# Numerical simulation of scattering of acoustic waves by inelastic bodies using hypersingular boundary integral equation

## Abstract

A numerical method for solving a problem of diffraction of acoustic waves by system of solid and thin objects based on the reduction the problem to a boundary integral equation in which the integral is understood in the sense of finite Hadamard value is proposed. To solve this equation we applied piecewise constant approximations and collocation methods numerical scheme. The difference between the constructed scheme and earlier known is in obtaining approximate analytical expressions to appearing system of linear equations coefficients by separating the main part of the kernel integral operator. The proposed numerical scheme is tested on the solution of the model problem of diffraction of an acoustic wave by inelastic sphere.

- Authors:

- Moscow State Technical University of Radio Technics, Electronics, and Autumatics, Vernadsky Prospect 78, Moscow, 119454 (Russian Federation)
- Lomonosov Moscow State University, Moscow, 119991 (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22391082

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 1648; Journal Issue: 1; Conference: ICNAAM-2014: International Conference on Numerical Analysis and Applied Mathematics 2014, Rhodes (Greece), 22-28 Sep 2014; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; COMPUTERIZED SIMULATION; DIFFRACTION; INTEGRAL EQUATIONS; INTEGRALS; KERNELS; MATHEMATICAL SOLUTIONS; SOLIDS; SOUND WAVES; SPHERES

### Citation Formats

```
Daeva, S.G., and Setukha, A.V.
```*Numerical simulation of scattering of acoustic waves by inelastic bodies using hypersingular boundary integral equation*. United States: N. p., 2015.
Web. doi:10.1063/1.4912614.

```
Daeva, S.G., & Setukha, A.V.
```*Numerical simulation of scattering of acoustic waves by inelastic bodies using hypersingular boundary integral equation*. United States. doi:10.1063/1.4912614.

```
Daeva, S.G., and Setukha, A.V. Tue .
"Numerical simulation of scattering of acoustic waves by inelastic bodies using hypersingular boundary integral equation". United States.
doi:10.1063/1.4912614.
```

```
@article{osti_22391082,
```

title = {Numerical simulation of scattering of acoustic waves by inelastic bodies using hypersingular boundary integral equation},

author = {Daeva, S.G. and Setukha, A.V.},

abstractNote = {A numerical method for solving a problem of diffraction of acoustic waves by system of solid and thin objects based on the reduction the problem to a boundary integral equation in which the integral is understood in the sense of finite Hadamard value is proposed. To solve this equation we applied piecewise constant approximations and collocation methods numerical scheme. The difference between the constructed scheme and earlier known is in obtaining approximate analytical expressions to appearing system of linear equations coefficients by separating the main part of the kernel integral operator. The proposed numerical scheme is tested on the solution of the model problem of diffraction of an acoustic wave by inelastic sphere.},

doi = {10.1063/1.4912614},

journal = {AIP Conference Proceedings},

number = 1,

volume = 1648,

place = {United States},

year = {Tue Mar 10 00:00:00 EDT 2015},

month = {Tue Mar 10 00:00:00 EDT 2015}

}

DOI: 10.1063/1.4912614

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