Abstracts Mathematics

Numerical methods for diffusion problems with a large contrast in the coefficients

by Rens (author) Breunissen

Numerical methods for solving problems with a large contrast in the coefficients are investigated in this report. These types of problems typically appear in basin modeling. Specifically, the deflation and restricted additive Schwarz (RAS) methods are compared for their effectiveness in solving this type of problem in combination with the conjugate gradient method, both in terms of iterations and computation time. It is shown that the RAS method converges to the correct solution in a small amount of iterations. However, the deflation method, in combination with another preconditioner, performs better in terms of computation time. An important observation is that the relative residual can only be used as a reliable stopping criterion when the deflation method is used. The methods can be combined into the DRASCG method, which converges in an extremely small number of iterations. In a parallel environment, the speedup of the RASCG method is limited by a load imbalance in the amount of work required for the application of the preconditioner for each subdomain. The deflation method obtains good speedup, that is close to the ideal speedup. The methods are compared when the number of subdomains is increased. It is shown that a classic data distribution is not effective for this type of problem. The deflation method is shown to be robust for a physics based domain decomposition. Applied Mathematics