Matrix decomposition MFS algorithms for elasticity and thermo-elasticity problems in axisymmetric domains
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TLDR
This work proposes an efficient matrix decomposition algorithm for the Method of Fundamental Solutions when applied to three-dimensional boundary value problems governed by elliptic systems of partial differential equations and makes use of fast Fourier transforms.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2007-09-20 and is currently open access. It has received 31 citations till now. The article focuses on the topics: Method of fundamental solutions & Matrix decomposition.read more
Citations
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Journal ArticleDOI
Matrix decomposition algorithms for elliptic boundary value problems: a survey
TL;DR: An overview of matrix decomposition algorithms (MDAs) for the solution of systems of linear equations arising when various discretization techniques are applied in the numerical solution of certain separable elliptic boundary value problems in the unit square is provided.
Journal ArticleDOI
The method of fundamental solutions for an inverse boundary value problem in static thermo-elasticity
TL;DR: In this article, a regularized method of fundamental solutions is employed in order to find a stable numerical solution to this ill-posed, but linear coupled inverse problem, and the choice of the regularization parameter is based on the L-curve criterion.
Journal ArticleDOI
A meshless generalized finite difference method for inverse Cauchy problems associated with three-dimensional inhomogeneous Helmholtz-type equations
TL;DR: The generalized finite difference method (GFDM) as discussed by the authors is a relatively new domain-type meshless method for the numerical solution of certain boundary value problems, which involves a coupling between the Taylor series expansions and weighted moving least-squares method.
Journal ArticleDOI
Regularized MFS solution of inverse boundary value problems in three-dimensional steady-state linear thermoelasticity
TL;DR: In this article, the authors investigate the numerical reconstruction of the missing thermal and mechanical boundary conditions on an inaccessible part of the boundary in the case of three-dimensional linear isotropic thermoelastic materials from the knowledge of over-prescribed noisy data on the remaining accessible boundary.
Journal ArticleDOI
Mathematical foundation of the MFS for certain elliptic systems in linear elasticity
TL;DR: A mathematical framework for the numerical implementation of the MFS in elliptic systems is developed and density results are obtained, with respect to the Cℓ-norms, which establish the applicability of the method in certain systems arising from the theory of elastostatic and thermo-elastostatics.
References
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Book
A treatise on the mathematical theory of elasticity
TL;DR: Webb's work on elasticity as mentioned in this paper is the outcome of a suggestion made to me some years ago by Mr R. R. Webb that I should assist him in the preparation of a work on Elasticity.
Journal ArticleDOI
The method of fundamental solutions for elliptic boundary value problems
TL;DR: Techniques by which MFS-type methods are extended to certain classes of non-trivial problems and adapted for the solution of inhomogeneous problems are outlined.
Journal ArticleDOI
The method of functional equations for the approximate solution of certain boundary value problems
V.D. Kupradze,M.A. Aleksidze +1 more
Journal ArticleDOI
Fundamental Solutions Method for Elliptic Boundary Value Problems
TL;DR: In this article, the fundamental solutions method for boundary value problems for elliptic homogeneous equations was proposed. But the fundamental solution method is not suitable for the case of the Laplacian.
Book
Discrete projection methods for integral equations
TL;DR: In this paper, discrete projection methods are analyzed for a variety of integral equations which arise from the reformulation of boundary value problems for partial differential equations, such as Fredholm, Volterra, Cauchy singular, hypersingular and boundary integral.
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