The solution of large sparse linear systems is a ubiquitous problem in chemistry, physics, and engineering applications. Krylov subspace methods are preferred to solve the large scale linear systems instead of direct methods as they are faster and use less memory. An effective preconditioner is needed to improve the convergence of the underlying simulation.
The iterative methods frequently incorporate incomplete LU (ILU) preconditioners because of its robustness, accuracy, and usability as a black-box preconditioner. However, The factorization and triangular solve subroutines are inherently sequential in ILU. Detailed model simulation and high resolution modelling has increased the demand of solving extremely large linear systems. Therefore, development of scalable preconditioners have become even more crucial.
We have developed a hybrid parallel preconditioner. Across the processes, we use additive Schwarz preconditioner, since it has built-in parallelism that decomposes the original problem into subproblems. These subproblems are then solved using the Crout variant of the ILU preconditioner in a process using multiple threads. We use a multilevel nested dissection approach to extract parallelism in the Crout ILU preconditioner. We use the restricted version of additive Schwarz (RAS) method to improve the convergence across the processes.
For scalable implementation, we have used a lightweight communication based programming model GASPI across the processes and task level parallelism using pthreads on a process.
In this talk, we present the scalability challenges and preliminary scalability results of the preconditioner on various linear systems. For ill-conditioned and non-diagonal dominant matrices, our implementation incorporates matching, row and col based permutation, and inverse based dropping to improve the robustness of the serial subroutines.
How to join:
The talk is held online via Zoom. You can join with the link https://uni-kl-de.zoom.us/j/94636397127?pwd=Y1g4dGVFQitzUHVRQUFpcFB4WVFKQT09.
Referent: Raju Ram, Fraunhofer ITWM, Kaiserslautern
Zeit: 11:30 Uhr