Combined Preconditioning with Applications in Reservoir Simulation

A Two-Level Variant of Additive Schwarz Preconditioning for Use in Reservoir Simulation

The computation time for reservoir simulation is dominated by the linear solver. The sets of linear equations which arise in reservoir simulation have two distinctive features: the problems are usually highly anisotropic, with a dominant vertical flow direction, and the commonly used fully implicit method requires a simultaneous solution for pressure and saturation or molar concentration variab...

Reservoir Simulation

Solving Reservoir Simulation Equations

Reservoir simulation is a necessary tool for making decisions. It is through numerical simulation that one can obtain knowledge pertaining to the processes occurring in the interior of an oil reservoir and hence, to enable an analysis of the various recovery strategies in order to guarantee optimal exploitation. History matching, optimization, and what-if scenarios require the simulation of lar...

Preconditioning the Matrix Exponential Operator with Applications

The idea of preconditioning is usually associated with solution techniques for solving linear systems or eigenvalue problems. It refers to a general method by which the original system is transformed into one which admits the same solution but which is easier to solve. Following this principle we consider in this paper techniques for preconditioning the matrix exponential operator, e A y 0 , us...

Preconditioning in Hdiv and applications

We consider the solution of the system of linear algebraic equations which arises from the finite element discretization of boundary value problems associated to the differential operator I−graddiv. The natural setting for such problems is in the Hilbert space H (div) and the variational formulation is based on the inner product in H (div). We show how to construct preconditioners for these equ...