Abstract
The method of fundamental solution (MFS) has been known as a simple and effective boundary meshless method. However, the MFS generates dense square coefficient matrix and thus requires a large amount of computational time and memory storage for solving large-scale problems. The fast multipole method (FMM) is a technique that reduces computational operations and storage requirements for solving such dense matrix equations. This study makes the first attempt to apply the FMM to the MFS calculation of acoustic problems, where the operations are reduced to O(N log N) while O(N2) operations are required for the traditional MFS using the standard iterative methods. Numerical examples with up to 100,000 points are successfully tested on a desktop personal computer. Our results clearly demonstrate efficiency and accuracy of the fast multipole MFS for solving large-scale Helmholtz-type problems.
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