A preconditioner for a kind of coupled FEM-BEM variational inequality  

作　　者：HU QiYa1 & YU DeHao2 LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 

出　　处：《Science China Mathematics》2010年第11期2811-2830,共20页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (GrantNo. 10771178);The Key Project of National Natural Science Foundation of China (Grant No. 10531080);National Basic Research Program of China (Grant No. 2005CB321702);supported by The Key Project of National Natural Science Foundation of China (Grant No. 10531080);National Basic Research Program of China (Grant No. 2005CB321701)

摘　　要：In this paper we are concerned with a kind of nonlinear transmission problem with Signorini contact conditions. This problem can be described by a coupled FEM-BEM variational inequality. We first develop a preconditioning gradient projection method for solving the variational inequality. Then we construct an effective domain decomposition preconditioner for the discrete system. The preconditioner makes the coupled inequality problem be decomposed into an equation problem and a "small" inequality problem, which can be solved in parallel. We give a complete analysis to the convergence speed of this iterative method.In this paper we are concerned with a kind of nonlinear transmission problem with Signorini contact conditions. This problem can be described by a coupled FEM-BEM variational inequality. We first develop a preconditioning gradient projection method for solving the variational inequality. Then we construct an effective domain decomposition preconditioner for the discrete system. The preconditioner makes the coupled inequality problem be decomposed into an equation problem and a "small" inequality problem, which can be solved in parallel. We give a complete analysis to the convergence speed of this iterative method.

关 键 词：Signorini contact FEM-BEM coupling variational INEQUALITY PRECONDITIONING gradient projection PRECONDITIONER condition number 

分 类 号：O178[理学—数学]