On the Use of Phase-Integral Methods in Two-State Scattering Problems

1981 ◽  
Vol 23 (6) ◽  
pp. 1096-1103 ◽  
Author(s):  
Anders Bárány ◽  
D S F Crothers
Keyword(s):  
Scattering Problems ◽  
Integral Methods ◽  
Phase Integral

An Introduction to Phase‐Integral Methods

Physics Today ◽  
1963 ◽  
Vol 16 (8) ◽  
pp. 58-58 ◽  
Author(s):  
J. Heading ◽  
George Weiss
Keyword(s):  
Integral Methods ◽  
Phase Integral

scholarly journals Long wave transmission, treated by phase integral methods

1932 ◽  
Vol 137 (831) ◽  
pp. 158-173 ◽  
Keyword(s):  
Transition Region ◽  
Mathematical Analysis ◽  
Wave Transmission ◽  
Upper Atmosphere ◽  
Conducting Layer ◽  
Electronic Density ◽  
Integral Methods ◽  
The Earth ◽  
Long Wave ◽  
Phase Integral

The effect of a sharply defined upper conducting layer in guiding long wireless waves round the earth has been considered by G. N. Watson, who gives a very comprehensive mathematical analysis of this case. Recent investigations of the upper Kennelly Heaviside layer by many investigators in England, America, Germany, etc., leave no doubt that the ionised conducting layer in the upper atmosphere is not sharply defined and the transition region from zero to maximum electronic density and conductivity may comprise many wave-lengths of the wave consider.

scholarly journals Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering

Acta Numerica ◽  
2012 ◽  
Vol 21 ◽  
pp. 89-305 ◽  
Author(s):  
Simon N. Chandler-Wilde ◽  
Ivan G. Graham ◽  
Stephen Langdon ◽  
Euan A. Spence
Keyword(s):  
High Frequency ◽  
Recent Progress ◽  
Design Analysis ◽  
Boundary Integral ◽  
Original Research ◽  
Scattering Problems ◽  
Asymptotic Boundary ◽  
Boundary Integral Methods ◽  
Integral Methods ◽  
Highly Oscillatory

In this article we describe recent progress on the design, analysis and implementation of hybrid numerical-asymptotic boundary integral methods for boundary value problems for the Helmholtz equation that model time harmonic acoustic wave scattering in domains exterior to impenetrable obstacles. These hybrid methods combine conventional piecewise polynomial approximations with high-frequency asymptotics to build basis functions suitable for representing the oscillatory solutions. They have the potential to solve scattering problems accurately in a computation time that is (almost) independent of frequency and this has been realized for many model problems. The design and analysis of this class of methods requires new results on the analysis and numerical analysis of highly oscillatory boundary integral operators and on the high-frequency asymptotics of scattering problems. The implementation requires the development of appropriate quadrature rules for highly oscillatory integrals. This article contains a historical account of the development of this currently very active field, a detailed account of recent progress and, in addition, a number of original research results on the design, analysis and implementation of these methods.

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