Domain Decomposition Methods for Low-Rank Correction Preconditioning and Solving Eigenvalue Problems
The goal of this research is to investigate robust preconditioning techniques for solving general large sparse linear systems with an emphasis on parallel techniques and a domain decomposition (DD) viewpoint. This approach is related to the parallel ARMS (Algebraic Recursive Multilevel Solvers) which this group developed in the past. What is new is that they are now considering using low-rank approximation techniques for approximating the Schur complement systems. They are developing these techniques for linear systems that arise from realistic applications such as computational fluid dynamics and other application areas. Special methods, such as eigenvalue deflation, will be used to enhance robustness.
DD type methods for eigenvalue problems are not as well studied as those for solving linear systems, however they hold a significant role too. These methods foster great opportunities for parallelism and the main idea of this project is to use massively parallel codes in order to deploy all the advantages of DD methods for solving eigenvalue problems. The researchers aim to show experiments with thousands of cores and how their implementations scale when dealing with real-life applications in which matrices can reach dimensions of hundreds of millions.
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