On the determination of locating the source points of the MFS using effective condition number

DOI10.1016/j.cam.2022.114955zbMath1505.65307OpenAlexW4309928085MaRDI QIDQ2112689

Yanyan Li

Publication date: 11 January 2023

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2022.114955

zbMATH Keywords

uncertainty principlemethod of fundamental solutionseffective condition numberleave-one-out cross validation

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Error bounds for boundary value problems involving PDEs (65N15) Numerical computation of matrix norms, conditioning, scaling (65F35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20) Fictitious domain methods for boundary value problems involving PDEs (65N85)

Related Items (1)

The enhanced boundary knot method with fictitious sources for solving Helmholtz-type equations

Cites Work

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• The adaptive algorithm for the selection of sources of the method of fundamental solutions
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• Optimality of the method of fundamental solutions
• Effective condition number for the selection of the RBF shape parameter with the fictitious point method
• An adaptive method of fundamental solutions for solving the Laplace equation
• An overview of the method of fundamental solutions -- solvability, uniqueness, convergence, and stability
• A meshfree local RBF collocation method for anti-plane transverse elastic wave propagation analysis in 2D phononic crystals
• Effectively Well-Conditioned Linear Systems
• The Lack of Influence of the Right-Hand Side on the Accuracy of Linear System Solution
• Effective condition number and its applications

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