The work presents a parallel symbolic tridiagonal matrix algorithm for a two-dimensional mathematical model of pressure distribution in an oil-containing fractured formation. In the integration domain with a uniform spatial step (macrogrid) covering the oil formation, a cell has been identified in which calculations need to be clarified (a cluster of wells). To do this, a finer partition is implemented in the dedicated macrocell—a microgrid. The pressure values in the macrocell nodes are calculated from the balanced equations obtained from the classical tridiagonal matrix algorithm. This leads to the need to solve the Dirichlet problem on a microgrid. The computational algorithm is based on a tridiagonal matrix algorithm modified by a polynomial representation of the desired grid function and some other quantities. This allows finding the exact pressure values in the microgrid nodes. To speed up the calculations, the MPI parallel computing technology is used and the principle of geometric parallelism is implemented. Calculation series of the pressure distribution in an oil-containing fractured formation has been performed at different values of absolute permeability, the results correspond to the physical processes in formations of the such type. The analysis of the developed parallel algorithm has been carried out; speedup by 10 times has been achieved using 36 processes. In the future, such a construction of the parallel algorithm will significantly speed up calculations in the study of oil formations of a more complex structure with a large number of well clusters.
R. M. Uzyanbaev (2025) studied this question.