An iterative solver for \(p\)-version finite elements in three dimensions

DOI10.1016/S0045-7825(94)80021-9zbMath0823.65122OpenAlexW2008994851MaRDI QIDQ1892458

Jan Mandel

Publication date: 24 October 1995

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0045-7825(94)80021-9

zbMATH Keywords

linear elasticitydomain decompositioniterative methodsadditive Schwarz preconditionerspectral condition number\(p\)-version finite elementaeroplane computations

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for second-order elliptic equations (35J25) Classical linear elasticity (74B05) Finite element methods applied to problems in solid mechanics (74S05) 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

Block SSOR preconditionings for high-order 3D FE systems. III: Incomplete BSSOR preconditionings based onp-partitionings ⋮ Iterative methods for \(p\)-version finite elements: Preconditioning thin solids ⋮ Preconditioned conjugate residual methods for mixed spectral discretizations of elasticity and Stokes problems ⋮ Adaptive BDDC in three dimensions ⋮ Error estimates and adaptive finite element methods

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A domain decomposition algorithm for elliptic problems in three dimensions
• Spectral element multigrid. I: Formulation and numerical results
• Iterative solvers by substructuring for the \(p\)-version finite element method
• Block SSOR preconditionings for high-order 3D FE systems. II: Incomplete BSSOR preconditionings
• Domain decomposition preconditioning for \(p\)-version finite elements with high aspect ratios
• Multilevel solution method for the \(p\)-version of finite elements
• On the spectra of sums of orthogonal projections with applications to parallel computing
• Two-level domain decomposition preconditioning for thep-version finite element method in three dimensions
• Some Estimates for a Weighted L 2 Projection
• A Taxonomy for Conjugate Gradient Methods
• The problem of selecting the shape functions for ap-type finite element
• The Construction of Preconditioners for Elliptic Problems by Substructuring. II
• Efficient Preconditioning for thep-Version Finite Element Method in Two Dimensions
• Domain Decomposition Algorithms with Small Overlap
• Balancing domain decomposition for problems with large jumps in coefficients
• The Construction of Preconditioners for Elliptic Problems by Substructuring. I