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Parallel finite element splitting‐up method for parabolic problems
Author(s) -
Tai XueCheng,
Neittaanmäki Pekka
Publication year - 1991
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690070302
Subject(s) - mathematics , finite element method , element (criminal law) , series (stratigraphy) , space (punctuation) , mixed finite element method , mathematical optimization , mathematical analysis , computer science , structural engineering , paleontology , political science , law , engineering , biology , operating system
Abstract An efficient method for solving parabolic systems is presented. The proposed method is based on the splitting‐up principle in which the problem is reduced to a series of independent 1D problems. This enables it to be used with parallel processors. We can solve multidimensional problems by applying only the 1D method and consequently avoid the difficulties in constructing a finite element space for multidimensional problems. The method is suitable for general domains as well as rectangular domains. Every 1D subproblem is solved by applying cubic B‐splines. Several numerical examples are presented.