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AN ITERATIVE SOLUTION SCHEME FOR SYSTEMS OF WEAKLY CONNECTED BOUNDARY ELEMENT EQUATIONS
Author(s) -
DAVEY K.,
ROSINDALE I.
Publication year - 1996
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(19961215)39:23<3933::aid-nme30>3.0.co;2-x
Subject(s) - scheme (mathematics) , boundary element method , mathematics , iterative method , mathematical analysis , element (criminal law) , finite element method , computer science , mathematical optimization , structural engineering , engineering , political science , law
In this paper an iterative scheme of first degree is developed for solving linear systems of equations. The systems investigated are those which are derived from boundary integral equations and are of the form ∑ N j =1 H ij x j = c i , i =1, 2,…, N , where H ij are matrices, x j and c i are column vectors. In addition, N denotes the number of domains and for i ≠ j , H ij is considered to be small in some sense. These systems, denoted as weakly connected, are solved using first‐order iterative techniques initially developed by the authors for solving single‐domain problems. The techniques are extended to solve multi‐domain problems. Novel solution strategies are investigated and procedures are developed which are computationally efficient. Computation times are determined for the iterative procedures and for elimination techniques indicating the benefits of iterative techniques over direct methods for problems of this nature.