Method of fundamental solutions: singular value decomposition analysis

By Palghat A. Ramachandran. 2002

162 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/77e435673f2f55729bfa1cbd8fe0d314e244d88a

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In Atomic and Molecular Physics, and Optics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Exponential basis functions in solution of static and time harmonic elastic problems in a meshless style (2010, methodology): “In the context of using boundary collocation methods like MFS, the readers may find such studies in References [36, 37].”
Some comments on the ill-conditioning of the method of fundamental solutions (2006, methodology): “In this paper, we reevaluate some of the results in [5] and find that his conclusions regarding the instability of Gaussian elimination is not entirely warranted.”
A new boundary meshfree method with distributed sources (2010, unknown): “[5–10] for potential and elastostatic problems.”
A meshless method for some inverse problems associated with the Helmholtz equation (2006, unknown): “Ramachandran [28] showed that the singular value decomposition can mitigate the critical dependence, which is also the case for forward problems with noisy data [29].”
The method of fundamental solutions for the Cauchy problem associated with two-dimensional Helmholtz-type equations (2005, unknown): “The MFS, in conjunction with singular value decomposition, has been employed by Ramachandran [16] in order to obtain numerical solutions of the Laplace and the Helmholtz equations.”
Improving the Ill-conditioning of the Method of Fundamental Solutions for 2D Laplace Equation (2008, methodology): “…2.70×10−11 2.71×10−11 8 2.26×10−9 1.85×10−8 1.85×10−8 10 4.45×10−10 2.09×10−7 2.09×10−7 20 1.02×10−7 2.24×10−7 2.47×10−7 In order to compare the present results with that calculated by Ramachandran (2002), we define theL2 error by Error(uL2) = N ∑ i=1 |u(i)−un(i)|2, (66) whereu andun denotes the…”