On Domain Decomposition,
STANFORD UNIV CA CENTER FOR LARGE SCALE SCIENTIFIC COMPUTATION
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This report discusses aspects of the method of domain decomposition for the solution of elliptic boundary value problems in two dimensions. The basic idea behind the technique is to piece together local solutions of the elliptic problem to form a global solution. There are several reasons for wanting to use such a procedure. The first is that a given domain may be irregular, but can be subdivided into regular pieces for which solutions are computationally efficient to obtain. Another reason is that the method may be suitable for for solving elliptic problems on multiple processor machines. If, for example, one breaks up the domain into many small pieces and allocates a processor to each piece, then there is the possibility of decreasing the computational time by constructing the local solutions in parallel and gluing them together. The purpose of this report is to examine model problems with the intention of providing motivation and insight concerning results previously presented as well as offer some new observations that may aid in the implementation of the method. Keywords Integral equations, variable coefficient problem discrete operators.
- Theoretical Mathematics