The Conditioning of Boundary Element Equations on Locally Refined Meshes and Preconditioning by Diagonal Scaling
From MaRDI portal
Publication:4271019
DOI10.1137/S0036142997330809zbMath0947.65125MaRDI QIDQ4271019
No author found.
Publication date: 22 November 1999
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
preconditioningcondition numberGalerkin boundary element methodlocally refined meshesweakly singular and hypersingular integral equations
Numerical methods for integral equations (65R20) Boundary value problems for second-order elliptic equations (35J25) Numerical computation of matrix norms, conditioning, scaling (65F35) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Boundary element methods for boundary value problems involving PDEs (65N38)
Related Items
The BEM with graded meshes for the electric field integral equation on polyhedral surfaces, Optimal additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations, Numerical methods for nonlocal and fractional models, Adaptive boundary element methods with convergence rates, Adaptive boundary element methods. A posteriori error estimators, adaptivity, convergence, and implementation, Finite element algorithms for nonlocal minimal graphs, Optimal additive Schwarz preconditioning for adaptive 2D IGA boundary element methods, Robust BPX preconditioner for fractional Laplacians on bounded Lipschitz domains, A wirebasket preconditioner for the mortar boundary element method, Fractional elliptic problems on Lipschitz domains: regularity and approximation, Discontinuous Galerkin \(hp\)-BEM with quasi-uniform meshes, Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains, Thehp-version of the boundary element method with quasi-uniform meshes in three dimensions, Conditioning of implicit Runge-Kutta integration for finite element approximation of linear diffusion equations on anisotropic meshes, On the Approximation of Electromagnetic Fields by Edge Finite Elements. Part 3: Sensitivity to Coefficients, Adaptive BEM with inexact PCG solver yields almost optimal computational costs, Bi-parametric operator preconditioning, Discontinuous Petrov-Galerkin boundary elements, Remarks on Sobolev norms of fractional orders, Is the Multigrid Method Fault Tolerant? The Two-Grid Case, Discrete extension operators for mixed finite element spaces on locally refined meshes, Additive Schwarz preconditioners for theh-pversion boundary-element approximation to the hypersingular operator in three dimensions, Overlapping additive Schwarz preconditioners for boundary element methods, Adaptive \(hp\)-FEM for the contact problem with Tresca friction in linear elasticity: The primal-dual formulation and a posteriori error estimation, Preconditioners for pseudodifferential equations on the sphere with radial basis functions, The \(p\)-version of the boundary element method for a three-dimensional crack problem, A note on the polynomial approximation of vertex singularities in the boundary element method in three dimensions, Optimal operator preconditioning for pseudodifferential boundary problems, An extension theorem for polynomials on triangles, Evaluation of the condition number in linear systems arising in finite element approximations, Conditioning of the finite volume element method for diffusion problems with general simplicial meshes, Aspects of an adaptive finite element method for the fractional Laplacian: a priori and a posteriori error estimates, efficient implementation and multigrid solver, Optimal quasi-diagonal preconditioners for pseudodifferential operators of order minus two, On the Convergence in $H^1$-Norm for the Fractional Laplacian, Sharp Bounds on the Smallest Eigenvalue of Finite Element Equations with Arbitrary Meshes without Regularity Assumptions, Linear and nonlinear fractional elliptic problems, On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion, MINRES for Second-Order PDEs with Singular Data, Multilevel decompositions and norms for negative order Sobolev spaces, Diagonal scaling of stiffness matrices in the Galerkin boundary element method, Optimal preconditioning for the symmetric and nonsymmetric coupling of adaptive finite elements and boundary elements
