Fast algorithms for spherical harmonic expansions, III
arXiv:0910.5435 · doi:10.1016/j.jcp.2010.05.004
Abstract
We accelerate the computation of spherical harmonic transforms, using what is known as the butterfly scheme. This provides a convenient alternative to the approach taken in the second paper from this series on "Fast algorithms for spherical harmonic expansions." The requisite precomputations become manageable when organized as a "depth-first traversal" of the program's control-flow graph, rather than as the perhaps more natural "breadth-first traversal" that processes one-by-one each level of the multilevel procedure. We illustrate the results via several numerical examples.
14 pages, 1 figure, 6 tables
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