Title: Waveform relaxation with fast direct methods as preconditioner
Authors: Simoens, Jo ×
Vandewalle, Stefan #
Issue Date: 2000
Publisher: SIAM
Series Title: SIAM Journal on Scientific Computing vol:21 issue:5 pages:1755-1773
Abstract: For a restricted class of parabolic PDEs one can devise a practical numerical solver
with a parallel complexity that is theoretically optimal. The method uses a multidimensional FFT
to decouple the unknowns in the spatial domain into independent scalar ODEs. These are discretized
to give recurrence relations in the time dimension solved by parallel cyclic reduction. This is the
FFT/CR algorithm. We discuss the use of FFT/CR as a preconditioner to iteratively solve more
general parabolic PDEs. This approach naturally leads to a waveformrelaxation scheme. Waveform
relaxation was developed as an iterative method for solving large systems of ODEs. It is the
continuous-in-time analogue of stationary iterative methods for linear algebraic equations. Using the
FFT/CR solver as a preconditioner preserves most of the potential for concurrency that accounts
for the attractiveness of waveformrelaxation with simple preconditioners like Jacobi or red-black
Gauss–Seidel, while showing an important advantage: the convergence rate of the resulting iteration
is independent of the mesh size used in the spatial discretization. The method can be accelerated by
applying an appropriate scaling of the systemb efore preconditioning.
ISSN: 1064-8275
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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