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A domain decomposition method for solving thin film elliptic interface problems with variable coefficients
Author(s) -
Dai Weizhong,
Nassar Raja
Publication year - 1999
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19991020)46:5<747::aid-nme696>3.0.co;2-6
Subject(s) - domain decomposition methods , discretization , gaussian elimination , mathematics , variable (mathematics) , interface (matter) , domain (mathematical analysis) , computation , elliptic curve , grid , gaussian , mathematical analysis , decomposition method (queueing theory) , algorithm , finite element method , geometry , computer science , discrete mathematics , physics , parallel computing , bubble , quantum mechanics , maximum bubble pressure method , thermodynamics
A domain decomposition method is developed for solving thin film elliptic interface problems with variable coefficients. In this study, the elliptic equation with variable coefficients is discretized using second‐order finite differences while a discrete interface equation is obtained using the immersed interface method in order to obtain a second‐order global accuracy. The obtained linear system is solved using a preconditioned Richardson iteration, which is shown to converge fast when the grid size in the thickness direction is much smaller than the grid sizes in both the length and width directions. To simplify the computation, a domain decomposition algorithm is obtained based on a parallel Gaussian elimination procedure. The method is illustrated by a numerical example. Copyright © 1999 John Wiley & Sons, Ltd.