International Journal of High Speed Computing · 1995 · 44 citations · 0 references
ComputingComputational EngineeringHigh-performance ComputingComputational MechanicsFinite Element AnalysisParallel ComputingConvergence AnalysisFinite Element DiscretizationFinite Element FormulationIterative SolversParallel Numerical Linear AlgebraParallel Numerical MethodsConvergence Rate AnalysisFinite Element ModelingLinear Elastic AnalysisOrthotropic MaterialsParallel PreconditioningPreconditioningPreconditioning TechniquesSparse Inverse Problems
An iterative method for solving large linear systems with sparse symmetric positive definite matrices on massively parallel computers is suggested. The method is based on the Factorized Sparse Approximate Inverse (FSAI) preconditioning of ‘parallel’ CG iterations. Efficiency of a concurrent implementation of the FSAI-CG iterations is analyzed for a model hypercube, and an estimate of the optimal hypercube dimension is derived. For finite element applications, two strategies for selecting the preconditioner sparsity pattern are suggested. A high convergence rate of the resulting iterations is demonstrated numerically for the 3D equilibrium equations for linear elastic orthotropic materials approximated using both h- and p-versions of the FEM.