The Fast Numerical Solution of Very Large Elliptic Difference Schemes |
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Authors: | HACKBUSCH WOLFGANG |
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Institution: |
Institut für Mathematik Ruhr-Universität Bochum Postfach 102148, 0-4630 Bochum 1
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Abstract: | Let Lkvk = gk be a system of difference equations discretizingan elliptic boundary value problem. Assume the system to be"very large", that means that the number of unknowns exceedsthe capacity of storage. We present a method for solving theproblem with much less storage requirement. For two-dimensionalproblems the size of the needed storage decreases from O(h2)to (or even O(h5/4)). The computational work increasesonly by a factor about six. The technique can be generalizedto nonlinear problems. The algorithm is also useful for computerswith a small number of parallel processors. |
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