Comparisons of fundamental solutions and particular solutions for Trefftz methods

DOI10.1016/j.enganabound.2009.10.001zbMath1244.65187OpenAlexW2067157018MaRDI QIDQ441566

Lih-Jier Young, Alexander H.-D. Cheng, Hung-Tsai Huang, Ya-Ping Liu, Zi Cai Li

Publication date: 7 August 2012

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

Full work available at URL: https://doi.org/10.1016/j.enganabound.2009.10.001

zbMATH Keywords

stability analysiserror analysismethod of fundamental solutionsparticular solutionscollocation Trefftz methodmethod of particular solutionsalgorithm comparisons

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) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (13)

Neumann problems of 2D Laplace's equation by method of fundamental solutions ⋮ Meshless analysis of soil-structure interaction using an MFS-MLPG coupled approach ⋮ Superconvergence of kernel-based interpolation ⋮ Optimality of the method of fundamental solutions ⋮ A Trefftz based method for solving Helmholtz problems in semi-infinite domains ⋮ Cauchy problems of Laplace's equation by the methods of fundamental solutions and particular solutions ⋮ Estimating the optimum number of boundary elements by error estimation in a defined auxiliary problem ⋮ Comparisons of method of fundamental solutions, method of particular solutions and the MFS-QR; stability analysis ⋮ The Trefftz method using fundamental solutions for biharmonic equations ⋮ An approximation theorist's view on solving operator equations -- with special attention to Trefftz, MFS, MPS, and DRM methods ⋮ Many names of the Trefftz method ⋮ Comparison of three meshless methods for 2D harmonic and biharmonic problems ⋮ Radial kernels via scale derivatives

Cites Work

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• Combinations of method of fundamental solutions for Laplace's equation with singularities
• Equivalence between the Trefftz method and the method of fundamental solution for the annular Green's function using the addition theorem and image concept
• The method of fundamental solutions for annular shaped domains
• The method of fundamental solutions for elliptic boundary value problems
• The method of fundamental solutions for the numerical solution of the biharmonic equation
• Effective condition number for finite difference method
• On the equivalence of the Trefftz method and method of fundamental solutions for Laplace and biharmonic equations
• A Modified Trefftz Method for Two-Dimensional Laplace Equation Considering the Domain's Characteristic Length
• Trefftz, collocation, and other boundary methods—A comparison
• Effective condition number for numerical partial differential equations
• Fundamental Solutions Method for Elliptic Boundary Value Problems
• The Almansi method of fundamental solutions for solving biharmonic problems
• The simple layer potential method of fundamental solutions for certain biharmonic problems
• Reviving the Method of Particular Solutions

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