An Unconventional Domain Decomposition Method for an Efficient Parallel Solution of Large-Scale Finite Element Systems

DOI10.1137/0913020zbMath0746.65086OpenAlexW2090499178MaRDI QIDQ3990923

Francois-Xavier Roux, Charbel Farhat

Publication date: 28 June 1992

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

Full work available at URL: https://doi.org/10.1137/0913020

zbMATH Keywords

Lagrange multipliers domain decomposition algorithm conjugate projected gradient algorithm parallel finite element solution parallel/vector computers with shared memory

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)

Related Items

Scalable total BETI based algorithm for 3D coercive contact problems of linear elastostatics ⋮ Triangle graphs ⋮ A TFETI domain decomposition solver for elastoplastic problems ⋮ Extending substructure based iterative solvers to multiple load and repeated analyses ⋮ Composite grid method for hybrid systems ⋮ On the spectrum of Schur complements of 2D elastic clusters joined by rigid edge modes and hybrid domain decomposition ⋮ Duality based domain decomposition with proportioning for the solution of free boundary problems ⋮ Implementation of a new expression for the search direction in simulations of structures with buckling and post-buckling: ``two-scale impedance ⋮ Highly scalable hybrid domain decomposition method for the solution of huge scalar variational inequalities ⋮ Sparse matrix factorization in the implicit finite element method on petascale architecture ⋮ A unified dual-primal finite element tearing and interconnecting approach for incompressible Stokes equations ⋮ The impact of enabling multiple subdomains per MPI process in the TFETI domain decomposition method ⋮ A coupled FETI-BDNM for solving 3D elastic frictional contact problem ⋮ A unified theory of non-overlapping Robin-Schwarz methods: continuous and discrete, including cross points ⋮ Solution of 3D contact shape optimization problems with Coulomb friction based on TFETI. ⋮ A theoretically supported scalable TFETI algorithm for the solution of multibody 3D contact problems with friction ⋮ Constructing efficient substructure-based preconditioners for BEM systems of equations ⋮ A parallel strategy for the multiparametric analysis of structures with large contact and friction surfaces ⋮ Hybrid TFETI domain decomposition with the clusters joined by faces' rigid modes for solving huge 3D elastic problems ⋮ A scalable TFETI algorithm for two-dimensional multibody contact problems with friction ⋮ FETI-DP: a dual-primal unified FETI method?part I: A faster alternative to the two-level FETI method ⋮ A two-step, two-field hybrid method for the static and dynamic analysis of substructure problems with conforming and non-conforming interfaces ⋮ An optimization based domain decomposition method for partial differential equations ⋮ Parallel computation approaches for flexible multibody dynamics simulations ⋮ A SBS-BD based solver for domain decomposition in BE methods ⋮ A continuous framework for FETI-DP with a mesh independent condition number for the dual problem ⋮ The two-level FETI method for static and dynamic plate problems I: An optimal iterative solver for biharmonic systems ⋮ The two-level FETI method II: Extension to shell problems, parallel implementation and performance results ⋮ A faster “Hybrid-Flux” calculation approach to output bounds for three dimensional problems ⋮ Parallel frictional contact algorithms and industrial applications ⋮ Efficient redesign of damped large structural systems via domain decomposition with exact dynamic condensation ⋮ Scalable TFETI algorithm for the solution of multibody contact problems of elasticity ⋮ Theoretically supported scalable BETI method for variational inequalities ⋮ FETI-DPH: A DUAL-PRIMAL DOMAIN DECOMPOSITION METHOD FOR ACOUSTIC SCATTERING ⋮ FETI-based algorithms for modelling of fibrous composite materials with debonding ⋮ Duality-based domain decomposition with natural coarse-space for variational inequalities ⋮ A unified framework for accelerating the convergence of iterative substructuring methods with Lagrange multipliers ⋮ Adaptive computations of a posteriori finite element output bounds: a comparison of the hybrid-flux approach and the flux-free approach ⋮ A scalable FETI-DP algorithm for a coercive variational inequality ⋮ A domain decomposition method for the parallelization of a three-dimensional Maxwell solver based on a constrained formulation ⋮ A convergence theory for an overlapping Schwarz algorithm using discontinuous iterates ⋮ An iterative domain decomposition method for the solution of a class of indefinite problems in computational structural dynamics ⋮ A scalable FETI-DP algorithm with non-penetration mortar conditions on contact interface ⋮ FETI based algorithms for contact problems: Scalability, large displacements and 3D Coulomb friction ⋮ Non-overlapping domain decomposition method for a nodal finite element method ⋮ Load balancing fictions, falsehoods and fallacies ⋮ Lagrangian formulation of domain decomposition methods: a unified theory ⋮ A posteriori finite element output bounds in three space dimensions using the FETI method ⋮ Efficient Implementation of Total FETI Solver for Graphic Processing Units Using Schur Complement ⋮ Solving Contact Mechanics Problems with PERMON ⋮ A FETI method with a mesh independent condition number for the iteration matrix ⋮ Schur complement spectral bounds for large hybrid FETI-DP clusters and huge three-dimensional scalar problems ⋮ A scalable FETI-DP algorithm for a semi-coercive variational inequality ⋮ Two-level domain decomposition methods with Lagrange multipliers for the fast iterative solution of acoustic scattering problems ⋮ The second generation FETI methods and their application to the parallel solution of large-scale linear and geometrically non-linear structural analysis problems ⋮ Total FETI-an easier implementable variant of the FETI method for numerical solution of elliptic PDE ⋮ Solution of contact problems by FETI domain decomposition with natural coarse space projections ⋮ A dual-primal FETI method for incompressible Stokes equations ⋮ Parallel Implementation of Total-FETI DDM with Application to Medical Image Registration ⋮ Balancing domain decomposition ⋮ Scalability and FETI based algorithm for large discretized variational inequalities ⋮ An iterative substructuring method for coupled fluid-solid acoustic problems