Abstract
Partitioned systems of ordinary differential equations are in qualitative terms characterized as monotonically max-norm stable if each sub-system is stable and if the couplings from one sub-system to the others are weak.
Each sub-system of the partitioned system may be discretized independently by the backward Euler formula using solution values from the other sub-systems corresponding to the previous time step. The monotone max-norm stability guarantees this discretization to be stable. This so-called decoupled implicit Euler method is ideally suited for parallel computers. With one or several sub-systems allocated to each processor, information only has to be exchanged after completion of a step but not during the solution of the nonlinear algebraic equations.
This paper considers strategies and techniques for partitioning a system into a monotonically max-norm stable system. It also presents error bounds to be used in controlling stepsize, relaxation between sub-systems and the validity of the partitioning. Finally a realistic example is presented.
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References
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© 1996 Springer-Verlag Berlin Heidelberg
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Skelboe, S. (1996). Integration of partitioned stiff systems of ordinary differential equations. In: Waśniewski, J., Dongarra, J., Madsen, K., Olesen, D. (eds) Applied Parallel Computing Industrial Computation and Optimization. PARA 1996. Lecture Notes in Computer Science, vol 1184. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62095-8_67
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DOI: https://doi.org/10.1007/3-540-62095-8_67
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