DD-DA PinT-based model: A Domain Decomposition approach in space and time, based on Parareal, for solving the 4D-Var Data Assimilation model

TL;DR

This paper introduces a novel domain decomposition method combining parallel-in-time techniques with 4D-Var data assimilation, enhancing accuracy, efficiency, and scalability in solving complex PDE-based forecasting models.

Contribution

It develops a new mathematical framework for a DD PinT-based approach that integrates data assimilation as a predictor, with convergence analysis and improved computational performance.

Findings

Improved accuracy of local solutions through data assimilation as a predictor.

Enhanced computational efficiency via parallel fine and coarse solvers.

Reduced data movement leading to better scalability.

Abstract

We present the mathematical framework of a Domain Decomposition (DD) aproach based on Parallel-in-Time methods (PinT-based approach) for solving the 4D-Var Data Assimilation (DA) model. The main outcome of the proposed DD PinT-based approach is: 1. DA acts as coarse/predictor for the local PDE-based forecasting model, increasing the accuracy of the local solution. 2. The fine and coarse solvers can be used in parallel, increasing the efficiency of the algorithm.3. Data locality is preserved and data movement is reduced, increasing the software scalability. We provide the mathematical framework including convergence analysis and error propagation.