Some Domain Decomposition Algorithms for Nonselfadjoint Elliptic and Parabolic Partial Differential Equations: Technical Report 461; September, 1989 (Classic Reprint) - Softcover

Xiao-Chuan Cai

 
9781333219604: Some Domain Decomposition Algorithms for Nonselfadjoint Elliptic and Parabolic Partial Differential Equations: Technical Report 461; September, 1989 (Classic Reprint)

Synopsis

This book presents numerical methods for solving large linear systems that emerge from finite element discretizations of partial differential equations. The author presents a unified abstract theory for additive Schwarz-type methods for general linear, non-selfadjoint, second order elliptic and parabolic problems. The convergence rate of the algorithms is estimated and shown to be optimal in both the elliptic and parabolic problems in R2 and R3. Numerical experiments are also presented. The algorithms introduced in this book are promising for parallel computation because they involve solving a number of smaller linear systems, which correspond to the restriction of the original problem to subregions, instead of the large original system.

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