A fast and accurate algorithm for a Galerkin boundary integral method |
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Authors: | J Wang S L Crouch S G Mogilevskaya |
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Affiliation: | (1) Department of Civil and Coastal Engineering, University of Florida, 345 Weil Hall, Gainesville, FL 32611, USA;(2) Department of Civil Engineering, University of Minnesota, 500 Pillsbury Drive S.E., Minneapolis, MN 55455, USA |
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Abstract: | A fast and accurate algorithm is presented to increase the computational efficiency of a Galerkin boundary integral method
for solving two-dimensional elastostatics problems involving numerous straight cracks and circular inhomogeneities. The efficiency
is improved by computing the combined influences of groups, or blocks, of elements—with each element being an inclusion, a
hole, or a crack—using asymptotic expansions, multiple shifts, and Taylor series expansions. The coefficients in the asymptotic
and Taylor series expansions are computed analytically. Implementation of this algorithm involves a single- or multi-level
grid, a clustering technique, and a tree data structure. An iterative procedure is adopted to solve the coefficients in the
series expansions of boundary unknowns block by block. The elastic fields in each block are calculated by superposition of
the direct influences from the nearby elements and the grouped far-field influences from all the other elements. This fast
multipole algorithm is considerably more efficient for large-scale practical problems than the conventional approach. |
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Keywords: | Fast multipole algorithm Galerkin boundary integral method Straight crack Circular inhomogeneity Orthogonal function Asymptotic expansion Taylor series expansion Tree data structure |
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