IMA Postdoc Seminar (February 17, 2009)

Speaker: Olivier Dubois (IMA)

Title: Minimizing the energy for efficient linear solvers in reservoir simulation

Abstract: In modern petroleum reservoir simulators, a significant computational bottleneck is the solution of large linear systems for the pressure variables. The difficulty comes mainly from the strong heterogeneity of the media: the permeability tensor has jumps of several orders of magnitude and is highly anisotropic in typical applications. We demonstrate the use of energy minimizing basis functions to improve the robustness of multigrid and domain decomposition preconditioners in the context of reservoir simulation. These basis functions have the same advantageous properties of other multiscale approaches. In addition, they can be computed with a purely algebraic procedure, which does not require the construction of a geometric coarse mesh.

This is joint work with Ilya D. Mishev (ExxonMobil Upstream Research) and Ludmil Zikatanov (PennState University).