Fast Convolution for Nonreflecting Boundary Conditions

Authors:
Christian Lubich;Achim Schädle
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2002

Citing 0
Cited 24

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Abstract

Nonreflecting boundary conditions for problems of wave propagation are nonlocal in space and time. While the nonlocality in space can be efficiently handled by Fourier or spherical expansions in special geometries, the arising temporal convolutions still form a computational bottleneck. In the present article, a new algorithm for the evaluation of these convolution integrals is proposed. To compute a temporal convolution over Nt successive time steps, the algorithm requires O(Nt log Nt) operations and O(log Nt) memory. In the numerical examples, this algorithm is used to discretize the Neumann-to-Dirichlet operators arising from the formulation of nonreflecting boundary conditions in rectangular geometries for Schrödinger and wave equations.