NUMERICAL TECHNIQUE OF PSEUDODIFFERENTIAL EQUATION SOLUTION IN A DIFFRACTION PROBLEM IN THE LAYERS CONNECTED THROUGH AN OPENING

Medvedik Mikhail Yuryevich, PhD in Mathematics, associate professor, sub-department of mathematics and supercomputer modeling, Penza State University
Rodionova Irina Anatolyevna, assistant professor, sub-department of mathematics and supercomputer modeling, Penza State University
Smirnov Yury Gennadyevich, Doctor of Science (in Mathematics), professor, head of sub-department of mathematics and supercomputer modeling, Penza State University

517.6

The paper is devoted to the solvability of boundary value problem of diffraction for Maxwell equations in layers connected though a hole. The layers are formed by three infinitely thin and perfectly conducting parallel planes. Electromagnetic parameters can be different in the layers. Radiation conditions by Werner-Sveshnikov are used at the infinity. Method of Green functions is applied for reduction of boundary value problem to the pseudodifferential equation on a hole in Sobolev spaces. Fredholm property is established. The problem belongs to the class of problems of connection of volumes via a hole.

boundary value problem, electromagnetic scattering, integral equations, numerical method.