Combined MPI+threads parallel implementation of the block method for heat-transfer simulation in structurally inhomogeneous media

Combined MPI+threads parallel algorithms are developed to approximate the solutions of the nonstationary heat conductivity equation with phase transition by the analytical block method. The block method is based on the approximation of the solution to a boundary value problem by the special functions that are the fundamental solutions of the Helmholtz equation. As a result, there appear block systems of linear algebraic equations with block sparse structures and dense submatrices. Intensive computations with dense submatrices are parallelized on the basis of threads with the use of shared memory. Relatively independent computations with block sparse structures are parallelized on distributed memory with the aid of MPI. Such a combined approach to the organization of parallel computing allows one to efficiently use the heterogeneous memory structure in the modern cluster systems.