A space-time multigrid method for parabolic partial differential equations. (English) Zbl 0828.65105

Horton, G.; Vandewalle, S.

SIAM J. Sci. Comput. 16, No. 4, 848-864 (1995).

The numerical solution of parabolic equations is considered. After the time discretization multigrid solvers can be used for the resulting elliptic equations. The method presented treats the whole of the space- time problem simultaneously.
The transfer operators (restriction and interpolation) depend at each grid level on the degree of anisotropy of the discretization stencil. Numerical results for the heat equation are presented and are shown to agree closely with predictions from Fourier mode analysis.

Reviewer: W.Heinrichs (Düsseldorf)

MSC:

65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M55	Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
65Y05	Parallel numerical computation
35K15	Initial value problems for second-order parabolic equations

Keywords:

space-time multigrid method; massively parallel computation; semicoarsening; numerical results; parabolic equations; heat equation