Parallel adaptive solution of 3D boundary value problems by Hessian recovery

DOI10.1016/S0045-7825(02)00654-0zbMath1025.65057MaRDI QIDQ1402575

Yuri V. Vassilevski, Konstantin N. Lipnikov

Publication date: 28 August 2003

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

zbMATH Keywords

finite element methodnumerical examplesparallel computationmesh generationPoisson equationiterative solutionquasi-optimal meshesHessian recoveryinertial bisection

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Parallel numerical computation (65Y05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items

Parallel solution of mixed finite element/spectral element systems for convection-diffusion equations on non-matching grids ⋮ Minimization of gradient errors of piecewise linear interpolation on simplicial meshes ⋮ Hessian-based anisotropic mesh adaptation in domains with discrete boundaries ⋮ On optimal convergence rate of finite element solutions of boundary value problems on adaptive anisotropic meshes ⋮ Optimal anisotropic meshes for minimizing interpolation errors in $L^p$-norm

Uses Software

• ITPACK
• ITPACK 2C

Cites Work

• Additive multilevel preconditioners based on bilinear interpolation, matrix-dependent geometric coarsening and algebraic multigrid coarsening for second-order elliptic PDEs
• On optimal triangular meshes for minimizing the gradient error
• Algebraic multigrid (AMG): Experiences and comparisons
• An Aggregation-Based Domain Decomposition Preconditioner for Groundwater Flow
• Partitioning Sparse Matrices with Eigenvectors of Graphs
• Algorithm 586: ITPACK 2C: A FORTRAN Package for Solving Large Sparse Linear Systems by Adaptive Accelerated Iterative Methods
• Long and Thin Triangles Can Be Good for Linear Interpolation
• Lower Bounds for Two-Level Additive Schwarz Preconditioners with Small Overlap
• On a discrete Hessian recovery for P 1 finite elements
• Balancing domain decomposition for problems with large jumps in coefficients
• An adaptive algorithm for quasioptimal mesh generation
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