Some comments on the ill-conditioning of the method of fundamental solutions

By Chingshyang Chen, Hokwon Cho, Michael A. Golberg. 2006

169 citations recorded by the source corpus.

Subfields: Electrical and Electronic Engineering, Mathematical Physics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/72486170fc599dc7b2cbabbfc5087b3b03f51e77

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Electrical and Electronic Engineering

1. Wen Chen
2. Zhuojia Fu
3. Yan Gu
4. Chein-Shan Liu
5. Fei Wang
6. Leevan Ling
7. Satya N. Atluri

In Mathematical Physics

1. Zhuojia Fu
2. Wen Chen
3. Ashley L. Meyer
4. T. Drombosky
5. Yan Gu
6. Chein-Shan Liu
7. Fei Wang
8. Leevan Ling

In Mechanics of Materials

1. Wen Chen
2. Zhuojia Fu
3. Yan Gu
4. Fei Wang
5. Ashley L. Meyer
6. T. Drombosky
7. Chein-Shan Liu
8. Leevan Ling

Citations in the corpus

• Infinite domain potential problems by a new formulation of singular boundary method (2013, background): “The determination of the distance between the physical and the fictitious boundaries is largely based on experiences and presents the most serious drawback in the MFS applications to the real-world problems [18–20].”
• Applicability of the method of fundamental solutions (2009, background): “Although the problem of ill-conditioning of the MFS is widely reported in the literature, the accuracy of the numerical solution is rarely affected [21] when u is harmonic on the entire plane.”
• A highly accurate collocation Trefftz method for solving the Laplace equation in the doubly connected domains (2008, background): “Although the MFS can avoid the difficulties associated with the BEM, it still has the problem that the resulting linear equations system may become highly ill-conditioned when the number of source points is increased [15] or when the distances of source points are increased [16].”
• A method of fundamental solutions without fictitious boundary (2010, methodology): “For instance, the method of fundamental solutions (MFS) [1,2], boundary knot method [3], boundary collocation method [4], regularized meshless method (RMM) [5,6], and modified method of fundamental solutions [7], etc.”
• BOUNDARY PARTICLE METHOD FOR INVERSE CAUCHY PROBLEMS OF INHOMOGENEOUS HELMHOLTZ EQUATIONS (2009, methodology): “To overcome mesh generation problem, facing the traditional mesh-based BEM, a variety of boundary-type meshless methods, in recent years, have been developed and attract a lot of attention, for example, method of fundamental solution (MFS) [4, 11, 22], boundary knot method (BKM) [10], plane wave met”