• Corpus ID: 245836845

Model Reduction Using Sparse Polynomial Interpolation for the Incompressible Navier-Stokes Equations

@article{Hess2022ModelRU,
  title={Model Reduction Using Sparse Polynomial Interpolation for the Incompressible Navier-Stokes Equations},
  author={Martin W. Hess and Gianluigi Rozza},
  journal={ArXiv},
  year={2022},
  volume={abs/2201.03228}
}
This work investigates the use of sparse polynomial interpolation as a model order reduction method for the incompressible Navier-Stokes equations. Numerical results are presented underscoring the validity of sparse polynomial approximations and comparing with established reduced basis techniques. Two numerical models serve to access the accuracy of the reduced order models (ROMs), in particular parametric nonlinearities arising from curved geometries are investigated in detail. Besides the… 

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References

SHOWING 1-10 OF 25 REFERENCES
A Spectral Element Reduced Basis Method for Navier–Stokes Equations with Geometric Variations
TLDR
It is shown that an expansion in element-wise local degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.
Reduced basis model order reduction for Navier–Stokes equations in domains with walls of varying curvature
ABSTRACT We consider the Navier–Stokes equations in a channel with a narrowing and walls of varying curvature. By applying the empirical interpolation method to generate an affine parameter
A Spectral Element Reduced Basis Method in Parametric CFD
TLDR
It is shown, how a multilevel static condensation in the pressure and velocity boundary degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.
Numerical Approximation of Partial Differential Equations
This is the softcover reprint of the very popular hardcover edition. This book deals with the numerical approximation of partial differential equations. Its scope is to provide a thorough
High-Dimensional Adaptive Sparse Polynomial Interpolation and Applications to Parametric PDEs
TLDR
An interpolation technique in which the sample set is incremented as the polynomial dimension increases, leading therefore to a minimal amount of PDE solving, which is based on the standard principle of tensorisation of a one-dimensional interpolation scheme and sparsification.
A localized reduced-order modeling approach for PDEs with bifurcating solutions
ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S
Parametric partial differential equations are commonly used to model physical systems. They also arise when Wiener chaos expansions are used as an alternative to Monte Carlo when solving stochastic
Reduced Basis Methods for Partial Differential Equations : Evaluation of multiple non-compliant flux-type output functionals for a non-affine electrostatics problem
A method for rapid evaluation of flux-type outputs of interest from solutions to partial differential equations (PDEs) is presented within the reduced basis framework for linear, elliptic PDEs. The
Efficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method
TLDR
The deflated continuation method can be obtained combining the classical continuation method and the deflation one: the former is used to entirely track each known branch of the diagram, while the latter is exploited to discover the new ones.
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