In the present paper we extend the method presented by 0. Axelsson and P. Vassilevski called AMLP version (i) of recursively constructing preconditioner for the stiffness matrix in the discretization of selfadjoint se...In the present paper we extend the method presented by 0. Axelsson and P. Vassilevski called AMLP version (i) of recursively constructing preconditioner for the stiffness matrix in the discretization of selfadjoint second order elliptic boundary value problems. In our extended method the systems to be eliminated on each level containing the major block matrices of the given matrix can be solved approximately, while they must be solved exactly in the original method.展开更多
A parallel hybrid linear solver based on the Schur complement method has the potential to balance the robustness of direct solvers with the efficiency of preconditioned iterative solvers.However,when solving large-sca...A parallel hybrid linear solver based on the Schur complement method has the potential to balance the robustness of direct solvers with the efficiency of preconditioned iterative solvers.However,when solving large-scale highly-indefinite linear systems,this hybrid solver often suffers from either slow convergence or large memory requirements to solve the Schur complement systems.To overcome this challenge,we in this paper discuss techniques to preprocess the Schur complement systems in parallel. Numerical results of solving large-scale highly-indefinite linear systems from various applications demonstrate that these techniques improve the reliability and performance of the hybrid solver and enable efficient solutions of these linear systems on hundreds of processors,which was previously infeasible using existing state-of-the-art solvers.展开更多
基金Supported by State Major Key Project for Basic Researches and the National Natural Science Foundation of China
文摘In the present paper we extend the method presented by 0. Axelsson and P. Vassilevski called AMLP version (i) of recursively constructing preconditioner for the stiffness matrix in the discretization of selfadjoint second order elliptic boundary value problems. In our extended method the systems to be eliminated on each level containing the major block matrices of the given matrix can be solved approximately, while they must be solved exactly in the original method.
基金supported in part by the Director,Office of Science,Office of Advanced Scientific Computing Research,of the U.S.Department of Energy under Contract No.DE-AC02-05CH11231.
文摘A parallel hybrid linear solver based on the Schur complement method has the potential to balance the robustness of direct solvers with the efficiency of preconditioned iterative solvers.However,when solving large-scale highly-indefinite linear systems,this hybrid solver often suffers from either slow convergence or large memory requirements to solve the Schur complement systems.To overcome this challenge,we in this paper discuss techniques to preprocess the Schur complement systems in parallel. Numerical results of solving large-scale highly-indefinite linear systems from various applications demonstrate that these techniques improve the reliability and performance of the hybrid solver and enable efficient solutions of these linear systems on hundreds of processors,which was previously infeasible using existing state-of-the-art solvers.
