A comparison of various deflation vectors applied to elliptic problems with discontinuous coefficients

Abstract

A mathematical model to predict excess fluid pressures in the earth's crust leads to a time-dependent diffusion equation for the pressure. Application of the finite element method to this equation results in a large system of linear equations. Due to the layered structure of the underground the permeability used in the diffusion equation has large jumps, so the coefficient matrix has a large condition number of order 10⁸. This leads to bad convergence of the ICCG method and a wrong termination criterion. Combining ICCG with a deflation technique leads to a robust solution method. A difficulty is the construction of the deflation vectors. In this paper we present three different choices of the deflation vectors and compare them from a theoretical point of view and from numerical experiments. This comparison shows that the best deflation technique is based on algebraic deflation vectors.