On the numerical modeling of convection-diffusion problems by finite element multigrid preconditioning methods

作     者：Filelis-Papadopoulos, Christos K. Gravvanis, George A. Lipitakis, Elias A. 

作者机构：Democritus Univ Thrace Sch Engn Dept Elect & Comp Engn GR-67100 Xanthi Greece Athens Univ Econ & Business Dept Informat GR-10434 Athens Greece 

出 版 物：《ADVANCES IN ENGINEERING SOFTWARE》 (Adv Eng Software)

年 卷 期：2014年第68卷

页      面：56-69页

核心收录：

学科分类：08[工学] 0835[工学-软件工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：Sparse linear systems Finite element method Multigrid methods Approximate inverse smoothing DOUR algorithm PR2 refinement Multigrid preconditioning 

摘      要：During the last decades, multigrid methods have been extensively used in order to solve large scale linear systems derived from the discretization of partial differential equations using the finite difference method. The effectiveness of the multigrid method can be also exploited by using the finite element method. Finite Element Approximate Inverses in conjunction with Richardon s iterative method could be used as smoothers in the multigrid method. Thus, a new class of smoothers based on approximate inverses can be derived. Effectiveness of explicit approximate inverses relies in the fact that they are close approximants to the inverse of the coefficient matrix and are fast to compute in parallel. Furthermore, the proposed class of finite element approximate inverses in conjunction with the explicit preconditioned Richardson method yield improved results against the classic smoothers such as Jacobi method. Moreover, a dynamic relaxation scheme is proposed based on the Dynamic Over/Under Relaxation (DOUR) algorithm. Furthermore, results for multigrid preconditioned Krylov subspace methods, such as GMRES(res), IDR(s) and BiCGSTAB based on approximate inverse smoothing and a dynamic relaxation technique are presented for the steady-state convection-diffusion equation. (C) 2013 Elsevier Ltd. All rights reserved.