Asynchronous domain decomposition methods for continuous casting problem. (English) Zbl 1023.65102
Authors’ abstract: Two asynchronous domain decomposition methods (which appear to be a two-stage Schwarz alternating algorithms) to solve the finite difference schemes approximating dynamic continuous casting problem are theoretically and numerically studied. Fully implicit and semi-implicit (implicit for the diffusion operator while explicit for the nonlinear convective term) finite difference schemes are considered. Unique solvability of the finite difference schemes as well as a monotone dependence of the solution on the right-hand side (the so-called comparison theorem) are proved. Geometric rate of convergence for the iterative methods is investigated, the comparison theorem being the main tool of this study. Numerical results are included and analyzed.
Reviewer: Song Jiang (Beijing)
MSC:
| 65M55 | Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs |
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
| 35K55 | Nonlinear parabolic equations |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 80M20 | Finite difference methods applied to problems in thermodynamics and heat transfer |
Keywords:
continuous casting problem; finite difference scheme; domain decomposition; finite-dimensional inclusion; asynchronous iteration; parallel solution; Schwarz alternating algorithms; convergence; comparison theorem; numerical resultsReferences:
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