Stability analysis via condition number and effective condition number for the first kind boundary integral equations by advanced quadrature methods, a comparison

DOI10.1016/j.enganabound.2010.11.006zbMath1259.65161OpenAlexW2061555402MaRDI QIDQ1944520

Jin Huang, Hung-Tsai Huang, Yi-Min Wei, Zi Cai Li

Publication date: 25 March 2013

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

Full work available at URL: https://doi.org/10.1016/j.enganabound.2010.11.006

zbMATH Keywords

stability analysiscondition numbereffective condition numbernumerical partial differential equationsfirst kind boundary integral equationadvanced (mechanical) quadrature method

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Boundary element methods for boundary value problems involving PDEs (65N38)

Cites Work

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• Advanced quadrature methods and splitting extrapolation algorithms for first kind boundary integral equations of Laplace's equation with discontinuity solutions
• Effective condition number for simplified hybrid Trefftz methods
• Study on effective condition number for collocation methods
• Stability analysis of Trefftz methods for the stick-slip problem
• Mechanical quadrature methods and their splitting extrapolations for boundary integral equations of first kind on open arcs
• Effective condition number of the Hermite finite element methods for biharmonic equations
• Splitting extrapolations for solving boundary integral equations of mixed boundary conditions on polygons by mechanical quadrature methods
• Effective condition number for the finite element method using local mesh refinements
• Quadrature methods for periodic singular and weakly singular Fredholm integral equations
• A modified discrete spectral collocation method for first kind integral equations with logarithmic kernel
• The effective condition number applied to error analysis of certain boundary collocation methods
• A new concept of modal participation factor for numerical instability in the dual BEM for exterior acoustics.
• On the pseudo-differential operators in the dual boundary integral equations using degenerate kernels and circulants
• On integral equations of the first kind with logarithmic kernels
• An alternative method for degenerate scale problems in boundary element methods for the two-dimensional Laplace equation
• The conditioning of some numerical methods for first kind boundary integral equations
• Effective condition number and superconvergence of the Trefftz method coupled with high-order FEM for singularity problems
• Stability analysis for the penalty plus hybrid and the direct Trefftz methods for singularity problems
• Stability analysis and superconvergence for the penalty Trefftz method coupled with FEM for singularity problems
• A study of free terms for plate problems in the dual boundary integral equations
• Effective condition number for finite difference method
• Effective condition number of Trefftz methods for biharmonic equations with crack singularities
• Superconvergence and stability for boundary penalty techniques of finite difference methods
• Effective condition number for numerical partial differential equations
• The Galerkin Method for Integral Equations of the First Kind with Logarithmic Kernel: Theory
• The Galerkin Method for Integral Equations of the First Kind with Logarithmic Kernel: Applications
• Effectively Well-Conditioned Linear Systems
• The Collocation Method for First-Kind Boundary Integral Equations on Polygonal Regions
• The Lack of Influence of the Right-Hand Side on the Accuracy of Linear System Solution
• The Numerical Solution of Integral Equations of the Second Kind
• Structured Perturbations Part I: Normwise Distances
• Analytical study and numerical experiments for true and spurious eigensolutions of a circular cavity using the real-part dual BEM
• Error norm estimation and stopping criteria in preconditioned conjugate gradient iterations
• Numerical solution of an integral equation with a logarithmic kernel
• On the sublinear and superlinear rate of convergence of conjugate gradient methods
• Effective condition number and its applications

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