Stability analysis of method of fundamental solutions for mixed boundary value problems of Laplace's equation

DOI10.1007/s00607-010-0081-4zbMath1223.65085OpenAlexW1992253001MaRDI QIDQ975313

Jin Huang, Hung-Tsai Huang, Zi Cai Li

Publication date: 9 June 2010

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00607-010-0081-4

zbMATH Keywords

stabilityDirichlet problemnumerical resultscondition numbermethod of fundamental solutionsLaplace's equationMotz's problemmixed boundary problem

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Numerical computation of matrix norms, conditioning, scaling (65F35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80)

Related Items (24)

The method of fundamental solutions for the Helmholtz equation ⋮ Neumann problems of 2D Laplace's equation by method of fundamental solutions ⋮ Ill-conditioning of the truncated singular value decomposition, Tikhonov regularization and their applications to numerical partial differential equations ⋮ 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 ⋮ 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 ⋮ Multiquadric and its shape parameter -- a numerical investigation of error estimate, condition number, and round-off error by arbitrary precision computation ⋮ 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 ⋮ Numerical computation for backward time-fractional diffusion equation ⋮ 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 ⋮ Fundamental kernel-based method for backward space-time fractional diffusion problem ⋮ Analysis on the method of fundamental solutions for biharmonic equations ⋮ The Trefftz method using fundamental solutions for biharmonic equations ⋮ Singularity problems from source functions as source nodes located near boundaries; numerical methods and removal techniques ⋮ Null field and interior field methods for Laplace's equation in actually punctured disks ⋮ 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

Cites Work

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• The method of fundamental solutions for annular shaped domains
• Asymptotic stability of the fundamental solution method
• Charge simulation method using exterior mapping functions
• Some aspects of the method of fundamental solutions for certain harmonic problems
• On convergence of the method of fundamental solutions for solving the Dirichlet problem of Poisson's equation
• Effective condition number for finite difference method
• Highly accurate solutions of Motz's and the cracked beam problems
• Fundamental Solutions Method for Elliptic Boundary Value Problems
• Boundary Methods for Solving Elliptic Problems with Singularities and Interfaces
• Condition number of matrices derived from two classes of integral equations
• Numerical analysis of the MFS for certain harmonic problems

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