The most powerful method for solution of diffraction problems of acoustical, electromagnetic or seismic waves on curved surfaces is the method of integral equations. In the framework of this method the problem is reduced to solution of exact Fredholm's integral equations of first or second kind for wave field or its normal derivative taken on the scattered surface. For the pulsed wave fields, possessed the wide spectrum of wavelengths, this method is in essence the only one, which permits to obtain the solutions as in domains of short and long wavelengths as well as in the intermediate resonance domain. The approach to regularization of exact boundary integral Fredholm's equation is proposed in the report on ICSV10. This approach allows to calculate the scattered or diffracted pulsed wave field on strongly curvilinear surfaces for practically arbitrary geometry. Mathematically the essence of the method consists in a replacement of exact Fredholm's integral equations by their truncated analogues, in which the contributions of geometrically shadowed areas are eliminated. This approach has a deep physical sense and allows to obtain the correct solutions when the direct numerical solution of exact integral equations leads to unstable results.
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