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	Uniform convergent multigrid methods for elliptic problems with strongly discontinuous coefficients
	Xu, Jinchao ; Zhu, Yunrong
	2008
关键词	preconditioned conjugate gradient multigrid BPX preconditioner MGCG variable coefficient effective condition number CONJUGATE-GRADIENT METHOD WEIGHTED L2 PROJECTION DOMAIN DECOMPOSITION 3 DIMENSIONS SCHWARZ METHODS PRECONDITIONERS ALGORITHMS CONSTRUCTION SYSTEMS SPACE
英文摘要	This paper gives a solution to an open problem concerning the performance of various multilevel preconditioners for the linear finite element approximation of second-order elliptic boundary value problems with strongly discontinuous coefficients. By analyzing the eigenvalue distribution of the BPX preconditioner and multigrid V-cycle preconditioner, we prove that only a small number of eigenvalues may deteriorate with respect to the discontinuous jump or meshsize, and we prove that all the other eigenvalues are bounded below and above nearly uniformly with respect to the jump and meshsize. As a result, we prove that the convergence rate of the preconditioned conjugate gradient methods is uniform with respect to the large jump and meshsize. We also present some numerical experiments to demonstrate the theoretical results.; Mathematics, Applied; SCI(E); EI; 32; ARTICLE; 1; 77-105; 18
语种	英语
出处	EI ; SCI
出版者	mathematical models methods in applied sciences
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/314898]
专题	数学科学学院
推荐引用方式 GB/T 7714	Xu, Jinchao,Zhu, Yunrong. Uniform convergent multigrid methods for elliptic problems with strongly discontinuous coefficients. 2008-01-01.

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