An Analysis of a Preconditioner for the Discretized Pressure Equation Arising in Reservoir Simulation

We analyze the use of fast solvers as preconditioners for the discretized pressure equation arising in reservoir simulation. Under proper conditions on the permeability functions and the source term, we show that the number of iterations for the Conjugate Gradient method is bounded independently of both the lower bound of the permeability and the discretization parameter h. Such results are obtained for a special class of self-adjoint second order elliptic problems with discontinuous coecients. We also discuss how fast solvers can be utilized in the presence of non-rectangular domains by applying a domain imbedding procedure. The theoretical results are illustrated and supplemented by a series of numerical experiments.