A first step toward a PGD-based time parallelisation strategy
DOI:
https://doi.org/10.13052/17797179.2012.714985Keywords:
model reduction, Proper Generalised Decomposition, parametric models, separated representation, time parallelisationAbstract
This paper proposes a new method for solving the heat transfer equation based on a parallelisation in time of the computation. A parametric multidimensional model is solved within the context of the Proper Generalised Decomposition (PGD). The initial field of temperature and the boundary conditions of the problem are treated as extra-coordinates, similar to time and space. Two main approaches are exposed: a “full” parallelisation based on an off-line parallel computation and a “partial” parallelisation based on a decomposition of the original problem. Thanks to an optimised overlapping strategy, the reattachment of the local solutions at the interfaces of the time subdomains can be improved. For large problems, the parallel execution of the algorithm provides an interesting speedup and opens new perspectives regarding real-time simulation.
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