MODIFICATION OF THE IMPLEMENTATION OF THE JACOBI METHOD IN SIMULATING SUPERDIFFUSION OF RADON ON RECONFIGURABLE COMPUTER SYSTEMS
Abstract
When studying natural objects, the problem of modeling complex systems with a structure that cannot be described by means of Euclidean geometry tools often arises, therefore, fractal geometry and the corresponding mathematical apparatus are used to represent them. So the model of radon transport in an inhomogeneous medium, using superdiffusion, displays real data more accurately than the classical one. An increase in the concentration of radon in the air is one of the signs of an approaching earthquake, which makes it necessary to simulate the propagation of this radioactive inert gas in real time. Reconfigurable computing systems have great potential for solving problems in real time, but the currently existing means for solving systems of linear equations have low efficiency due to the irregular structure of matrices obtained by discretizing the radon superdiffusion model using adaptive grids. The basic subgraph of the Jacobi method is transformed as follows: the input data is vectorized, the structure of the frame in which the value of one unknown is calculated is divided into several microframes, parallelizing the calculations in the first microframe, where the sum of the products of the matrix coefficients and the values of the unknowns from the previous iteration is performed. The results obtained are buffered for subsequent delivery to the second microframe, where the final processing and output of the iteration result takes place. The described approach allows to reduce equipment downtime when solving a system of linear equations with sparse irregular matrices, and gives a speed gain by 5–15 times in comparison with existing methods for solving linear system on reconfigurable computing systems.
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