An Adaptive Fast Multipole Boundary Element Method for Three-dimensional Potential Problems |
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Authors: | Liang Shen Yijun J Liu |
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Affiliation: | (1) Computer-Aided Engineering Research Laboratory, Department of Mechanical Engineering, University of Cincinnati, Cincinnati, OH 45221-0072, USA |
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Abstract: | An adaptive fast multipole boundary element method (FMBEM) for general three-dimensional (3-D) potential problems is presented
in this paper. This adaptive FMBEM uses an adaptive tree structure that can balance the multipole to local translations (M2L)
and the direct evaluations of the near-field integrals, and thus can reduce the number of the more costly direct evaluations.
Furthermore, the coefficients used in the preconditioner for the iterative solver (GMRES) are stored and used repeatedly in
the direct evaluations of the near-field contributions. In this way, the computational efficiency of the adaptive FMBEM is
improved significantly. The adaptive FMBEM can be applied to both the original FMBEM formulation and the new FMBEM with diagonal
translations. Several numerical examples are presented to demonstrate the efficiency and accuracy of the adaptive FMBEM for
studying large-scale 3-D potential problems. The adaptive FMBEM is found to be about 50% faster than the non-adaptive version
of the new FMBEM in solving the model (with 558,000 elements) for porous materials studied in this paper. The computational
efficiencies and accuracies of the FMBEM as compared with the finite element method (FEM) are also studied using a heat-sink
model. It is found that the adaptive FMBEM is especially advantageous in modeling problems with complicated domains for which
free meshes with much more finite elements would be needed with the FEM. |
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Keywords: | Fast multipole method Boundary element method Three-dimensional potential problems |
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