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Low frequency acoustic and electromagnetic scattering
Affiliation:1. Department of Mathematics, University of Manitoba, Winnipeg, Canada;2. School of Mathematics and Statistics, The University of Sydney, Sydney, Australia;1. Argonne National Laboratory, Lemont, IL, USA;2. University of Kentucky, Lexington, KY, USA;3. Fermi National Accelerator Laboratory, Batavia, IL, USA;4. University of Virginia, Charlottesville, VA, USA;5. Oak Ridge National Lab, Oak Ridge, TN, USA;6. University of Michigan, Ann Arbor, MI, USA;7. University of Washington, Seattle, WA, USA;8. Johannes Gutenberg-Universität Mainz, Mainz, Germany;9. University of Massachusetts, Amherst, MA, USA;10. James Madison University, Harrisonburg, VA, USA;11. Shanghai Jiao Tong University, Shanghai, China;1. College of Civil Engineering, Tongji University, Shanghai, 200092, China;2. Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai, 200092, China;3. Department of Civil Engineering, The University of Hong Kong, Hong Kong, China
Abstract:This paper deals with two classes of problems arising from acoustics and electromagnetic scattering in the low frequency situations. The first class of problem involves solving the Helmholtz equation with Dirichlet boundary conditions on an arbitrary two-dimensional body whereas the second one is an interior-exterior interface problem with the Helmholtz equation in the exterior. Low frequency analysis shows that there are two intermediate problems shich solve the above problems to accuracy O(k2(logk)2) where k is the wave number. These solutions are more accurate than the simpler zero frequency approximations but require very little more work to compute. For the Dirichlet problem numerical examples are shown to verify our theoretical estimates.
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