Geodesic
Parallel algorithms of solving the Poisson equation using oblique cross grids in backward-facing step domains
Numerical methods and programming, Tome 14 (2013) no. 2, pp. 18-23.

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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”.
Keywords: gas dynamics; hydrodynamics; Poisson equation; method of fictitious components; parallel computing; MPI; PETSc. 
@article{VMP_2013_14_2_a7,
     author = {A. M. Ryazanov and S. A. Finogenov},
     title = {Parallel algorithms of solving the {Poisson} equation using oblique cross grids in backward-facing step domains},
     journal = {Numerical methods and programming},
     pages = {18--23},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2013_14_2_a7/}
}
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A. M. Ryazanov; S. A. Finogenov. Parallel algorithms of solving the Poisson equation using oblique cross grids in backward-facing step domains. Numerical methods and programming, Tome 14 (2013) no. 2, pp. 18-23. http://geodesic.mathdoc.fr/item/VMP_2013_14_2_a7/