@Article{cmc.2020.08864,
AUTHOR = {Kue-Hong Chen, Cheng-Tsung Chen},
TITLE = {A Novel Technique for Estimating the Numerical Error in Solving the Helmholtz Equation},
JOURNAL = {Computers, Materials \& Continua},
VOLUME = {64},
YEAR = {2020},
NUMBER = {1},
PAGES = {145--160},
URL = {http://www.techscience.com/cmc/v64n1/39134},
ISSN = {1546-2226},
ABSTRACT = {In this study, we applied a defined auxiliary problem in a novel error 
estimation technique to estimate the numerical error in the method of fundamental 
solutions (MFS) for solving the Helmholtz equation. The defined auxiliary problem is 
substituted for the real problem, and its analytical solution is generated using the 
complementary solution set of the governing equation. By solving the auxiliary problem 
and comparing the solution with the quasianalytical solution, an error curve of the MFS 
versus the source location parameters can be obtained. Thus, the optimal location 
parameter can be identified. The convergent numerical solution can be obtained and 
applied to the case of an unavailable analytical solution condition in the real problem. 
Consequently, we developed a systematic error estimation scheme to identify an optimal 
parameter. Through numerical experiments, the optimal location parameter of the source 
points and the optimal number of source points in the MFS were studied and obtained 
using the error estimation technique.},
DOI = {10.32604/cmc.2020.08864}
}