On the application of the dynamic mode decomposition in problems of computational fluid dynamics

Alekseev, A. K.; Bondarev, A. E.

doi:10.20948/prepr-2018-154

Cited by 2 publications

(2 citation statements)

References 31 publications

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“…The dynamic mode decomposition (DMD) (for the unsteady Euler equations presented by [5,6]) may be provided as another example for implicit vectorization of the solution and the matrization of the propagator. In the DMD frame, the numerical solution of the aero-gasdynamics problem is vectorized at time step i and is written as…”

Section: The Tensor Form For Problems Of the Aerogasdynamicmentioning

confidence: 99%

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On the Visualization of Multidimensional Functions using Canonical Decomposition

Alekseev¹,

Bondarev²,

Pyatakova³

2022

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The approximation of a multidimensional function by means of tensor decompositions is considered in terms of storage, processing and visualization of the results of parametric calculations in computational aerogasdynamics problems. An algorithm for calculating the canonical decomposition using a combination of the alternative least squares method and stochastic gradient descent is described. Numerical results for interpolation of functions in sixdimensional space obtained using the canonical decomposition are presented, demonstrating the high computational efficiency and quality of results. Visual representations of the results are provided.

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Section: The Tensor Form For Problems Of the Aerogasdynamicmentioning

confidence: 99%

“…(6) This form enables the radical reduction of the memory necessary for storage of the operator A . This circumstance enables to use the propagator for the resolution of the set of interesting problems, such as the search for the singular vectors, approximation of the Perron-Frobenius and Koopman operators [5,6].…”

Section: Aa Rlmentioning

confidence: 99%

On the Visualization of Multidimensional Functions using Canonical Decomposition

Alekseev¹,

Bondarev²,

Pyatakova³

2022

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On the Prager-Synge method for a posteriori error

Alekseev

Bondarev

2021

KIAM Prepr.

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The classic method by Prager and Synge ("hypercircle" method) for a posteriori error estimation in addressed from the viewpoint of the extension of the applicability domain (the range of analyzed problems and methods of the realization). The nonintrusive version of the approximation error estimation that implements the method by Prager and Synge for the arbitrary PDE system is presented. The semiheuristical variant of the Prager and Synge method may be related with the modern approaches for approximation error estimation on the ensemble of solutions obtained by the algorithms of different inner structure.

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On the application of the dynamic mode decomposition in problems of computational fluid dynamics

Cited by 2 publications

References 31 publications

On the Visualization of Multidimensional Functions using Canonical Decomposition

On the Visualization of Multidimensional Functions using Canonical Decomposition

On the Prager-Synge method for a posteriori error

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