Конференции ИВТ СО РАН

Abstracts

Numerical simulation problems of spreading and scattering processes of waves of various physical nature in unlimited areas with three-dimensional inclusions are considered.

For developing effective algorithms of numerical solving of such problems integral statements of these problems can be used. In this case solutions are searched in the form of integrals of potential type, defined on the inclusion boundary. They should satisfy corresponding equations for oscillations inside and outside the inclusion, and also to comply with conditions in infinite for the waves reflected from the inclusion. Unknown integrands (densities) are determined from contact (conjugation) conditions for wave fields on inclusion boundary.

At such approach there are no essential distinctions between interior and exterior boundary value problems as well as boundary-contact problems. Along with lowering of dimensions of initial problems it allows to reduce a quantity of required functions, and also to reduce the same problem to integral equations with various properties. In this work the solutions of initial problems are searched in a form of such combinations of integrals of potential type which allow to reduce them to two different weakly singular integral equations of I or II kind with one unknown density, each of which taken separately is equivalent to the initial problem. Approximate solutions of initial problems are searched by approximation of the mentioned integral equations by linear algebraic equation systems and their numerical solving. In this case for approximation of integral operators with power singularities in kernels the method of averaging of such kerns, coordinated with sampling step, is used, which allows to create rather simple and exact computational algorithms.

Outcomes of theoretical researches of the developed algorithms and computing experiments for three-dimensional diffraction (transmission) problems of acoustic, elastic and electromagnetic waves are described.

The work was carried out under financial support of the RFFI and FEB RAS (grants 08-01-00947, 09-I-P2-01).

Note. Abstracts are published in author's edition

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