Invited Talk - On Improved Monte Carlo Hybrid Methods for Preconditioner Computations
Workshop: 8th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems
Authors: Vassil Alexandrov (Barcelona Supercomputing Center)
Abstract: In this talk, we present certain improvements of the Markov Chain Monte Carlo Matrix Inversion and show their impact on performance and scalability of the method. The method is used for the computation of preconditioners for iterative methods, such as generalized minimal residuals (GMRES) or bi-conjugate gradient stabilized (BICGstab), for the solution of linear systems of equations. The problem of communication overhead is addressed via a modification of the method and via optimizations in the communication patterns of a chosen implementation of the method. Numerical experiments are carried out to highlight the benefits and deficiencies of both approaches and to assess their overall usefulness in light of scalability of the method.