Parallel MIC(0) preconditioning of 3D elliptic problems discretized by Rannacher–Turek finite elements

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• 作者：P. Arbenz ; S. Margenov ; Y. Vutov
• 关键词：Nonconforming FEM ; MIC(0) preconditioning ; Parallel algorithms
• 刊名：Computers and Mathematics with Applications
• 出版年：2008
• 出版时间：May 2008
• 年：2008
• 卷：55
• 期：10
• 页码：2197-2211
• 全文大小：880 K

文摘

Novel parallel algorithms for the solution of large FEM linear systems arising from second order elliptic partial differential equations in 3D are presented. The problem is discretized by rotated trilinear nonconforming Rannacher–Turek finite elements. The resulting symmetric positive definite system of equations RWC525-3&_mathId=mml42&_user=1067359&_cdi=5620&_rdoc=4&_acct=C000050221&_version=1&_userid=10&md5=2e79603eb543ab7916831eaf22714ba1""> is solved by the preconditioned conjugate gradient algorithm. The preconditioners employed are obtained by the modified incomplete Cholesky factorization MIC(0) of two kinds of auxiliary matrices B that both are constructed as locally optimal approximations of c4aefa0b839d1d5725c5"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">A in the class of M-matrices. Uniform estimates for the condition number κ(B⁻¹A) are derived. Two parallel algorithms based on the different block structures of the related matrices c4960412"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">B are studied. The numerical tests confirm theory in that the algorithm scales as in the matrix order c46d99a48a8d19043d04908bfab1f"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">N.