A modified upwind difference domain decomposition method for convection--diffusion equations
Applied Numerical Mathematics
Optimized waveform relaxation methods for longitudinal partitioning of transmission lines
IEEE Transactions on Circuits and Systems Part I: Regular Papers - Special section on 2008 custom integrated circuits conference (CICC 2008)
SIAM Journal on Numerical Analysis
Optimized Domain Decomposition Methods for the Spherical Laplacian
SIAM Journal on Numerical Analysis
Optimized Schwarz Waveform Relaxation for the Primitive Equations of the Ocean
SIAM Journal on Scientific Computing
The Optimized Schwarz Method with a Coarse Grid Correction
SIAM Journal on Scientific Computing
Optimization of Schwarz waveform relaxation over short time windows
Numerical Algorithms
A mathematical analysis of optimized waveform relaxation for a small RC circuit
Applied Numerical Mathematics
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We study in this paper a new class of waveform relaxation algorithms for large systems of ordinary differential equations arising from discretizations of partial differential equations of advection reaction diffusion type. We show that the transmission conditions between the subsystems have a tremendous influence on the convergence speed of the waveform relaxation algorithms, and we identify transmission conditions with optimal performance. Since these optimal transmission conditions are expensive to use, we introduce a class of local transmission conditions of Robin type, which approximate the optimal ones and can be used at the same cost as the classical transmission conditions. We determine the transmission conditions in this class with the best performance of the associated waveform relaxation algorithm. We show that the new algorithm is well posed and converges much faster than the classical one. We illustrate our analysis with numerical experiments.