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

Authors:
C. Vuik;A. Segal;L. el Yaakoubi;E. Dufour
Affiliations:
Delft University of Technology, Faculty of Information Technology and Systems, Department of Applied Mathematical Analysis, Mekelweg 4, 2628 CD Delft, The Netherlands;Delft University of Technology, Faculty of Information Technology and Systems, Department of Applied Mathematical Analysis, Mekelweg 4, 2628 CD Delft, The Netherlands;Delft Univ. of Technology, Delft, The Netherlands and Shell International Exploration and Production, P.O. Box 60, 2280 AB Rijswijk, The Netherlands;Shell International Exploration and Production, P.O. Box 60, 2280 AB Rijswijk, The Netherlands
Venue:
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
Year:
2002

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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.