A Tutorial on Elliptic PDE Solvers and Their Parallelization

DOI10.1137/1.9780898718171zbMath1029.65121OpenAlexW579331379MaRDI QIDQ4414852

Ulrich Langer, Gundolf Haase, Craig C. Douglas

Publication date: 27 July 2003

Full work available at URL: https://doi.org/10.1137/1.9780898718171

zbMATH Keywords

performancefinite element methodfinite difference methodtextbookparallel computationmultigrid methodPoisson equationmatrix-vector operationsdirect and iterative solvers

Mathematics Subject Classification ID

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) Parallel numerical computation (65Y05) Linear first-order PDEs (35F05) Finite difference methods for boundary value problems involving PDEs (65N06) Complexity and performance of numerical algorithms (65Y20) Direct numerical methods for linear systems and matrix inversion (65F05) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis (65-01)

Related Items (10)

Parallelization of continuous and discontinuous Galerkin dual-primal isogeometric tearing and interconnecting methods ⋮ Parallel Schur Complement Techniques Based on Multiprojection Methods ⋮ Comparison of the deflated preconditioned conjugate gradient method and algebraic multigrid for composite materials ⋮ High-performance modeling acoustic and elastic waves using the parallel dichotomy algorithm ⋮ Geometric multigrid method for solving Poisson's equation on octree grids with irregular boundaries ⋮ Parallel multiprojection preconditioned methods based on subspace compression ⋮ A Brief History of the Parallel Dawn in Karl-Marx-Stadt/Chemnitz ⋮ Numerical simulation of fluid-structure interaction problems with hyperelastic models: a monolithic approach ⋮ A Hilbert-order multiplication scheme for unstructured sparse matrices ⋮ Parallel geometric multigrid for global weather prediction

Uses Software

• JOSTLE
• MPI

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