Parallel algorithms of solving the Poisson equation using oblique cross grids in backward-facing step domains

In problems of hydrodynamics for incompressible fluid, the procedure of solving the Poisson equation to determine the pressure is a main computing unit. The paper suggests a parallel implementation of the fictitious domain method for the Poisson equation in a three-dimensional backward-facing step domain. This method is based on the parallel realization of a fast algorithm for solving the Poisson equation in a parallelepiped. Some standard methods of solving this equation on the basis of the PETSc package are also considered. A comparative analysis of these two approaches is discussed using the numerical results obtained on a multiprocessor complex named “Lomonosov”.