Fast convolution for non-reflecting boundary conditions

Non-reflecting boundary conditions for problems of wave propagation are

non-local in space and time. While the non-locality 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 talk, a new algorithm for the evaluation of these convolution

integrals is proposed. To compute a temporal convolution over

successive time steps, the algorithm requires operations

and active memory. In the numerical examples, this algorithm

is used to discretize the Dirichlet-to-Neumann and Neumann-to-Dirichlet

operators arising from the formulation of non-reflecting boundary conditions

in rectangular geometries for Schrödinger and wave equations.