Proper Orthogonal Decomposition In Decoupling Large Dynamical Systems
We investigate the proper orthogonal decomposition (POD) as a powerfull tool in decoupling dynamical systems suitable for parallel computing. POD method is well known to be useful method for model reduction applied to dynamical system having slow and fast dynamics. It is based on snapshot of previous time iterate solutions that allows to generate a low dimension space for the approximation of the solution.Here we focus on the parallelism potential with decoupling the dynamical system into subsystems spread between processors. The non local to the processor sub-systems are approximated by POD leading to have a number of unknowns smaller than the original system on each processor. We provide a mathematical analysis to obtain a criterion on the error behavior in using POD for decoupling dynamical systems. Therefore, we use this result to verify when the reduced model is still appropriated for the system in order to update the basis. Several examples show the efficient gain in term of computational effort of the present method.
Key wordsPOD reduced-order modelling dynamical systems parallel computing
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