Solution to the problem of thermal conductivity in a two-dimensional formulation on a graphics processing unit using parallel computing

Subject: technology and algorithms of parallel programming. Objective: to compare the execution speed of a sequential algorithm on a central processor with a parallel algorithm on a graphics processor when solving a two-dimensional thermal conductivity problem. Methods: the Crank Nicholson method modified by the author for solving the problem of two-dimensional thermal conductivity on a graphics processor. Research results: 1. The solution of the two-dimensional thermal conductivity problem according to the Crank Nicholson scheme is not absolutely parallel and the maximum possible acceleration is not achieved 2. With a matrix dimension of 16 by 16 and single precision, the execution time on the GPU turned out to be 1.32 1.72 times faster than on the CPU. With a 32 by 32 matrix dimension, the execution time on the GPU turned out to be 3.66 6.07 times faster than on the CPU. 3. When calculating with double precision, the greatest acceleration is observed at 71.89 with 10 iterations of calculation, if there are more than 104 iterations, then the acceleration in calculations on a GPU with double precision approaches calculations with single precision.