Introduction To The Method Of Fundamental Solutions
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A01=Alexander H-d Cheng
A01=Andreas Karageorghis
A01=Ching-shyang Chen
Author_Alexander H-d Cheng
Author_Andreas Karageorghis
Author_Ching-shyang Chen
BEM
Biharmonic Equation
Boundary Element Method
Boundary Integral Equation
Boundary Value Problem
Category=PBKJ
Category=PBKS
Cauchy Problem
Collocation Method
Condition Number
Effective Condition Number
Elasticity Problem
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Fundamental Solution
Geometric Modelling
Green's Function
Helmholtz Equation
Inverse Geometric Problem
Inverse Problem
Laplace Equation
Localized Method of Fundamental Solutions
Matrix Decomposition
Meshless Method
Method of Fundamental Solutions
Method of Particular Solution
MFS
Numerical Method
Partial Differential Equation
Particular Solution
Polyharmonic Equation
Potential Problem
Radial Basis Function
Strong Form
Trefftz Method
Weak Form
Product details
- ISBN 9789811298479
- Publication Date: 11 Apr 2025
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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Over the past two decades, the method of fundamental solutions (MFS) has attracted great attention and has been used extensively for the solution of scientific and engineering problems. The MFS is a boundary meshless collocation method which has evolved from the boundary element method. In it, the approximate solution is expressed as a linear combination of fundamental solutions of the operator in the governing partial differential equation.One of the main attractions of the MFS is the simplicity with which it can be applied to the solution of boundary value problems in complex geometries in two and three dimensions. The method is also known by many different names in the literature such as the charge simulation method, the de-singularization method, the virtual boundary element method, etc.Despite its effectiveness, the original version of the MFS is confined to solving boundary value problems governed by homogeneous partial differential equations. To address this limitation, we introduce various types of particular solutions to extend the method to solving general inhomogeneous boundary value problems employing the method of particular solutions.This book consists of two parts. Part I aims to provide theoretical support for beginners. In the spirit of reproducible research and to facilitate the understanding of the method and its implementation, several MATLAB codes have been included in Part II.This book is highly recommended for use by post-graduate researchers and graduate students in scientific computing and engineering.
