A SPACE-TIME MULTIGRID METHOD FOR PARABOLIC PARTIAL-DIFFERENTIAL EQUATIONS

We consider the solution of parabolic partial differential equations ( PDEs). In standard time-stepping techniques multigrid can be used as a n iterative solver for the elliptic equations arising at each discrete time step. By contrast, the method presented in this paper treats the whole of the space-time problem simultaneously. Thus the multigrid op erations of smoothing and coarse-grid correction are defined on all of the space-time variables of a given grid level. The method is charact erized by a coarsening strategy with prolongation and restriction oper ators which depend at each grid level on the degree of anisotropy of t he discretization stencil. Numerical results for the one- and two-dime nsional heat equations are presented and are shown to agree closely wi th predictions from Fourier mode analysis.