# On some numerical scheme of solving diffraction problem on open and closed screens

## Abstract

In the paper, the problem of diffraction on thin ideally conductive screens is reduced to vector hypersingular integral equation with integral treated in the sense of finite Hadamard value. An numerical scheme to solve the equation is introduced. The scheme is based on piecewise approximation of unknown function. The advantage of the scheme is that integral of singular part is reduced to contour integral which can be analytically calculated so numerical calculation are significantly accelerated. Several examples of resulting numerical experiments are given in comparison with known theoretical and experimental data.

- Authors:

- Skolkovo Institute of Science and Technology, Moscow Region, 143025 (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22391083

- 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; ANALYTICAL SOLUTION; APPROXIMATIONS; COMPARATIVE EVALUATIONS; DIFFRACTION; FUNCTIONS; INTEGRAL EQUATIONS; INTEGRALS; NUMERICAL SOLUTION; VECTORS

### Citation Formats

```
Ryzhakov, Gleb V.
```*On some numerical scheme of solving diffraction problem on open and closed screens*. United States: N. p., 2015.
Web. doi:10.1063/1.4912620.

```
Ryzhakov, Gleb V.
```*On some numerical scheme of solving diffraction problem on open and closed screens*. United States. doi:10.1063/1.4912620.

```
Ryzhakov, Gleb V. Tue .
"On some numerical scheme of solving diffraction problem on open and closed screens". United States.
doi:10.1063/1.4912620.
```

```
@article{osti_22391083,
```

title = {On some numerical scheme of solving diffraction problem on open and closed screens},

author = {Ryzhakov, Gleb V.},

abstractNote = {In the paper, the problem of diffraction on thin ideally conductive screens is reduced to vector hypersingular integral equation with integral treated in the sense of finite Hadamard value. An numerical scheme to solve the equation is introduced. The scheme is based on piecewise approximation of unknown function. The advantage of the scheme is that integral of singular part is reduced to contour integral which can be analytically calculated so numerical calculation are significantly accelerated. Several examples of resulting numerical experiments are given in comparison with known theoretical and experimental data.},

doi = {10.1063/1.4912620},

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: 10.1063/1.4912620

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