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TW 369
Jan Van lent and Stefan Vandewalle
Multigrid Methods for Implicit Runge-Kutta and
Boundary Value Method Discretizations of Parabolic PDEs
Abstract
Sophisticated high order time discretization methods, such as implicit Runge--Kutta and boundary value methods, are often disregarded when solving time dependent partial differential equations, despite several appealing properties. This is mainly because it is considered hard to develop efficient methods for the more complex linear systems involved. We show here that for implicit Runge--Kutta and boundary value method discretizations of time dependent parabolic problems, multigrid methods for the elliptic case can be extended in a straightforward way. The key to this approach is the use of a smoother that updates several unknowns at a spatial grid point simultaneously. Combination of the multigrid principle with both time stepping and waveform relaxation techniques are described, together with a convergence analysis. Numerical results are presented for the isotropic heat equation and a
report.pdf / mailto: S. Vandewalle