Meshless Subdomain Deflation Vectors in the Preconditioned Krylov Subspace Iterative Solvers
A. Lukyanov, J. van der Linden, T.B. Jönsthövel and C. Vuik
Event name: ECMOR XIV - 14th European Conference on the Mathematics of Oil Recovery
Session: Linear and Nonlinear Solvers
Publication date: 08 September 2014
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In reservoir models, the numerical domains are large and as a consequence a robust preconditioned iterative solver applied to the sparse linear system is required. Due to large contrasts either in the permeability field or grid aspect ratio, a large difference in the extreme eigenvalues of the resulting matrix is observable. This leads to slow convergence of iterative methods. A preconditioned Krylov subspace method such as the preconditioned GMRES method can significantly improve the convergence and robustness. Deflation based preconditioners were successfully applied for the problems with discontinuous jumps in coefficients. This paper considers the Deflated Preconditioned GMRES method for solving such systems. The deflation technique proposed in this paper uses a meshless approximation method to construct a priori the deflation space. We justify our approach through numerical experiments on both academic and realistic test problems which show improved convergence rates. For a number of cases, the fundamentals, potential, and parallel computational aspects will be presented.