Sparse Approximations of the Schur Complement for Parallel Algebraic Hybrid Solvers in 3D  

作　　者：L.Giraud A.Haidar Y.Saad 

机构地区：[1]Joint INRIA-CERFACS Lab-42 AV.Coriolis,31057,Toulouse,France [2]Department of Computer Science,University of Tennessee,Knoxville,TN37996,USA. [3]Department of Computer Science and Engineering,University of Minnesota,Minneapolis,MN55455,USA

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2010年第3期276-294,共19页高等学校计算数学学报（英文版）

基　　金：developed in the framework of the associated team PhyLeas(Study of parallel hybrid sparse linear solvers) funded by INRIA where the partners are INRIA,T.U.Brunswick and University of Minnesota;supported by the US Department of Energy under grant DE-FG-08ER25841 and by the Minnesota Supercomputer Institute.

摘　　要：In this paper we study the computational performance of variants of an algebraic additive Schwarz preconditioner for the Schur complement for the solution of large sparse linear systems.In earlier works,the local Schur complements were computed exactly using a sparse direct solver.The robustness of the preconditioner comes at the price of this memory and time intensive computation that is the main bottleneck of the approach for tackling huge problems.In this work we investigate the use of sparse approximation of the dense local Schur complements.These approximations are computed using a partial incomplete LU factorization.Such a numerical calculation is the core of the multi-level incomplete factorization such as the one implemented in pARMS. The numerical and computing performance of the new numerical scheme is illustrated on a set of large 3D convection-diffusion problems;preliminary experiments on linear systems arising from structural mechanics are also reported.In this paper we study the computational performance of variants of an algebraic additive Schwarz preconditioner for the Schur complement for the solution of large sparse linear systems. In earlier works, the local Schur complements were computed exactly using a sparse direct solver. The robustness of the preconditioner comes at the price of this memory and time intensive computation that is the main bottleneck of the approach for tackling huge problems. In this work we investigate the use of sparse approximation of the dense local Schur complements. These approximations are computed using a partial incomplete LU factorization. Such a numerical calculation is the core of the multi-level incomplete factorization such as the one implemented in pARMS. The numerical and computing performance of the new numerical scheme is illustrated on a set of large 3D convection-diffusion problems; preliminary experiments on linear systems arising from structural mechanics are also reported.

关 键 词：Hybrid direct/iterative solver domain decomposition incomplete/partial factorization Schur approximation scalable preconditioner CONVECTION-DIFFUSION large 3D problems parallelscientific computing High Performance Computing. 

分 类 号：O241.82[理学—计算数学]