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.
Keywords:
block element method, boundary-value problem, Helmholtz equation, pseudo-differential equations.
Citation:
V. A. Babeshko, O. V. Evdokimova, O. M. Babeshko, “Investigation of the three-dimensional Helmholtz equation for a wedge using the block element method”, Prikl. Mekh. Tekh. Fiz., 62:5 (2021), 15–21; J. Appl. Mech. Tech. Phys., 62:5 (2021), 717–722
\Bibitem{BabEvdBab21}
\by V.~A.~Babeshko, O.~V.~Evdokimova, O.~M.~Babeshko
\paper Investigation of the three-dimensional Helmholtz equation for a wedge using the block element method
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2021
\vol 62
\issue 5
\pages 15--21
\mathnet{http://mi.mathnet.ru/pmtf105}
\crossref{https://doi.org/10.15372/PMTF20210502}
\elib{https://elibrary.ru/item.asp?id=46709895}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2021
\vol 62
\issue 5
\pages 717--722
\crossref{https://doi.org/10.1134/S0021894421050023}
Linking options:
https://www.mathnet.ru/eng/pmtf105
https://www.mathnet.ru/eng/pmtf/v62/i5/p15
This publication is cited in the following 1 articles:
Vladimir A. Babeshko, Olga V. Evdokimova, Olga M. Babeshko, Advanced Structured Materials, 186, Deformation and Destruction of Materials and Structures Under Quasi-static and Impulse Loading, 2023, 29
Citation in format AMSBIB
Contact us: