МОДИФИКАЦИЯ РЕАЛИЗАЦИИ МЕТОДА ЯКОБИ ПРИ МОДЕЛИРОВАНИИ СУПЕРДИФФУЗИИ РАДОНА НА РЕКОНФИГУРИРУЕМЫХ ВЫЧИСЛИТЕЛЬНЫХ СИСТЕМАХ

Abstract

When studying natural objects, the problem of modeling complex systems with a structurethat cannot be described by means of Euclidean geometry tools often arises, therefore, fractalgeometry and the corresponding mathematical apparatus are used to represent them. So the modelof radon transport in an inhomogeneous medium, using superdiffusion, displays real data moreaccurately than the classical one. An increase in the concentration of radon in the air is one of thesigns of an approaching earthquake, which makes it necessary to simulate the propagation of thisradioactive inert gas in real time. Reconfigurable computing systems have great potential for solvingproblems in real time, but the currently existing means for solving systems of linear equationshave low efficiency due to the irregular structure of matrices obtained by discretizing the radonsuperdiffusion model using adaptive grids. The basic subgraph of the Jacobi method is transformedas follows: the input data is vectorized, the structure of the frame in which the value of oneunknown is calculated is divided into several microframes, parallelizing the calculations in thefirst microframe, where the sum of the products of the matrix coefficients and the values of theunknowns from the previous iteration is performed. The results obtained are buffered for subsequentdelivery to the second microframe, where the final processing and output of the iterationresult takes place. The described approach allows to reduce equipment downtime when solving asystem of linear equations with sparse irregular matrices, and gives a speed gain by 5–15 times incomparison with existing methods for solving linear system on reconfigurable computing systems.