A New Paradigm for Parallel Adaptive Meshing Algorithms

DOI10.1137/S1064827599353701zbMath0979.65110MaRDI QIDQ2706443

Randolph E. Bank, Michael Holst

Publication date: 19 March 2001

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

domain decompositionfinite elementparallel computationmesh refinementelliptic problemmultigrid algorithmsmortar methodinterior error estimates

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Parallel numerical computation (65Y05)

Related Items (28)

The influence of partitioning on domain decomposition convergence rates ⋮ A new parallel domain decomposition method for the adaptive finite element solution of elliptic partial differential equations ⋮ Quasi-optimality of adaptive finite element methods for controlling local energy errors ⋮ An element agglomeration nonlinear additive Schwarz preconditioned Newton method for unstructured finite element problems. ⋮ A parallel partition of unity scheme based on two-grid discretizations for the Navier-Stokes problem ⋮ Algebraic Multigrid Domain and Range Decomposition (AMG-DD/AMG-RD) ⋮ Stability and convergence of some parallel iterative subgrid stabilized algorithms for the steady Navier-Stokes equations ⋮ New local and parallel finite element algorithm based on the partition of unity ⋮ On the convergence of an optimal additive Schwarz method for parallel adaptive finite elements ⋮ The partition of unity parallel finite element algorithm ⋮ Local and parallel finite element algorithm based on the partition of unity for incompressible flows ⋮ A parallel stabilized finite element method based on the lowest equal-order elements for incompressible flows ⋮ Local and parallel finite element algorithms for the Stokes problem ⋮ Domain Decomposition and hp-Adaptive Finite Elements ⋮ Hierarchical matrix techniques for a domain decomposition algorithm ⋮ Two-grid partition of unity method for second order elliptic problems ⋮ Local and parallel finite element algorithms based on two-grid discretizations for the transient Stokes equations ⋮ Gradient recovery type a posteriori error estimates for finite element approximations on irregular meshes ⋮ An analysis of discontinuous Galerkin methods for elliptic problems ⋮ Local energy estimates for the finite element method on sharply varying grids ⋮ A Comparison of Additive Schwarz Preconditioners for Parallel Adaptive Finite Elements ⋮ Fast and scalable algorithms for constructing solvent-excluded surfaces of large biomolecules ⋮ Preparing sparse solvers for exascale computing ⋮ How to best choose the outer coarse mesh in the domain decomposition method of Bank and Jimack ⋮ A parallel finite element variational multiscale method based on fully overlapping domain decomposition for incompressible flows ⋮ Progress in developing Poisson-Boltzmann equation solvers ⋮ Local and parallel finite element algorithms for eigenvalue problems ⋮ An optimal Schwarz preconditioner for a class of parallel adaptive finite elements

Uses Software

• PLTMG

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