scholarly journals Localized Method of Fundamental Solutions for Three-Dimensional Elasticity Problems: Theory

2021 ◽  
Vol 13 (6) ◽  
pp. 1520-1534 ◽  
Author(s):  
global sci
Keyword(s):  
Three Dimensional ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Elasticity Problems ◽  
Three Dimensional Elasticity

The Uniform Flexure of an Incomplete Tore

1949 ◽  
Vol 2 (4) ◽  
pp. 469
Author(s):  
W Freiberger ◽  
RCT Smith
Keyword(s):  
General Solution ◽  
Cross Section ◽  
Harmonic Functions ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Elasticity Problems ◽  
Three Dimensional Elasticity ◽  
Derivatives Of ◽  
Special Case

In this paper we discuss the flexure of an incomplete tore in the plane of its circular centre-line. We reduce the problem to the determination of two harmonic functions, subject to boundary conditions on the surface of the tore which involve the first two derivatives of the functions. We point out the relation of this solution to the general solution of three-dimensional elasticity problems. The special case of a narrow rectangular cross-section is solved exactly in Appendix II.

A Moving Pseudo-Boundary MFS for Three-Dimensional Void Detection

2013 ◽  
Vol 5 (04) ◽  
pp. 510-527 ◽  
Author(s):  
Andreas Karageorghis ◽  
Daniel Lesnic ◽  
Liviu Marin
Keyword(s):  
Three Dimensional ◽  
Nonlinear Least Squares ◽  
Fundamental Solutions ◽  
Cauchy Data ◽  
Three Dimensions ◽  
Method Of Fundamental Solutions ◽  
Void Detection ◽  
Spherical Parametrization ◽  
Least Squares Minimization

AbstractWe propose a new moving pseudo-boundary method of fundamental solutions (MFS) for the determination of the boundary of a three-dimensional void (rigid inclusion or cavity) within a conducting homogeneous host medium from overdetermined Cauchy data on the accessible exterior boundary. The algorithm for imaging the interior of the medium also makes use of radial spherical parametrization of the unknown star-shaped void and its centre in three dimensions. We also include the contraction and dilation factors in selecting the fictitious surfaces where the MFS sources are to be positioned in the set of unknowns in the resulting regularized nonlinear least-squares minimization. The feasibility of this new method is illustrated in several numerical examples.

The Method of Fundamental Solutions for Solving Exterior Axisymmetric Helmholtz Problems with High Wave-Number

2013 ◽  
Vol 5 (04) ◽  
pp. 477-493 ◽  
Author(s):  
Wen Chen ◽  
Ji Lin ◽  
C.S. Chen
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Matrix Decomposition ◽  
Coefficient Matrix ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Wave Number ◽  
High Wave Number ◽  
Memory Space ◽  
High Wave

AbstractIn this paper, we investigate the method of fundamental solutions (MFS) for solving exterior Helmholtz problems with high wave-number in axisymmetric domains. Since the coefficient matrix in the linear system resulting from the MFS approximation has a block circulant structure, it can be solved by the matrix decomposition algorithm and fast Fourier transform for the fast computation of large-scale problems and meanwhile saving computer memory space. Several numerical examples are provided to demonstrate its applicability and efficacy in two and three dimensional domains.

Fast Solution of Three-Dimensional Modified Helmholtz Equations by the Method of Fundamental Solutions

2016 ◽  
Vol 20 (2) ◽  
pp. 512-533 ◽  
Author(s):  
Ji Lin ◽  
C. S. Chen ◽  
Chein-Shan Liu
Keyword(s):  
Three Dimensional ◽  
Homogeneous Solution ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Singular Problem ◽  
Helmholtz Equations ◽  
Particular Solutions ◽  
Radial Basis ◽  
Particular Solution ◽  
Polyharmonic Spline

AbstractThis paper describes an application of the recently developed sparse scheme of the method of fundamental solutions (MFS) for the simulation of three-dimensional modified Helmholtz problems. The solution to the given problems is approximated by a two-step strategy which consists of evaluating the particular solution and the homogeneous solution. The homogeneous solution is approximated by the traditional MFS. The original dense system of the MFS formulation is condensed into a sparse system based on the exponential decay of the fundamental solutions. Hence, the homogeneous solution can be efficiently obtained. The method of particular solutions with polyharmonic spline radial basis functions and the localized method of approximate particular solutions in combination with the Gaussian radial basis function are employed to approximate the particular solution. Three numerical examples including a near singular problem are presented to show the simplicity and effectiveness of this approach.

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