Fast transform eigenfunction methods for boundary value problems |
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| Authors: | John A Scales |
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| Institution: | Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado 80309, USA |
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| Abstract: | An extension of the classic eigenfunction expansion method is presented for solving boundary value problems on boundaries of essentially arbitrary shape in R 3. the algorithm yields approximate solutions in terms of simple eigenfunctions of the underlying differential operator. the coefficients of these eigenfunctions are calculated with two-dimensional FFTs. the algorithm has many applications in geophysics, such as potential theory, scattering theory, earthquake source dynamics, and wave propagation, where non-separable boundaries are common. |
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| Keywords: | boundary value problems integral equations eigenfunction expansions fast transforms |
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