Journal of Computational Physics
Computers & Mathematics with Applications
International Journal of Computer Mathematics
Applied Numerical Mathematics
A modified upwind difference domain decomposition method for convection--diffusion equations
Applied Numerical Mathematics
Parallel domain decomposition procedures of improved D-D type for parabolic problems
Journal of Computational and Applied Mathematics
An efficient S-DDM iterative approach for compressible contamination fluid flows in porous media
Journal of Computational Physics
HPCA'09 Proceedings of the Second international conference on High Performance Computing and Applications
Computational Mathematics and Mathematical Physics
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Domain decomposition algorithms for parallel numerical solution of parabolic equations are studied for steady state or slow unsteady computation. Implicit schemes are used in order to march with large time steps. Parallelization is realized by approximating interface values using explicit computation. Various techniques are examined, including a multistep second order explicit scheme and a one-step high-order scheme. We show that the resulting schemes are of second order global accuracy in space, and stable in the sense of Osher or in $L_{\infty }$. They are optimized with respect to the parallel efficiency.