Parallel framework for Dynamic Domain Decomposition of Data Assimilation problems a case study on Kalman Filter algorithm. (arXiv:2203.16535v1 [cs.LG])

We focus on Partial Differential Equation (PDE) based Data Assimilatio
problems (DA) solved by means of variational approaches and Kalman filter
algorithm. Recently, we presented a Domain Decomposition framework (we call it
DD-DA, for short) performing a decomposition of the whole physical domain along
space and time directions, and joining the idea of Schwarz’ methods and
parallel in time approaches. For effective parallelization of DD-DA algorithms,
the computational load assigned to subdomains must be equally distributed.
Usually computational cost is proportional to the amount of data entities
assigned to partitions. Good quality partitioning also requires the volume of
communication during calculation to be kept at its minimum. In order to deal
with DD-DA problems where the observations are nonuniformly distributed and
general sparse, in the present work we employ a parallel load balancing
algorithm based on adaptive and dynamic defining of boundaries of DD — which
is aimed to balance workload according to data location. We call it DyDD. As
the numerical model underlying DA problems arising from the so-called
discretize-then-optimize approach is the constrained least square model (CLS),
we will use CLS as a reference state estimation problem and we validate DyDD on
different scenarios.



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