TY - JOUR
T1 - Fast Solution of Three-Dimensional Modified Helmholtz Equations by the Method of Fundamental Solutions
JO - Communications in Computational Physics
VL - 2
SP - 512
EP - 533
PY - 2018
DA - 2018/04
SN - 20
DO - http://doi.org/10.4208/cicp.060915.301215a
UR - https://global-sci.org/intro/article_detail/cicp/11162.html
KW - 
AB - <p style="text-align: justify;">This 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.</p>