Fast Solution of Three-Dimensional Modified Helmholtz Equations by the Method of Fundamental Solutions. (21st July 2016)

• Record Type: Journal Article
• Authors: Lin, Ji; Chen, C. S.; Liu, Chein-Shan
• Is Part Of: Communications in computational physics. Volume 20:Number 2(2016:Aug.)
• Page Start: 512
• Page End: 533
• Publication Date: 2016-07-21
• Subjects: 65N10, -- 65N30; Method of fundamental solutions, -- exponential decay, -- modified Helmholtz problem, -- sparse scheme, -- localized method of approximate particular solutions, -- method of particular solutions; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.060915.301215a
• Languages: English
• ISSNs: 1815-2406

Abstract

Abstract: 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.