An overview of the method of fundamental solutions -- solvability, uniqueness, convergence, and stability

DOI10.1016/j.enganabound.2020.08.013zbMath1464.65264OpenAlexW3088798054MaRDI QIDQ2209388

Yongxing Hong, Alexander H.-D. Cheng

Publication date: 31 October 2020

Published in: Engineering Analysis with Boundary Elements (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.enganabound.2020.08.013

zbMATH Keywords

inverse problemboundary element methoderror estimatecollocationmethod of fundamental solutionsmeshless methodeffective condition numbernonsingular MFSspurious frequency

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80)

Related Items (43)

On the supporting nodes in the localized method of fundamental solutions for 2D potential problems with Dirichlet boundary condition ⋮ Localized Method of Fundamental Solutions for Acoustic Analysis Inside a Car Cavity with Sound-Absorbing Material ⋮ A method of fundamental solutions with time-discretisation for wave motion from lateral Cauchy data ⋮ Numerical methods with particular solutions for nonhomogeneous Stokes and Brinkman systems ⋮ Singular boundary method for 2D and 3D acoustic design sensitivity analysis ⋮ A meshless collocation method for solving the inverse Cauchy problem associated with the variable-order fractional heat conduction model under functionally graded materials ⋮ A Comparative Study on Polynomial Expansion Method and Polynomial Method of Particular Solutions ⋮ Bending analysis of simply supported and clamped thin elastic plates by using a modified version of the LMFS ⋮ Localized method of fundamental solutions for two-dimensional anisotropic elasticity problems ⋮ Singular matrices arising in the MFS from certain boundary and pseudo-boundary symmetries ⋮ A new global and direct integral formulation for 2D potential problems ⋮ Helmholtz equation for a Neumann condition on a curved boundary: spurious resonances ⋮ The method of fundamental solutions for pointwise source reconstruction ⋮ The localized method of fundamental solutions for 2D and 3D inhomogeneous problems ⋮ Transient Green's functions of dislocations in transversely isotropic and layered poroelastic half-spaces ⋮ Method of fundamental solution using Erdogan's solution: static and dynamic ⋮ Efficient fundamental solution based finite element for 2-D dynamics ⋮ The method of fundamental solutions for the scattering problem of an open cavity ⋮ Fading regularization MFS algorithm for the Cauchy problem associated with the two-dimensional Stokes equations ⋮ Indirect boundary element formulation with dual reciprocity in elastodynamics ⋮ A singular boundary method for transient coupled dynamic thermoelastic analysis ⋮ Solving subsurface flow toward wells in layered soils using hybrid method of fundamental solutions ⋮ Analysis of Navier-Stokes equations by a BC/GE embedded local meshless method ⋮ The enhanced boundary knot method with fictitious sources for solving Helmholtz-type equations ⋮ General time-dependent Green's functions of line forces in a two-dimensional, anisotropic, elastic, and infinite solid ⋮ An efficient boundary-type meshfree method for analysis of two-dimensional laser heating problems ⋮ Efficient numerical solution of boundary identification problems: MFS with adaptive stochastic optimization ⋮ The elastoplastic analysis of functionally graded materials using a meshfree RRKPM ⋮ Localized singular boundary method for solving Laplace and Helmholtz equations in arbitrary 2D domains ⋮ The elastic dynamics analysis of FGM using a meshless RRKPM ⋮ Improved geometric modeling using the method of fundamental solutions ⋮ The method of fundamental solutions for two-dimensional elasticity problems based on the Airy stress function ⋮ A coupled fictitious stress method and eshelby inclusions as a meshless technique for inhomogeneity problems ⋮ A simple formula for obtaining OIFs on Neumann boundary in 2D potential problems and its applications ⋮ BEM analysis of multilayer thin structures using a composite transformation method for boundary integrals ⋮ A method of fundamental solutions for heat and wave propagation from lateral Cauchy data ⋮ A well-conditioned method of fundamental solutions for Laplace equation ⋮ Three-dimensional application of the meshless generalized finite difference method for solving the extended Fisher-Kolmogorov equation ⋮ A SFBEM-FEM coupling method for solving crack problems based on Erdogan fundamental solutions ⋮ On the determination of locating the source points of the MFS using effective condition number ⋮ New locations of source nodes for method of fundamental solutions solving Laplace's equation; pseudo radial-lines ⋮ Integration over discrete closed surfaces using the method of fundamental solutions ⋮ A new approach to solve the anti-plane crack problems by the method of fundamental solutions

Uses Software

• DLMF
• rbf_qr

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