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A.Lapin, J.Pieska

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On the parallel domain decomposition algorithms for
time-dependent problems

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*## (Lobachevskii Journal of Mathematics,

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Vol.10, pp.27-44)

Several new finite-difference schemes for a nonlinear
convection-diffusion problem are constructed and numerically studied.
These schemes are constructed on the basis of non-overlapping domain
decomposition and predictor-corrector approach.
We construct the predictor-corrector schemes for a nonlinear
problem, which serves as a mathematical model for the continuous
casting problem, where implicit and characteristic grid approximations
of the continuous casting problem have been theoretically and
experimentally studied). We use different non-overlapping
decomposition of a domain, with cross-points and angles, schemes with
grid refinement in time in some subdomains. All proposed algorithms
are extensively numerically tested and are founded stable and accurate
under natural assumptions for time and space grid steps. Also, the
parallel algorithms scales well as the number of processors increases.

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