Investigation of the Three-Dimensional Helmholtz Equation for a Wedge Using the block Element Method
V. A. Babeshko1,2, O. V. Evdokimova1, O. M. Babeshko2
1Southern Scientific Center, Russian Academy of Sciences, Rostov-on-Don, 344006, Russia
2Kuban State University, Krasnodar, 350040, Russia
Keywords: block element method, boundary-value problem, Helmholtz equation, pseudo-differential equations
Abstract
For boundary-value problems, the Helmholtz equations in wedge-shaped domains, it is shown that in packed block elements corresponding to the same boundary-value problem can be combined taking into account the type of boundary conditions, also forming a packed block element. The result is verified using another method. It is shown that in the presence of corner points in the domain in which the boundary-value problem is considered, combining block elements does not involve additional complications. It is found that since the solutions of some boundary-value problems in continuum mechanics and physics can be represented as a combination of solutions of boundary-value problems of the Helmholtz equation, this approach can be used to study more complex boundary-value problems and design materials with mosaic structure.
DOI: 10.1134/S0021894421050023
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