scholarly journals A nonlinear multigrid method for the efficient solution of the steady Euler equations

2006 ◽  
pp. 308-313
Author(s):  
P. W. Hemker ◽  
B. Koren ◽  
S. P. Spekreijse
Keyword(s):  
Euler Equations ◽  
Efficient Solution ◽  
Multigrid Method ◽  
Nonlinear Multigrid ◽  
Nonlinear Multigrid Method

A nonlinear multigrid method for inversion of two-dimensional acoustic wave equation

2014 ◽  
Vol 22 (3) ◽  
Author(s):  
Jingjun Zhao ◽  
Tao Liu ◽  
Guofeng Feng
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Multigrid Method ◽  
Finite Difference Methods ◽  
Least Square ◽  
Necessary Condition ◽  
Two Dimensional ◽  
Acoustic Wave Equation ◽  
Nonlinear Multigrid ◽  
Nonlinear Multigrid Method

Abstract.We investigate the problem of estimating the velocity in a two-dimensional acoustic wave equation, which plays an important role in geological survey. The forward problem is discretized using finite-difference methods and the estimation is formulated as a least-square minimization problem with a regularization term. To reduce the computational burden, a nonlinear multigrid method is applied to solve this inverse problem. In the multigrid inversion process, in order to make the objective functionals at different scales compatible, they are dynamically adjusted. In this way, the necessary condition of “the optimal solution should be the fixed point of multigrid inversion” can be met. The stable and fast regularized Gauss–Newton method is applied to each grid. The results of numerical simulations indicate that the proposed method can effectively reduce the required computation, improve the inversion results, and have the anti-noise ability.

scholarly journals Estimation of a Permeability Field within the Two-Phase Porous Media Flow Using Nonlinear Multigrid Method

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Tao Liu ◽  
Jie Song
Keyword(s):  
Porous Media ◽  
Multigrid Method ◽  
Computational Cost ◽  
Estimation Method ◽  
Porous Media Flow ◽  
Computational Accuracy ◽  
Two Phase ◽  
Nonlinear Multigrid ◽  
Nonlinear Multigrid Method ◽  
Permeability Field

Estimation of spatially varying permeability within the two-phase porous media flow plays an important role in reservoir simulation. Usually, one needs to estimate a large number of permeability values from a limited number of observations, so the computational cost is very high even for a single field-model. This paper applies a nonlinear multigrid method to estimate the permeability field within the two-phase porous media flow. Numerical examples are provided to illustrate the feasibility and effectiveness of the proposed estimation method. In comparison with other existing methods, the most outstanding advantage of this method is the computational efficiency, computational accuracy, and antinoise ability. The proposed method has a potential applicability to a variety of parameter estimation problems.

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