A rigorous and numerically efficient approach, based on the Analytical Regularization Method, has been developed for the Dirichlet scalar diffraction problem of a smooth arbitrarily shaped open screen of revolution. The initial integral equation of the first kind is transformed so that the integral kernel is decomposed into a singular canonical part and a smooth remainder. Then the technique of dual series equations involving Jacoby polynomials reduces the problem to the infinite system of linear algebraic equations of the second kind. This provides desired solution accuracy depending on the truncation number alone. The numerical tests are presented for an open prolate spheroid and some open screens obtained by the revolution of the “Cassini Oval” and ”Pascal Lima¸con” curves. A high accuracy, efficiency and potential of the approach are shown.
|Number of pages||20|
|Journal||International electronic journal of pure and applied mathematics|
|Publication status||Published - 2011|
- analytical regularization
- scalar wave diffraction
- open arbitrarily shaped screen of revolution
- Dirichlet problem
Panin, S. B., Smith, P. D., Vinogradova, E. D., Tuchkin, Y. A., & Vinogradov, S. S. (2011). Analytical regularization of the Dirichlet diffraction problem for screen of revolution. International electronic journal of pure and applied mathematics, 3(4), 289-308.