The method of fundamental solutions for annular shaped domains

DOI10.1016/j.cam.2008.09.027zbMath1166.65060OpenAlexW2081900403MaRDI QIDQ1019807

J. Martínez

Publication date: 28 May 2009

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.2008.09.027

zbMATH Keywords

Dirichlet problemfundamental solutionsharmonic polynomialserror analysisLaplace equationcollocationTrefftz methodannular shaped domain

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Error bounds for boundary value problems involving PDEs (65N15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (35)

The method of fundamental solutions for the Helmholtz equation ⋮ Neumann problems of 2D Laplace's equation by method of fundamental solutions ⋮ Asymptotic analysis of the conventional and invariant schemes for the method of fundamental solutions applied to potential problems in doubly-connected regions ⋮ Ill-conditioning of the truncated singular value decomposition, Tikhonov regularization and their applications to numerical partial differential equations ⋮ Singularities and regularity of stationary Stokes and Navier-Stokes equations on polygonal domains and their treatments ⋮ Application of the method of fundamental solutions to 2D and 3D Signorini problems ⋮ The interior field method for Laplace's equation in circular domains with circular holes ⋮ A variational-type method of fundamental solutions for a Cauchy problem of Laplace's equation ⋮ Combined Trefftz methods of particular and fundamental solutions for corner and crack singularity of linear elastostatics ⋮ The Laplace equation in three dimensions by the method of fundamental solutions and the method of particular solutions ⋮ Source nodes on elliptic pseudo-boundaries in the method of fundamental solutions for Laplace's equation; selection of pseudo-boundaries ⋮ Spurious eigenvalue-free algorithms of the method of fundamental solutions for solving the Helmholtz equation in bounded multiply connected domains ⋮ Solving inverse Stokes problems by modified collocation Trefftz method ⋮ Optimality of the method of fundamental solutions ⋮ Hybrid and collocation Trefftz methods for traction boundary conditions in linear elastostatics ⋮ A meshless method for nonhomogeneous polyharmonic problems using method of fundamental solution coupled with quasi-interpolation technique ⋮ Comparisons of fundamental solutions and particular solutions for Trefftz methods ⋮ The method of fundamental solutions and its combinations for exterior problems ⋮ The null-field method of Dirichlet problems of Laplace's equation on circular domains with circular holes ⋮ New series expansions for fundamental solutions of linear elastostatics in 2D ⋮ Cauchy problems of Laplace's equation by the methods of fundamental solutions and particular solutions ⋮ Comparisons of method of fundamental solutions, method of particular solutions and the MFS-QR; stability analysis ⋮ Error analysis of the method of fundamental solutions for linear elastostatics ⋮ Analysis of the method of fundamental solutions for the modified Helmholtz equation ⋮ A regularization method for a Cauchy problem of Laplace's equation in an annular domain ⋮ Analysis on the method of fundamental solutions for biharmonic equations ⋮ The Trefftz method using fundamental solutions for biharmonic equations ⋮ Stability analysis of method of fundamental solutions for mixed boundary value problems of Laplace's equation ⋮ The modified method of fundamental solutions for exterior problems of the Helmholtz equation; spurious eigenvalues and their removals ⋮ Singularity problems from source functions as source nodes located near boundaries; numerical methods and removal techniques ⋮ An overlapping domain decomposition Schwarz method applied to the method of fundamental solution ⋮ Scattering of sound from point sources by multiple circular cylinders using addition theorem and superposition technique ⋮ A method of fundamental solutions for heat and wave propagation from lateral Cauchy data ⋮ Stability analysis of the method of fundamental solutions with smooth closed pseudo-boundaries for Laplace's equation: better pseudo-boundaries ⋮ New locations of source nodes for method of fundamental solutions solving Laplace's equation; pseudo radial-lines

Uses Software

• COMODI

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Combinations of method of fundamental solutions for Laplace's equation with singularities
• The method of fundamental solutions for elliptic boundary value problems
• A linear least-squares MFS for certain elliptic problems
• The collocation points of the fundamental solution method for the potential problem
• The method of fundamental solutions: a weighted least-squares approach
• Highly accurate solutions of Motz's and the cracked beam problems
• Trefftz, collocation, and other boundary methods—A comparison
• Fundamental Solutions Method for Elliptic Boundary Value Problems
• Boundary Methods for Solving Elliptic Problems with Singularities and Interfaces
• A BOUNDARY APPROXIMATION METHOD FOR FOURTH ORDER PROBLEMS
• The Approximate Solution of Elliptic Boundary-Value Problems by Fundamental Solutions
• Numerical analysis of the method of fundamental solution for harmonic problems in annular domains

This page was built for publication: The method of fundamental solutions for annular shaped domains