Parallel sparsity patterns for factored incomplete inverse matrices

The solution of large sparse linear systems is an essential part in many scientific fields. Numerical solution of such systems is usually performed using iterative methods in conjunction with effective preconditioning schemes. Recently, an adaptive factored approached based on adaptive sparsity patterns was proposed. Utilizing their recursive form novel dynamic sparsity patterns are introduced. These novel sparsity patterns enable fully parallel implementation of the factored approximate inverse matrices. In order to further improve performance pre-filling and post-filling is introduced. These strategies reduce the amount of repetitive solutions of local linear systems required during dynamic pattern formation. The parallel performance and effectiveness of the proposed scheme are assessed by solving a multitude of model problems. Furthermore, comparative results are also given.