Two-level additive Schwarz methods using rough polyharmonic splines-based coarse spaces
DOI10.1007/s11401-015-0977-6zbMath1326.65168OpenAlexW1813203346MaRDI QIDQ746375
Publication date: 16 October 2015
Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11401-015-0977-6
convergencenumerical examplefinite element methoddomain decompositionelliptic equationnumerical homogenizationrough coefficientrough polyharmonic splinestwo-level Schwarz additive preconditioner
Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for second-order elliptic equations (35J25) 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) PDEs with low regular coefficients and/or low regular data (35R05) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Preconditioners for iterative methods (65F08)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Flux norm approach to finite-dimensional homogenization approximations with non-separated scales and high contrast
- Multiscale finite element methods for porous media flows and their applications
- Domain decomposition methods for the numerical solution of partial differential equations
- Elementary \(m\)-harmonic cardinal B-splines
- A multiscale finite element method for elliptic problems in composite materials and porous media
- Multiscale domain decomposition methods for elliptic problems with high aspect ratios
- Domain decomposition for multiscale PDEs
- Robust domain decomposition preconditioners for abstract symmetric positive definite bilinear forms
- Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization
- Localized Bases for Finite-Dimensional Homogenization Approximations with Nonseparated Scales and High Contrast
- A Domain Decomposition Preconditioner for Multiscale High-Contrast Problems
- Optimal Local Approximation Spaces for Generalized Finite Element Methods with Application to Multiscale Problems
- Domain Decomposition Preconditioners for Multiscale Flows in High-Contrast Media
- Domain Decomposition Preconditioners for Multiscale Flows in High Contrast Media: Reduced Dimension Coarse Spaces
- Localization of elliptic multiscale problems
- Metric-based upscaling
- Robust domain decomposition algorithms for multiscale PDEs
- Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients
- Can a finite element method perform arbitrarily badly?