Summary: RAPID EVALUATION OF NONREFLECTING BOUNDARY
KERNELS FOR TIME-DOMAIN WAVE PROPAGATION
BRADLEY ALPERT, LESLIE GREENGARD, AND THOMAS HAGSTROM§
SIAM J. NUMER. ANAL. c 2000 Society for Industrial and Applied Mathematics
Vol. 37, No. 4, pp. 1138­1164
Abstract. We present a systematic approach to the computation of exact nonreflecting bound-
ary conditions for the wave equation. In both two and three dimensions, the critical step in our
analysis involves convolution with the inverse Laplace transform of the logarithmic derivative of a
Hankel function. The main technical result in this paper is that the logarithmic derivative of the Han-
kel function H
(1)
(z) of real order can be approximated in the upper half z-plane with relative error
by a rational function of degree d O(log || log 1

+log2
||+||-1 log2 1

) as || , 0, with
slightly more complicated bounds for = 0. If N is the number of points used in the discretization of
a cylindrical (circular) boundary in two dimensions, then, assuming that < 1/N, O(N log N log 1

Source: Alpert, Bradley K. - Mathematical and Computational Sciences Division, National Institute of Standards and Technology (NIST)

Collections: Mathematics; Computer Technologies and Information Sciences