@Article{CiCP-17-3,
author = {},
title = {Fast Solution for Solving the Modified Helmholtz Equation with the Method of Fundamental Solutions},
journal = {Communications in Computational Physics},
year = {2015},
volume = {17},
number = {3},
pages = {867--886},
abstract = {<p style="text-align: justify;">The method of fundamental solutions (MFS) is known as an effective boundary
meshless method. However, the formulation of the MFS results in a dense and
extremely ill-conditioned matrix. In this paper we investigate the MFS for solving
large-scale problems for the nonhomogeneous modified Helmholtz equation. The key
idea is to exploit the exponential decay of the fundamental solution of the modified
Helmholtz equation, and consider a sparse or diagonal matrix instead of the original
dense matrix. Hence, the homogeneous solution can be obtained efficiently and accurately.
A standard two-step solution process which consists of evaluating the particular
solution and the homogeneous solution is applied. Polyharmonic spline radial basis
functions are employed to evaluate the particular solution. Five numerical examples in
irregular domains and a large number of boundary collocation points are presented to
show the simplicity and effectiveness of our approach for solving large-scale problems.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.181113.241014a},
url = {https://global-sci.com/article/80402/fast-solution-for-solving-the-modified-helmholtz-equation-with-the-method-of-fundamental-solutions}
}