Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 91, Issue 10, Pages 1045-1072Publisher
WILEY-BLACKWELL
DOI: 10.1002/nme.4302
Keywords
acoustic scattering; combined field integral equations; pseudo-differential operators
Funding
- NSF
- AFOSR
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1008631, 1251859] Funding Source: National Science Foundation
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This text introduces the following: (1) new regularized combined field integral equations (CFIE-R) for frequency-domain sound-hard scattering problems; and (2) fast, high-order algorithms for the numerical solution of the CFIE-R and related integral equations. Similar to the classical combined field integral equation (CFIE), the CFIE-R are uniquely-solvable integral equations based on the use of single and double layer potentials. Unlike the CFIE, however, the CFIE-R utilize a composition of the double-layer potential with a regularizing operator that gives rise to highly favorable spectral propertiesthus making it possible to produce accurate solutions by means of iterative solvers in small numbers of iterations. The CFIE-R-based fast high-order integral algorithms introduced in this text enable highly accurate solution of challenging sound-hard scattering problems, including hundred-wavelength cases, in single-processor runs on present-day desktop computers. A variety of numerical results demonstrate the qualities of the numerical solvers as well as the advantages that arise from the new integral equation formulation. Copyright (c) 2012 John Wiley & Sons, Ltd.
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