Название: An Introduction to the Method of Fundamental Solutions
Автор: Alexander H.-D. Cheng, C.S. Chen, Andreas Karageorghis
Издательство: World Scientific Publishing
Год: 2025
Страниц: 617
Язык: английский
Формат: pdf (true)
Размер: 38.2 MB

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: Fundamentals is aimed at providing the theoretical support of the MFS for newcomers to the method. The presentation however is intended to be practical rather than theoretical. Part II: Advanced Topics gives a sample of applications together with MATLAB codes, aimed at assisting users to build their own advanced codes.

This book is highly recommended for use by post-graduate researchers and graduate students in scientific computing and engineering.






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