TY - JOUR
T1 - High-order solutions of three-dimensional rough-surface scattering problems at high frequencies. I
T2 - The scalar case
AU - Reitich, F.
AU - Turc, C.
N1 - Funding Information:
Fernando Reitich gratefully acknowledges support from Air Force Office of Scientific Research (AFOSR) through contract number F49620-02-1-0052, from NSF through grant number DMS–0311763, and from the Army High Performance Computing Research Center (AHPCRC) under Army Research Laboratory cooperative agreement number DAAD19-01-2-0014.
Funding Information:
Effort sponsored by the Air Force Office of Scientific Research, Air Force Materials Command, USAF, under grant number F49620-02-1-0052, and by AHPCRC under the auspices of the Department of the Army, Army Research Laboratory cooperative agreement number DAAD19-01-2-0014. The US Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research, the Army Research Laboratory, or the US Government.
Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2005/2
Y1 - 2005/2
N2 - We present a new high-order numerical method for the solution of high-frequency scattering problems from rough surfaces in three dimensions. The method is based on the asymptotic solution of appropriate integral equations in the high-frequency regime, in a manner that bypasses the need to resolve the fields on the scale of the wavelength of radiation. Indeed, inspired by prior work in two dimensions, we seek a solution of the integral equation in the form of a slow modulation of the incoming radiation, and we choose a series expansion in inverse powers of the wavenumber to represent the unknown slowly varying envelope. As we show, this framework can be made to yield an efficiently computable recursion for the terms in the series to any arbitrary order. The resulting algorithms generally provide a very significant improvement over classical (e.g. Kirchhoff) approximations in both accuracy and applicability and they can, in fact, effectively produce results with full double-precision accuracy for configurations of practical interest and up to the resonance regime.
AB - We present a new high-order numerical method for the solution of high-frequency scattering problems from rough surfaces in three dimensions. The method is based on the asymptotic solution of appropriate integral equations in the high-frequency regime, in a manner that bypasses the need to resolve the fields on the scale of the wavelength of radiation. Indeed, inspired by prior work in two dimensions, we seek a solution of the integral equation in the form of a slow modulation of the incoming radiation, and we choose a series expansion in inverse powers of the wavenumber to represent the unknown slowly varying envelope. As we show, this framework can be made to yield an efficiently computable recursion for the terms in the series to any arbitrary order. The resulting algorithms generally provide a very significant improvement over classical (e.g. Kirchhoff) approximations in both accuracy and applicability and they can, in fact, effectively produce results with full double-precision accuracy for configurations of practical interest and up to the resonance regime.
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U2 - 10.1080/17455030500053393
DO - 10.1080/17455030500053393
M3 - Article
AN - SCOPUS:23044470287
SN - 1745-5030
VL - 15
SP - 1
EP - 16
JO - Waves in Random and Complex Media
JF - Waves in Random and Complex Media
IS - 1
ER -