Splitting extrapolation method for solving second-order parabolic equations with curved boundaries by using domain decomposition and d-quadratic isoparametric finite elements

作     者：He, Xiaoming Lu, Tao 

作者机构：Virginia Tech Dept Math Blacksburg VA 24061 USA Sichuan Univ Dept Math Chengdu 610064 Peoples R China 

出 版 物：《INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS》 (国际计算机数学杂志)

年 卷 期：2007年第84卷第6期

页      面：767-781页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：National Natural Science Foundation of China, NSFC, (10671136) National Natural Science Foundation of China, NSFC 

主　　题：splitting extrapolation domain decomposition d-quadratic iso-parametric mapping parallel algorithm 

摘      要：This article discusses a splitting extrapolation method for solving second-order parabolic equations with curved boundaries by using domain decomposition and d-quadratic isoparametric finite elements. This method possesses superconvergence, a high order of accuracy and a high degree of parallelism. First, we prove the multi-variable asymptotic expansion of fully discrete d-quadratic isoparametric finite element errors. Based on the expansion, we generate splitting extrapolation formulas. These formulas generate a numerical solution on a globally fine grid with higher accuracy by solving only a set of smaller discrete subproblems on different coarser grids. Therefore, a large-scale multidimensional problem with a curved boundary is turned into a set of smaller discrete subproblems on a polyhedron. Because these subproblems are independent of each other and have similar scales, our algorithm possesses a high degree of parallelism. In addition, this method is effective for solving discontinuous problems if we regard the interfaces of the problems as the interfaces of the initial domain decomposition. Our numerical results also show that the algorithm is effective for solving nonlinear parabolic equations.