Benchmarking preconditioners

Benchmarking preconditioners

Benchmarking preconditioners 150 150 UKAEA Opendata
UKAEA-STEP-PR(23)02

Benchmarking preconditioners

Preconditioners are meant to improve both, the efficiency and robustness of iterative techniques while solving very large linear systems on a Krylov subspace. However, determining which preconditioner is suitable to be applied on a certain multiphysic simulation requires a combination of knowledge of preconditioning matrices techniques, types of matrices, Krylov subspaces, iterative methods, among other Linear Algebra’s foundation. The present work provides a benchmark of the most popular preconditioners available today, emphasising their respective performance in terms of time of solution of the Finite Element problem, usage of memory, number of iterations, the value of |R| achieved when converged. The performance evaluation is made using the University Cambridge Research Computing Service (CDS3) using Message Passing Interface (MPI) implementations that allows parallelisation using 2 nodes of the cluster. The overview is restricted to three phenomema solved by Partial Differential Equations (PDEs) with the Finite Elements Method taking into consideration million Degrees of Freedom (DoF) to be solved. Along with the preconditioners, a variety of options were tested to optimise its performance.

Collection:
Journals
Journal:
Physics of Plasmas
Publisher:
AIP (American Institute of Physics)