On POD-based Deflation Vectors for DPCG applied to porous media problems

We study fast and robust iterative solvers for large systems of linear equations resulting from simulation of flow trough strongly heterogeneous porous media. We propose the use of preconditioning and deflation techniques, based on information obtained frfrom the system, to reduce the time spent in the solution of the linear system.An important...

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

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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...