A hyper-reduced MAC scheme for the parametric Stokes and Navier-Stokes equations

@article{Chen2021AHM,
  title={A hyper-reduced MAC scheme for the parametric Stokes and Navier-Stokes equations},
  author={Yanlai Chen and Lijie Ji and Zhu Wang},
  journal={ArXiv},
  year={2021},
  volume={abs/2110.11179}
}
The need for accelerating the repeated solving of certain parametrized systems motivates the development of more efficient reduced order methods. The classical reduced basis method is popular due to an offline-online decomposition and a mathematically rigorous a posterior error estimator which guides a greedy algorithm offline. For nonlinear and nonaffine problems, hyper reduction techniques have been introduced to make this decomposition efficient. However, they may be tricky to implement and… 
View PDF on arXiv

Figures and Tables from this paper

References

SHOWING 1-10 OF 50 REFERENCES
L1-based reduced over collocation and hyper reduction for steady state and time-dependent nonlinear equations
TLDR
This paper augment and extend the EIM approach as a direct solver, as opposed to an assistant, for solving nonlinear pPDEs on the reduced level, and the resulting method, called Reduced Over-Collocation method (ROC), is stable and capable of avoiding the efficiency degradation inherent to a traditional application of EIM.
An EIM-degradation free reduced basis method via over collocation and residual hyper reduction-based error estimation
TLDR
The EIM approach is augmented and extended as a direct solver, as opposed to an assistant, for solving nonlinear partial differential equations on the reduced level and the resulting method, called Reduced Over-Collocation method (ROC), is stable and capable of avoiding the efficiency degradation.
On the stability of the reduced basis method for Stokes equations in parametrized domains
We present an application of reduced basis method for Stokes equations in domains with affine parametric dependence. The essential components of the method are (i) the rapid convergence of global…
Reduced basis method for multi-parameter-dependent steady Navier-Stokes equations: Applications to natural convection in a cavity
TLDR
The feasibility and efficiency of the a posteriori error estimation by the natural norm approach considering several test cases by varying two different parameters are shown and the gain in terms of CPU time with respect to a parallel finite element approximation is of three magnitude orders.
A Reduced Basis Technique for Long-Time Unsteady Turbulent Flows
We present a reduced basis technique for long-time integration of parametrized incompressible turbulent flows. The new contributions are threefold. First, we propose a constrained Galerkin…
Efficient geometrical parametrization for finite‐volume‐based reduced order methods
TLDR
This work presents an approach for the efficient treatment of parametrized geometries in the context of POD-Galerkin reduced order methods based on Finite Volume full order approximations, which relies on basis functions defined on an average deformed configuration and makes use of the Discrete Empirical Interpolation Method (D-EIM).
A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations
In this paper, we extend the reduced-basis methods and associated a posteriori error estimators developed earlier for elliptic partial differential equations to parabolic problems with affine…
Generalized parametric solutions in Stokes flow
Abstract Design optimization and uncertainty quantification, among other applications of industrial interest, require fast or multiple queries of some parametric model. The Proper Generalized…
An LP empirical quadrature procedure for reduced basis treatment of parametrized nonlinear PDEs
Abstract We present a model reduction formulation for parametrized nonlinear partial differential equations (PDEs). Our approach builds on two ingredients: reduced basis (RB) spaces which provide…
A Progressive Reduced Basis/Empirical Interpolation Method for Nonlinear Parabolic Problems
TLDR
A new methodology, the Progressive RB-EIM (PREIM) method, which is to reduce the offline cost while maintaining the accuracy of the RB approximation in the online stage, in contrast to the standard approach where the EIM approximation and the RB space are built separately.
...
1
2
3
4
5
...