COMPUTATIONAL ASPECTS OF SOLVING GRID EQUATIONS ON GRAPHICS ACCELERATORS

Abstract

To predict emergencies and irreversible consequences of human activities, scientists use
mathematical modeling. When an emergency occurs, it is very important to minimize the decisionmaking
time. The development of the project solution can be based on the forecast of changes in
the modeled process. In the numerical solution of problems of hydrophysics and biological kinetics,
it becomes necessary to develop effective methods for solving systemic equations of large dimension
with a non-self-adjoint operator. The large volume of processed information and the
complexity of computations necessitate the use of computational clusters, which include video
adapters to increase the performance of the computing system and the speed of information processing.
The aim of the research is to develop a solution for a module that implements the algorithm
of the system of linear algebraic equations (SLAE) by the modified alternative triangular
iterative method (MATM) (self-adjoint and non-self-adjoint case) using NVIDIA CUDA technology.
A method for decomposition of the computational domain in a three-dimensional case is described.
A graph model of a parallel pipeline computational process is proposed, focused on the
GPU (Graphics Processing Unit). To determine the two-dimensional configuration of flows in the
computational unit, when performing one step of one step, the MATM is minimal. The studies have
shown that the choice of the method of decomposition of the computational domain in the form of
parallelepipeds must be performed taking into account the architecture of the video adapter. The
developed algorithm and software module make it possible to more effectively use the computational
resources of the GPU used to solve computationally laborious problems of hydrophysics.