An adaptive multigrid conjugate gradient method for permeability identification of nonlinear diffusion equation
-
Jingjun Zhao
and
Tao Liu
Abstract
In this paper, the adaptive multigrid conjugate gradient method is applied to the inversion of the space-dependent permeability function in a nonlinear diffusion equation, which plays an important role in promoting the permeability estimation within multiphase porous media flow. The forward problem is discretized using finite-difference methods and the estimation is formulated as a least-square minimization problem with a regularization term. Firstly, the conjugate gradient method for optimization is used to solve this parameter identification problem. Secondly, to reduce the amount of calculation, the idea of multigrid inversion and the necessary condition of “the optimal solution should be the fixed point of multigrid inversion” is considered. Then, by combining the multigrid multiscale method with the conjugate gradient method, a new inversion method called the adaptive multigrid conjugate gradient method is designed. The results of numerical simulations indicate that the proposed method can effectively reduce the required computation burden and have good ability in anti-noise.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11101109
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11271102
Funding source: Natural Science Foundation of Hei-long-jiang Province of China
Award Identifier / Grant number: A201107
The authors are very grateful to the referees for their valuable comments.
© 2016 by De Gruyter
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Articles in the same Issue
- Frontmatter
- Preface
- Lq-regularization for the inverse Robin problem
- Hybrid Newton-type methods for reconstructing sound-soft obstacles from a single far field
- Numerical simulation and parameters inversion for non-symmetric two-sided fractional advection-dispersion equations
- A coupled model of partial differential equations for uranium ores heap leaching and its parameters identification
- An optimal filtering method for a time-fractional inverse advection-dispersion problem
- Simultaneous determination of thickness, thermal conductivity and porosity in textile material design
- Nuclear norm and indicator function model for matrix completion
- Calibrating the model parameters in pricing using the trust region method
- An adaptive multigrid conjugate gradient method for permeability identification of nonlinear diffusion equation
- Reconstruction of prograde and retrograde Chandler excitation
