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.