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}
}
• Published 21 October 2021
• Computer Science
• ArXiv
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…

References

SHOWING 1-10 OF 50 REFERENCES
L1-based reduced over collocation and hyper reduction for steady state and time-dependent nonlinear equations
• Computer Science
J. Sci. Comput.
• 2021
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.
A Reduced Basis Technique for Long-Time Unsteady Turbulent Flows
• Computer Science
• 2017
An \emph{a posteriori} error indicator, which corresponds to the dual norm of the residual associated with the time-averaged momentum equation, is proposed and demonstrated that the error indicator is highly-correlated with the error in mean flow prediction, and can be efficiently computed through an offline/online strategy.
A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations
• Mathematics, Computer Science
• 2005
The reduced-basis methods and associated a posteriori error estimators developed earlier for elliptic partial differential equations to parabolic problems with affine parameter dependence are extended and time is treated as an additional, albeit special, parameter in the formulation and solution of the problem.
Efficient geometrical parametrization for finite‐volume‐based reduced order methods
• Mathematics
International Journal for Numerical Methods in Engineering
• 2020
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).
An LP empirical quadrature procedure for reduced basis treatment of parametrized nonlinear PDEs
• Mathematics
Computer Methods in Applied Mechanics and Engineering
• 2019
A Progressive Reduced Basis/Empirical Interpolation Method for Nonlinear Parabolic Problems
• Computer Science
SIAM J. Sci. Comput.
• 2018
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.