On an algorithm for resolving spatial structures with internal non-matching boundaries

Title	On an algorithm for resolving spatial structures with internal non-matching boundaries
Authors	I. M. Gubaydullin^{1, 2}, I. R. Yanglyaev^{1, 3}, Y. A. Poveshchenko⁴, V. O. Podryga^{4, 5}, O. S. Yazovtseva^{1, 3} ¹USPTU ²IPC UFRC RAS ³National Research Mordovian State University ⁴KIAM ⁵MADI
Annotation	The work presents an algorithm for the direct resolution of domain structures with internal non-matching boundaries. A grid with a coarse spatial partition (a macrogrid with macrocells) is organized in the integration area, and grids with a finer spatial step (microgrids with microcells) are built inside some of its cells for detailed computations. The boundaries of macrocells with adjoining microcells are non-matching in the steps of spatial grids. The symbolic tridiagonal matrix algorithm (TDMA) is implemented on microgrids, a modification of the classical tridiagonal matrix algorithm, the main difference of which is in the polynomial representation of the grid function, the TDMA coefficients and the residual. The polynomials depend on the function values at the nodes of the decomposed macrocells. To coupling solutions on non-matching boundaries, preconditioners are used to preserve the properties of self-conjugacy, sign-definiteness, and monotonicity of the complete operator of the boundary value problem.
Keywords	mathematical modeling, two-phase filtration, tridiagonal matrix algorithm, mortar grids, piezoconductivity equation, fractured-porous medium, carbonate reservoir.
Citation	Gubaydullin I. M., Yanglyaev I. R., Poveshchenko Y. A., Podryga V. O., Yazovtseva O. S. ''On an algorithm for resolving spatial structures with internal non-matching boundaries'' [Electronic resource]. Mathematical modeling, numerical methods, and software systems: Collection of materials from the 12th All‑Russian Scientific Youth School‑Seminar named after E. V. Voskresensky (Saransk, July 21–24, 2026). - pp. 61-63. Available at: https://conf.svmo.ru/files/2026/papers/paper74.pdf. - Date of access: 25.09.2026.

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On an algorithm for resolving spatial structures with internal non-matching boundaries

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