THE ITERATION METHOD FOR SOLVING DIRECT AND INVERSE                                            TWO-DIMENSIONAL ACOUSTIC PROBLEMS

Evstigneev Roman Olegovich, Student, Penza State University (40 Krasnaya street, Penza, Russia), mmm@pnzgu.ru
Medvedik Mikhail Yur'evich, Candidate of physical and mathematical sciences, associate professor, sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia), _medv@mail.ru

517.3 517.9

Background. The interest in direct and inverse diffraction problems is caused by active development of radio devices and mechanisms. Of particular interest are the problems in the resonance bandwidth, when the regular methods do not work. In this case, scientists use the methods of volume singular equations. The aim of this work is to study the diffraction problem of an acoustic wave on a plane, namely to find an approximate solution of the Helmholtz equation for the full field of an acoustic wave and to develop a reconstruction algorithm of the material’s wave parameter.
Materials and methods. By using the Green’s function the boundary value problem of differential formulation is reduced to a volume singular equation. As opposed to the differential formulation of the problem, where the solution is found on the infinite domain, the integral equation is solved only in the figure.
Results. The authors present the solution results of the direct problem for different dimensions of computational grids and different wave numbers k, as well as the results of reconstruction of the wave number k from the known value of the acoustic field.
Conclusions. The authors suggest the method of the material’s wave parameter reconstruction. The method was tested at different frequencies and for different materials. The test results show good stability of body’s acoustic parameters reconstructtion.

integral equation, boundary value problem, Helmholtz equation, conjugate gradient method, numerical solution, diffraction problem.

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