Parallel programming of boundary-valued problems for the Poisson and Helmholtz equations by a multigrid algorithm

Journal Article · Fri Sep 01 04:00:00 EDT 1995 · Programming and Computer Software

OSTI ID:244166

Mamedova, I G; Serebryakov, V A ^[1]

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1. Russian Academy of Sciences, Moscow (Russian Federation)

New iterative methods with complete and incomplete splitting of boundary conditions were developed and investigated. These methods were developed for the highly efficient numerical solution of the boundary-valued problems for the Stokes-type system with a small parameters. The numerical solution of these problems encounters, in addition to the singularity of a problem, some difficulties due to presence of the pressure and the continuity equation in the system, especially in the three-dimensional case. Thus, the development of iterative methods to solve the boundary-valued problem separately for velocity and pressure in each iteration becomes an important problem. The iterative methods used for numerical solution of these problems have an important feature that gives one an opportunity to split the boundary conditions and generate two separate problems: the Neumann problem for pressure and the Dirichlet-Neumann vector problem for velocity in the case of incomplete boundary condition splitting, or the Dirichlet scalar problems (for each velocity component in the Helmholtz equation) in the case of complete splitting. We should note the high convergence rates for these methods, which increase with a decrease in the parameter F, value.

• OSTI ID: 244166
• Journal Information: Programming and Computer Software, Journal Name: Programming and Computer Software Journal Issue: 5 Vol. 21; ISSN PCSODA; ISSN 0361-7688
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
BOUNDARY-VALUE PROBLEMS
ITERATIVE METHODS
MESH GENERATION
PARALLEL PROCESSING
POISSON EQUATION