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Adaptive Nonlinear Reduced-Order Mod...

Razavi, Alireza H.,

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Adaptive Nonlinear Reduced-Order Models for Parametrized Partial Differential Equations of Transonic Flows /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Adaptive Nonlinear Reduced-Order Models for Parametrized Partial Differential Equations of Transonic Flows // Alireza H Razavi.
Author:	Razavi, Alireza H.,
Description:	1 electronic resource (94 pages)
Notes:	Source: Masters Abstracts International, Volume: 86-05.
Contained By:	Masters Abstracts International86-05.
Subject:	Applied mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30989433
ISBN:	9798342741026

Adaptive Nonlinear Reduced-Order Models for Parametrized Partial Differential Equations of Transonic Flows /
Razavi, Alireza H.,

Adaptive Nonlinear Reduced-Order Models for Parametrized Partial Differential Equations of Transonic Flows /Alireza H Razavi. - 1 electronic resource (94 pages)

Source: Masters Abstracts International, Volume: 86-05.

We consider rapid and reliable solution of parametrized partial differential equations (PDEs) in many-query scenarios. One approach to reduce the computational cost of standard high-dimensional PDE discretizations (e.g., finite element method) by several orders of magnitude is linear model order reduction (MOR), which seeks solutions in low-dimensional linear spaces. However, PDEs with discontinuities whose location depends on the parameter yield solution manifolds with a slowly decaying Kolmogorov N-width, which renders linear MOR ineffective. We develop a nonlinear MOR framework that mitigates the Kolmogorov barrier using the following ingredients: a dilation-based indicator that locates shocks; a parameter-dependent transformation which aligns the shocks; MOR with hyperreduction applied in the transformed space; and goal-oriented output error estimates for the reduced model. We demonstrate our method on transonic flows governed by the Euler and Reynolds-averaged Navier-Stokes equations. 

English

ISBN: 9798342741026Subjects--Topical Terms:

2122814
Applied mathematics.
Subjects--Index Terms:

Kolmogorov

Adaptive Nonlinear Reduced-Order Models for Parametrized Partial Differential Equations of Transonic Flows /
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100 1 $a Razavi, Alireza H., $e author. $3 3829857
245 1 0 $a Adaptive Nonlinear Reduced-Order Models for Parametrized Partial Differential Equations of Transonic Flows / $c Alireza H Razavi.
264 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2024
300 $a 1 electronic resource (94 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Masters Abstracts International, Volume: 86-05.
500 $a Advisors: Yano, Masayuki Committee members: Nair, Prasanth B.; Zingg, David W.
502 $b M.A.S. $c University of Toronto (Canada) $d 2024.
520 $a We consider rapid and reliable solution of parametrized partial differential equations (PDEs) in many-query scenarios. One approach to reduce the computational cost of standard high-dimensional PDE discretizations (e.g., finite element method) by several orders of magnitude is linear model order reduction (MOR), which seeks solutions in low-dimensional linear spaces. However, PDEs with discontinuities whose location depends on the parameter yield solution manifolds with a slowly decaying Kolmogorov N-width, which renders linear MOR ineffective. We develop a nonlinear MOR framework that mitigates the Kolmogorov barrier using the following ingredients: a dilation-based indicator that locates shocks; a parameter-dependent transformation which aligns the shocks; MOR with hyperreduction applied in the transformed space; and goal-oriented output error estimates for the reduced model. We demonstrate our method on transonic flows governed by the Euler and Reynolds-averaged Navier-Stokes equations. 
546 $a English
590 $a School code: 0779
650 4 $a Applied mathematics. $3 2122814
650 4 $a Aerospace engineering. $3 1002622
650 4 $a Computational physics. $3 3343998
653 $a Kolmogorov
653 $a Model order reduction
653 $a Nonlinear
653 $a Numerical method
653 $a Partial differential equations
653 $a Transonic
690 $a 0364
690 $a 0538
690 $a 0216
710 2 $a University of Toronto (Canada). $b Aerospace Science and Engineering. $e degree granting institution. $3 3829858
720 1 $a Yano, Masayuki $e degree supervisor.
773 0 $t Masters Abstracts International $g 86-05.
790 $a 0779
791 $a M.A.S.
792 $a 2024
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30989433