parameter diminishing method. A specific type of boundary value problem, called the Sturm-Liouville eigenvalue problem, is very important in science and engineering. They can also be solved by our semi-analytic method. This is our focus in the third chapter. Our adaptive method works very well to compute its eigenvalues and eigenfunctions with desired accuracy. The numerical results are very satisfactory.
Kao, Jeng-Hung, and 高政宏. "Regularized meshless method for boundary value problems with multiply-connected domain." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/48092373281516078268.
Full text國立臺灣海洋大學
河海工程學系
93
Abstract In this thesis, the regularized meshless method is adopted to solve Laplace problems and eigenproblems with multiply-connected domain, respectively. Here, the solution is represented by using double-layer potential. The subtracting and adding-back technique is used to regularize the singularity and hypersingularity of the kernel functions. Only boundary nodes on the real boundary are required by using the proposed technique in a different way of conventional MFS by putty singularities on fictition boundaries. A linear algebraic equation is obtained free of mesh generation. After matching boundary conditions, the unknown densities in the algebraic system can be easily determined. Test of convergence and sensitivity study of the proposed method are also done. Finally, several engineering problems including multiple inclusions problem under antiplane shear, piezoelectricity problems with multiple inclusions and multiply-connected acoustic eigenproblem, were given to demonstrate the validity of the proposed method. Numerical results agree well after comparing with the available exact solution and those of boundary element method, point-matching method and finite element method. A general-purpose program for multiple cavities and inclusions of various shapes and arbitrary positions was developed. Keywords: Laplace problem, multiple holes, multiply-connected domain, eigenproblem, method of fundamental solution, Regularized meshless method, inclusion, piezoelectricity, eigenproblem, antiplane shear