Scalable in Time Algorithms for Large Scale Predictive Science

We address the design and development of innovative mathematical models for Predictive Science simulations described by Variational Data Assimilation (DA) methods tightly coupled with time-dependent Partial Differential Equations (PDEs). The result is a PDE-based variational problem that is extremely large scale. The innovation refers to the simultaneous introduction of space-andtime decomposition approaches, consisting of Parallel in Time (PinT)-based approaches for solving the PDEs and functional decomposition for solving the Variational DA model; finally, domain is decomposed both along the space and the time dimension. The core of our approach is that the DA model acts as coarse-propagator/predictor for local PDEs, by providing the background values for the local initial conditions. The main outcome of this approach is that, in contrast to other PinT-based approaches, local solvers run concurrently, so that the resulting algorithm only requires exchange of boundary conditions between adjacent sub-domains. This work is carried on in collaboration with E. Constantinescu (ANL) and L. Carracciuolo (CNR-IT).