Ocean Data Assimilation achievements on HPC systems: experiments OceanVar in the Mediterranean Sea

We present a framework based on Domain Decomposition approach (we call it DD-framework), for solving Variational Data Assimilation problem. DD-framework involves a size reduction of the physical domain, a partitioning of the solution and a modification of the regularization functional describing the Variational DA problem. We provide a mathematical justification and we show a study of DD approach (in terms of numerical conditioning and in terms of time complexity). We present a project for the design of a DD- framework to OceanVAR software to effectively take advantage of the available High Performance Computing resources and to handle very big data. That was achieved using multi-level parallelism and scalability of the current and the next generation of leadership computing facility systems (multi processors, many cores and GPUs).