A scalable space-time domain decomposition approach for solving large-scale nonlinear regularized inverse ill-posed problems in 4D variational data assimilation

TL;DR

This paper introduces a scalable space-time domain decomposition method for large-scale 4D variational data assimilation, improving computational efficiency and scalability in solving complex inverse problems.

Contribution

It proposes a novel space-time domain decomposition algorithm that partitions both the solution and operators, enabling efficient large-scale 4D variational data assimilation.

Findings

Algorithm converges effectively in large-scale tests.

Significant reduction in computational complexity.

Demonstrated scalability on shallow water equation simulations.

Abstract

We develop innovative algorithms for solving the strong-constraint formulation of four-dimensional variational data assimilation in large-scale applications. We present a space-time decomposition approach that employs domain decomposition along both the spatial and temporal directions in the overlapping case and involves partitioning of both the solution and the operators. Starting from the global functional defined on the entire domain, we obtain a type of regularized local functionals on the set of subdomains providing the order reduction of both the predictive and the data assimilation models. We analyze the algorithm convergence and its performance in terms of reduction of time complexity and algorithmic scalability. The numerical experiments are carried out on the shallow water equation on the sphere according to the setup available at the Ocean Synthesis/Reanalysis Directory provided by Hamburg University.