Summary: A Representation of Acoustic Waves
in Unbounded Domains
BRADLEY K. ALPERT
National Institute of Standards and Technology
AND
YU CHEN
Courant Institute
Abstract
Compact, time-harmonic, acoustic sources produce waves that decay too slowly
to be square-integrable on a line away from the sources. We introduce an inner
product, arising directly from Green's second theorem, to form a Hilbert space
of these waves and present examples of its computation.1 c 2005 Wiley Peri-
odicals, Inc.
1 Introduction
Consider the scattering problem governed by the Helmholtz equation
(1.1) + k2
(1 + q) = 0
in two dimensions for a scatterer q L2
(D) supported in a compact domain D in
the half-plane above the x-axis. A function u : R2

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

Collections: Mathematics; Computer Technologies and Information Sciences