On The Acceleration Of Ill-Conditioned Linear Systems: A Pod-Based Deflation Method For The Simulation Of Two-Phase Flow

We explore and develop POD-based deflation methods to accelerate the solution of large-scale linear systems resulting from two-phase flow simulation. The techniques here presented collect information from the system in a POD basis, which is later used in a deflation scheme. The snapshots required to obtain the POD basis are captured in two ways:...

Physics-based Pre-conditioners for Large-scale Subsurface Flow Simulation

We consider deflation-based pre-conditioning of the pressure equation for large-scale reservoir models with strong spatial variations in the permeabilities. The use of deflation techniques involves the search for good deflation vectors, which usually are problem-dependent. We propose the use of proper orthogonal decomposition (POD) to generate...