Exact integration of polynomial-exponential products with application to wave-based numerical methods
Exact integration of polynomial-exponential products with application to wave-based numerical methods
Wave-based numerical methods often require to integrate products of polynomials and exponentials. With quadrature methods, this task can be particularly expensive at high frequencies as large numbers of integration points are required. This paper presents a set of closed-form solutions for the integrals of polynomial-exponential products in two and three dimensions.
These results apply to arbitrary polygons in two dimensions, and for arbitrary polygonal surfaces or polyhedral volumes in three dimensions. Quadrature methods are therefore not required for this class of integrals that can be evaluated quickly and exactly.
wave-based numerical methods, quadrature, highly oscillatory integrals
237-246
Gabard, G.
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7
2009
Gabard, G.
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7
Gabard, G.
(2009)
Exact integration of polynomial-exponential products with application to wave-based numerical methods.
Communications in Numerical Methods in Engineering, 25 (3), .
(doi:10.1002/cnm.1123).
Abstract
Wave-based numerical methods often require to integrate products of polynomials and exponentials. With quadrature methods, this task can be particularly expensive at high frequencies as large numbers of integration points are required. This paper presents a set of closed-form solutions for the integrals of polynomial-exponential products in two and three dimensions.
These results apply to arbitrary polygons in two dimensions, and for arbitrary polygonal surfaces or polyhedral volumes in three dimensions. Quadrature methods are therefore not required for this class of integrals that can be evaluated quickly and exactly.
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Published date: 2009
Keywords:
wave-based numerical methods, quadrature, highly oscillatory integrals
Organisations:
Acoustics Group
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Local EPrints ID: 145525
URI: http://eprints.soton.ac.uk/id/eprint/145525
ISSN: 1069-8299
PURE UUID: 73d0c811-9888-4b22-a598-2131726a5401
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Date deposited: 19 Apr 2010 09:42
Last modified: 14 Mar 2024 00:51
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G. Gabard
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