Study on effective condition number for collocation methods

DOI10.1016/j.enganabound.2008.02.001zbMath1244.65186OpenAlexW2067633756MaRDI QIDQ443338

Hung-Tsai Huang, 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.2008.02.001

zbMATH Keywords

condition numbercollocation Trefftz methodeffective condition numbersingularity problemmethod of fundamental solution

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80)

Related Items

Ill-conditioning of the truncated singular value decomposition, Tikhonov regularization and their applications to numerical partial differential equations ⋮ The MFS for the solution of harmonic boundary value problems with non-harmonic boundary conditions ⋮ Numerical solution of three-dimensional Laplacian problems using the multiple scale Trefftz method ⋮ A multiple scale Trefftz method for the Laplace equation subjected to large noisy boundary data ⋮ Models of corner and crack singularity of linear elastostatics and their numerical solutions ⋮ Optimality of the method of fundamental solutions ⋮ Stability analysis via condition number and effective condition number for the first kind boundary integral equations by advanced quadrature methods, a comparison ⋮ A Trefftz based method for solving Helmholtz problems in semi-infinite domains ⋮ Comparisons of fundamental solutions and particular solutions for Trefftz methods ⋮ Multiquadric and its shape parameter -- a numerical investigation of error estimate, condition number, and round-off error by arbitrary precision computation ⋮ Stability estimate on meshless unsymmetric collocation method for solving boundary value problems ⋮ Exponential convergence for numerical solution of integral equations using radial basis functions ⋮ On the determination of locating the source points of the MFS using effective condition number

Cites Work

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• Stability analysis for the penalty plus hybrid and the direct Trefftz methods for singularity problems
• Effective condition number for finite difference method
• Trefftz, collocation, and other boundary methods—A comparison
• Fundamental Solutions Method for Elliptic Boundary Value Problems
• Modified methods of fundamental solutions for harmonic and biharmonic problems with boundary singularities
• The Approximate Solution of Elliptic Boundary-Value Problems by Fundamental Solutions
• The Lack of Influence of the Right-Hand Side on the Accuracy of Linear System Solution
• Exponential convergence andH-c multiquadric collocation method for partial differential equations
• Error norm estimation and stopping criteria in preconditioned conjugate gradient iterations
• A Theory of Condition

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