A Preconditioner Based on Domain Decomposition forh-pFinite-Element Approximation on Quasi-Uniform Meshes
From MaRDI portal
Publication:4891714
DOI10.1137/S0036142993258221zbMath0855.65044MaRDI QIDQ4891714
Publication date: 3 February 1997
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35)
Related Items (42)
A new parallel domain decomposition method for the adaptive finite element solution of elliptic partial differential equations ⋮ Fast domain decomposition algorithm discretizations of 3-d elliptic equations by spectral elements ⋮ Sobolev space preconditioning for Newton's method using domain decomposition ⋮ Non-overlapping domain decomposition methods for adaptive \(hp\) approximations of the Stokes problem with discontinuous pressure fields ⋮ An iterative and parallel solver based on domain decomposition for the \(h-p\) version of the finite element method ⋮ Rapid error reduction for block Gauss-Seidel based onp-hierarchical basis ⋮ A Systematic Approach to Constructing Preconditioners for the $hp$-Version Mass Matrix on Unstructured and Hybrid Finite Element Meshes ⋮ Multilevel preconditioned QMR methods for unstructured mesh computation ⋮ Improved p‐version finite element matrix conditioning using semi‐orthogonal modal approximation functions ⋮ Spectral discretizations of 3-D elliptic problems and fast domain decomposition methods ⋮ A p‐version finite element approach for two‐ and three‐dimensional problems of the J2 flow theory with non‐linear isotropic hardening ⋮ A class of domain decomposition preconditioners for \(hp\)-discontinuous Galerkin finite element methods ⋮ A numerical study on Neumann-Neumann and FETI methods for \(hp\) approximations on geometrically refined boundary layer meshes in two dimensions. ⋮ A Multilevel Algebraic Error Estimator and the Corresponding Iterative Solver with $p$-Robust Behavior ⋮ Spectral element FETI-DP and BDDC preconditioners with multi-element subdomains ⋮ Preconditioning the Mass Matrix for High Order Finite Element Approximation on Triangles ⋮ Domain decomposition method for the \(h\)-\(p\) version finite element method ⋮ $H^2$-Stable Polynomial Liftings on Triangles ⋮ Substructuring preconditioners for an \(h\)-\(p\) domain decomposition method with interior penalty mortaring ⋮ Domain Decomposition Preconditioning for High Order Hybrid Discontinuous Galerkin Methods on Tetrahedral Meshes ⋮ The \(p\)-version of the finite element method compared to an adaptive \(h\)-version for the deformation theory of plasticity. ⋮ Domain decomposition techniques for reaction-diffusion equations in two-dimensional regions with re-entrant corners ⋮ Error estimates and adaptive finite element methods ⋮ The efficiency of the p‐version finite element method in a distributed computing environment ⋮ The p‐version of the finite element method for three‐dimensional curved thin walled structures ⋮ Impact of element-level static condensation on iterative solver performance ⋮ Optimal extensions on tensor-product meshes ⋮ A domain decomposition preconditioner for \(p\)-FEM discretizations of two-dimensional elliptic problems ⋮ Fully discrete \(hp\)-finite elements: Fast quadrature ⋮ New shape functions for triangular \(p\)-FEM using integrated Jacobi polynomials ⋮ Preconditioning high order \(H^2\) conforming finite elements on triangles ⋮ Wavelet solvers for \(hp\)-FEM discretizations in 3D using hexahedral elements ⋮ Condition number bounds for IETI-DP methods that are explicit in h and p ⋮ Aspects of an adaptive \(hp\)-finite element method: Adaptive strategy, conforming approximation and efficient solvers ⋮ Inexact solvers on element interfaces for the \(p\) and \(h\)-\(p\) finite element method ⋮ Preconditioning of the \(p\)-version of the finite element method ⋮ A numerical study on Neumann-Neumann methods forhpapproximations on geometrically refined boundary layer meshes II. Three-dimensional problems ⋮ BDDC and FETI-DP preconditioners for spectral element discretizations ⋮ Domain decomposition preconditioning in the hierarchical \(p\)-version of the finite element method ⋮ Domain decomposition preconditioners for \(p\) and \(hp\) finite element approximation of Stokes equations ⋮ BPS preconditioners for a weak Galerkin finite element method for 2D diffusion problems with strongly discontinuous coefficients ⋮ Convergence theory for IETI-DP solvers for discontinuous Galerkin isogeometric analysis that is explicit in \(h\) and \(p\)
This page was built for publication: A Preconditioner Based on Domain Decomposition forh-pFinite-Element Approximation on Quasi-Uniform Meshes
