Improving the Ill-conditioning of the Method of Fundamental Solutions for 2D Laplace Equation
By Chein-Shan Liu. 2008
59 citations recorded by the source corpus.
Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials
View Paper: https://www.semanticscholar.org/paper/01da8716cea1d38aa20802aa58b52174a5fefec1
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In Computational Mechanics
In Electrical and Electronic Engineering
In Mechanics of Materials
Citations in the corpus
- 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”
- Novel Algorithms Based on the Conjugate Gradient Method for Inverting Ill-Conditioned Matrices, and a New Regularization Method to Solve Ill-Posed Linear Systems (2010, methodology): “…MLPG method [ Atluri, Kim and Cho (1999); Atluri and Shen (2002); Tang, Shen and Atluri (2003); Atluri (2004); Atluri and Zhu (1998)], or the method of fundamental solutions [ Fairweather and Karageorghis (1998); Young, Tsai, Lin and Chen (2006); Tsai, Lin, Young and Atluri (2006); Liu (2008) ].”
- Numerical solution of the Laplacian Cauchy problem by using a better postconditioning collocation Trefftz method (2013, methodology): “Then, Liu [47] found that the excellent property of the modified Trefftz method can be used to modify the MFS by relating the coefficients obtained from these two methods by a linear transformation, which is later known as one of the Laplacian preconditioners and postconditioners [48].”
- Potential Problems by Singular Boundary Method Satisfying Moment Condition (2009, background): “…fundamental solutions (MFS) [Chen, Golberg and Hon (1998); Cheng, Young and Tsai (2000); Fairweather and Karageorghis (1998); Karageorghis (1992); Liu (2008); Marin (2008,2010a,2010b); Poullikkas, Karageorghis and Georgiou (1998); Reutskiy (2005); Smyrlis and Karageorghis (2001)], boundary knot…”