Astronomy and Astrophysics – Astronomy
Scientific paper
Jan 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000geoji.140..198f&link_type=abstract
Geophysical Journal International, Volume 140, Issue 1, pp. 198-210.
Astronomy and Astrophysics
Astronomy
14
Green'S Functions, Numerical Techniques, Sedimentary Basin, Topography, Wave Propagation
Scientific paper
The fast multipole method is developed for the solution of the boundary integral equations arising in wave scattering problems involving 3-D topography and 3-D basin problems. When coupled with an iterative solver for linear equations, the fast multipole method can significantly reduce memory requirements. The order of operations for the product of the matrix obtained from the discretization of the integral kernel and a vector is reduced from N2 to the order of pα N, where p is the order of the multipole expansion and α depends on the details of the implementation. In order to achieve efficient implementation the translation operators for the multipole expansion need to be used in the diagonal form based on a spherical wave decomposition. For problems with topography, the number of iterations required of the linear equation solver to achieve convergence is small and no preconditioning is necessary. However, for a basin problem, block-diagonal preconditioning is essential in the application of the iterative solver. Both the memory requirements and the CPU time are considerably reduced for topography problems. Although the memory requirement is reduced for a basin problem used in this numerical experiment, the CPU time would be still longer than that for the ordinary boundary element method if sufficient memory were available. These results indicate that the fast multipole method might be much more efficient than the ordinary method for 3-D elastic wave scattering problems with more than several tens of thousands of unknown variables.
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