THE GALERKIN METHOD FOR SOLVING THE SCALAR PROBLEM OF SCATTERING                                  BY AN OBSTACLE OF COMPLEX SHAPE

Derevyanchuk Ekaterina Dmitrievna, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), mmm@pnzgu.ru
Smol'kin Evgeniy Yur'evich, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), e.g.smolkin@hotmail.com
Tsupak Aleksey Aleksandrovich, Candidate of physical and mathematical sciences, associate professor, sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia), altsupak@yandex.ru

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Background. The aim of this work is to numerically study the scalar problem of scattering by an obstacle of complex shape consisting of solid bodies and infinitely thin acoustically soft screens.
Material and methods. The problem is considered in the quasiclassical statement; the original boundary value problem for the Helmholtz equation in unbounded space is reduced to a system of integral equations over bounded manifolds of dimension 2 and 3. To find the numerical solution to the problem of diffraction the Galerkin method is applied using finite piecewise constant basis functions.
Results. The projection method for solving the system of integral equations of the scalar diffraction problem was developed and implemented; several computational experiments were performed.
Conclusions. The proposed numerical method is an effective way to find approximate solutions to the scalar problems of diffraction on obstacles of complex shape; it can also be used to solve problems of a wider range.

scalar diffraction problem, integral equations, Galerkin method, basis functions, approximation condition

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