About Packed Vector Block Elements of Boundary Value Problems
UDC
539.3EDN
CKFYPVDOI:
10.31429/vestnik-17-2-14-17Abstract
This paper provides an example of a Packed vector block element for boundary value problems described by a system of partial differential equations with constant coefficients in the classical domain. The developed method of constructing Packed, both scalar and vector block elements is applicable for solving boundary problems not only in quadrants, but also in such areas as a rectangle, a rectangular parallelepiped, cylinders with rectangular and acute-angle sections. Previously, this was not possible to implement. The variability of the parameters of the differential equations of the considered medium is achieved by introducing meshes with dimensions in which the coefficients of the differential equations can be considered constant. The Union of block elements is obtained by constructing the corresponding factor topologies of vector topological spaces. This approach makes it possible to design materials with variable properties, study wave processes in inhomogeneous media, and study the behavior of block structures with inhomogeneous blocks.
Keywords:
boundary value problems, packed scalar and vector block elements, Lame equationFunding information
Отдельные фрагменты работы выполнены в рамках реализации Госзадания Минобрнауки России на 2020 г. (проект FZEN-2020-0022), Южного научного центра РАН на 2020 г. (проект 00-20-13) № госрег. 01201354241, и при поддержке грантов Российского фонда фундаментальных исследований (проекты 19-41-230003, 19-41-230004, 19-48-230014, 18-08-00465, 18-01-00384, 18-05-80008).
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