On the integration of highly oscillatory functions: Algorithms based on critical points and semi-periodic zones in scalar diffraction (Q5934194)
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scientific article; zbMATH DE number 1606128
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the integration of highly oscillatory functions: Algorithms based on critical points and semi-periodic zones in scalar diffraction |
scientific article; zbMATH DE number 1606128 |
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On the integration of highly oscillatory functions: Algorithms based on critical points and semi-periodic zones in scalar diffraction (English)
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19 June 2001
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highly oscillatory functions
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diffraction integrals
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electromagnetic waves
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semi-periodic zones
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critical points
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Two methods for the computation of the diffraction integrals appearing in the scalar approximation of the theory of diffraction of electromagnetic waves are developed. The algorithms are based on two main ideas.NEWLINENEWLINENEWLINEFirst, the division of the aperture according to semi-periodic zones isolates the integrand oscillations and allows the computation of each semi-periodic zone contribution with only a few evaluations of the integrand.NEWLINENEWLINENEWLINESecond, the relations between semi-periodic zones and the critical points provides criteria for selecting the zones really contributing to the diffracted field.
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