A Decomposition of the Tikhonov Regularization Functional Oriented to Exploit Hybrid Multilevel Parallelism

We introduce a decomposition of the Tikhonov Regularization (TR) functional which split this operator into several TR functionals, suitably modified in order to enforce the matching of their solutions. As a consequence, instead of solving one problem we can solve several problems reproducing the initial one at smaller dimensions. Such approach leads to a reduction of the time complexity of the resulting algorithm. Since the subproblems are solved in parallel, this decomposition also leads to a reduction of the overall execution time. Main outcome of the decomposition is that the parallel algorithm is oriented to exploit the highest performance of parallel architectures where concurrency is implemented both at the coarsest and finest levels of granularity. Performance analysis is discussed in terms of the algorithm and software scalability. Validation is performed on a reference parallel architecture made of a distributed memory multiprocessor and a Graphic Processing Unit. Results are presented on the Data Assimilation problem, for oceanographic models.