Tiling optimization for the solution of two-dimensional time-dependent heat equation

Tiling optimization for the solution of the Dirichlet problem for the two-dimensional heat equation on computers with distributed memory is investigated. Estimates of the amount of communications and computations are obtained. The tiling optimization problem is reduced to the minimization of a function that explicitly expresses the dependence of the execution time on the tile size and the parameters of the target supercomputer – the dimension and size of the computing environment, processor performance, initialization time, and capacity of the communication channels.