Time-parallel iterative methods for parabolic PDES: Multigrid waveform relaxation and time-parallel multigrid

Conference · Sat Dec 31 04:00:00 EST 1994

OSTI ID:219578

Vandewalle, S ^[1]

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1. Caltech, Pasadena, CA (United States)

Time-stepping methods for parabolic partial differential equations are essentially sequential. This prohibits the use of massively parallel computers unless the problem on each time-level is very large. This observation has led to the development of algorithms that operate on more than one time-level simultaneously; that is to say, on grids extending in space and in time. The so-called parabolic multigrid methods solve the time-dependent parabolic PDE as if it were a stationary PDE discretized on a space-time grid. The author has investigated the use of multigrid waveform relaxation, an algorithm developed by Lubich and Ostermann. The algorithm is based on a multigrid acceleration of waveform relaxation, a highly concurrent technique for solving large systems of ordinary differential equations. Another method of this class is the time-parallel multigrid method. This method was developed by Hackbusch and was recently subject of further study by Horton. It extends the elliptic multigrid idea to the set of equations that is derived by discretizing a parabolic problem in space and in time.

• Research Organization: Front Range Scientific Computations, Inc., Boulder, CO (United States); USDOE, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
• OSTI ID: 219578
• Report Number(s): CONF-9404305--Vol.2; ON: DE96005736
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
CALCULATION METHODS
ITERATIVE METHODS
PARALLEL PROCESSING
PARTIAL DIFFERENTIAL EQUATIONS