High Oscillating Integral Algorithm Research And Its Application In Electromagnetic Calculation

The problem of numerical integration of highly oscillatory functions consists in many fields, such as quantum mechanics, signal processing, electromagnetic calculation, etc. Last decades witnessed a fast develop-ment of numerical methods of highly oscillatory integrals, and many new methods have been developed, such as Filon-type method, Levin-type method, complex integration method, etc. The innovations of this thesis are the asymptotic expansion of a kind of Bessel transformation and caculating Sommerfeld intergral and Pollaczek integral with the Filon-type method. The asymptotic expansion of Bessel transformation over semiaxis is based on Iserles’methodology with the use of some properties of Bessel function’s derivatives. Generalized Sommerfeld integrals, which can be encountered in non-destructive eddy current testing, are calculated with the Filon-type method. Also, AET algorithm for Pollaczek integrals is modified with Filon-type method.The efficiency of these methods is testified by numerical examples.