Some aspects of parallel implementation of the finite-element method on message passing architectures

DOI10.1016/0377-0427(89)90365-8zbMath0693.65077OpenAlexW2095992374MaRDI QIDQ908670

Howard C. Elman, Ivo M. Babuška

Publication date: 1989

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(89)90365-8

zbMATH Keywords

finite element methoditerative methodsdirect methodsh-versionparallel computationsnested dissectionpreconditioned conjugate gradientp-versionh-p-versionglobal eliminationlocal eliminationsparse direct solverssuper-elements

Mathematics Subject Classification ID

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) Parallel numerical computation (65Y05) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (12)

Performance study of the domain decomposition method with direct equation solver for parallel finite element analysis ⋮ A parallel finite element method for the analysis of crystalline solids ⋮ Parallel implementation of the \(p\)-version of the finite element method for elliptic equations on a shared-memory architecture ⋮ The problem of selecting the shape functions for ap-type finite element ⋮ Nonconforming spectral element method: a friendly introduction in one dimension and a short review in higher dimensions ⋮ Efficient quadrature rules for finite element discretizations of nonlocal equations ⋮ Efficient parallel implementations of finite element methods based on the conjugate gradient method ⋮ 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 ⋮ An algorithm for domain partitioning with load balancing ⋮ The p- and h-p versions of the finite element method. An overview

Uses Software

• symrcm

Cites Work

• Data-flow algorithms for parallel matrix computation
• A Comparison of Domain Decomposition Techniques for Elliptic Partial Differential Equations and their Parallel Implementation
• The Optimal Convergence Rate of the p-Version of the Finite Element Method
• Parallel Solution of Triangular Systems on Distributed-Memory Multiprocessors
• Complexity of Parallel Implementation of Domain Decomposition Techniques for Elliptic Partial Differential Equations
• Development of Parallel Methods for a $1024$-Processor Hypercube
• The $h{\text{ - }}p$ Version of the Finite Element Method for Domains with Curved Boundaries
• Iterative Methods for the Solution of Elliptic Problems on Regions Partitioned into Substructures
• Nested Dissection of a Regular Finite Element Mesh
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