Domain Decomposition Preconditioners for Mixed Finite-Element Discretization of High-Contrast Elliptic Problems  

作　　者：Hui Xie Xuejun Xu 

机构地区：[1]Institute of Applied Physics and Computational Mathematics,Beijing 100094,China [2]LSEC,Institute of Computational Mathematics,Academy of Mathematics and System Sciences,Chinese Academy of Sciences,P.O.Box 2719,Beijing 100190,China [3]School of Mathematical Sciences,Tongji University,Shanghai 200092,China

出　　处：《Communications on Applied Mathematics and Computation》2019年第1期141-165,共25页应用数学与计算数学学报（英文）

摘　　要：In this paper,we design an efficient domain decomposition(DD)preconditioner for the saddle-point problem resulting from the mixed finite-element discretization of multiscale elliptic problems.By proper equivalent algebraic operations,the original saddle-point system can be transformed to another saddle-point system which can be preconditioned by a block-diagonel matrix efficiently.Actually,the first block of this block-diagonal matrix corresponds to a multiscale H(div)problem,and thus,the direct inverse of this block is unpractical and unstable for the large-scale problem.To remedy this issue,a two-level overlapping DD preconditioner is proposed for this//(div)problem.Our coarse space consists of some velocities obtained from mixed formulation of local eigenvalue problems on the coarse edge patches multiplied by the partition of unity functions and the trivial coarse basis(e.g.,Raviart-Thomas element)on the coarse grid.The condition number of our preconditioned DD method for this multiscale H(div)system is bounded by C(1+务)(1+log4(^)),where 6 denotes the width of overlapping region,and H,h are the typical sizes of the subdomain and fine mesh.Numerical examples are presented to confirm the validity and robustness of our DD preconditioner.

关 键 词：High contrast.Mixed FEM DD PRECONDITIONER Spectral coarse space 

分 类 号：O1[理学—数学]