A characterization of sparse linear solver performance in subsurface flow simulations

Open Access
Fermoyle, Kelly
Graduate Program:
Computer Science and Engineering
Master of Science
Document Type:
Master Thesis
Date of Defense:
December 16, 2010
Committee Members:
  • Padma Raghavan, Thesis Advisor
  • Sparse linear systems
  • subsurface flow
  • performance
We study the performance of the primary kernel used in the computational simulation of subsurface flow by varying the solver and preconditioner parameters for sparse linear system solution. The subsurface flow problem requires time integration, each step of which uses a nonlinear solver. There are a number of ways to solve the nonlinear equation, one of which is Picard method which forms a symmetric positive-definite (SPD) linear system. Since the majority of computation involves the solution of large sparse linear systems, we evaluate solving systems with iterative preconditioned methods. SPD systems are often solved efficiently by a conjugate gradient (CG) solver using a preconditioner. There are a large number of available preconditioners to use. Two of the most promising preconditioners are incomplete Cholesky factorization (IC) and one formed from an algebraic multigrid (AMG) method. For the IC solver, we try reverse Cuthill-McKee (RCM), minimum degree, and dissection reordering algorithms to improve performance. We also propose the use of thresholding small values from the matrix during the construction of the preconditioner to improve performance. Another avenue to improve performance is the use of mixed-precision algorithms, which we evaluate and propose as future work. Our results indicate that preconditioned CG with IC using RCM reordering can beat the best known performance of basic solvers, but the AMG preconditioner with application knowledge for parameter tuning showed the best overall performance.