Permeability Estimation with the Augmented Lagrangian Method for a Nonlinear Diffusion Equation |
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Authors: | Trygve K Nilssen Trond Mannseth Xue-Cheng Tai |
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Institution: | (1) Department of Mathematics, University of Bergen, Johannes Brunsgt. 12, N-5008 Bergen, Norway;(2) Rogalandsforskning, Thormøhlensgt. 55, N-5008 Bergen, Norway;(3) Department of Mathematics, University of Bergen, Johannes Brunsgt. 12, N-5008 Bergen, Norway |
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Abstract: | We consider numerical identification of the piecewise constant permeability function in a nonlinear parabolic equation, with the augmented Lagrangian method. By studying this problem, we aim at also gaining some insight into the potential ability of the augmented Lagrangian method to handle permeability estimation within the full two-phase porous-media flow setting. The identification is formulated as a constrained minimization problem. The parameter estimation problem is reduced to a coupled nonlinear algebraic system, which can be solved efficiently with the conjugate gradient method. The methodology is developed and numerical experiments with the proposed method are presented. |
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Keywords: | inverse problems nonlinear parabolic permeability |
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