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Efficient Hyperreduction by Empirical Quadrature Procedure With Constraint Reduction for Large-Scale Parameterized Nonlinear Problems.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Efficient Hyperreduction by Empirical Quadrature Procedure With Constraint Reduction for Large-Scale Parameterized Nonlinear Problems./
Author:	Humphry, Adrian Stewart.
Description:	1 online resource (101 pages)
Notes:	Source: Masters Abstracts International, Volume: 85-01.
Contained By:	Masters Abstracts International85-01.
Subject:	Aerospace engineering. -
Online resource:	click for full text (PQDT)
ISBN:	9798379769802

Efficient Hyperreduction by Empirical Quadrature Procedure With Constraint Reduction for Large-Scale Parameterized Nonlinear Problems.
Humphry, Adrian Stewart.

Efficient Hyperreduction by Empirical Quadrature Procedure With Constraint Reduction for Large-Scale Parameterized Nonlinear Problems. - 1 online resource (101 pages)

Source: Masters Abstracts International, Volume: 85-01.

Thesis (M.A.S.)--University of Toronto (Canada), 2023.

Includes bibliographical references

Many engineering applications require rapid and reliable approximations of parameterized nonlinear partial differential equations. Model order reduction (MOR) constructs a low-dimensional model in the offline stage such that we can rapidly calculate outputs for any parameter value in the online stage. For equations with general nonlinearities, MOR requires hyperreduction, which can be computationally expensive. In this work, we improve the offline-efficiency of empirical quadrature procedure (EQP) used for hyperreduction. EQP involves solving a constrained minimization problem, often with a large set of constraints. We propose four modifications to EQP. First, we consider second-order error contributions to achieve smaller error tolerances. Second, we propose a rounding-error stable constraint residual calculation method, reducing offline cost. Third, and most importantly, we develop a constraint reduction method, employing QR factorization to reduce the number of constraints and thus improve offline-efficiency. Fourth, we develop an efficient sampling procedure for problems with high-dimensional parameter spaces.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798379769802Subjects--Topical Terms:

686400
Aerospace engineering.
Subjects--Index Terms:

Constraint reductionIndex Terms--Genre/Form:

554714
Electronic books.

Efficient Hyperreduction by Empirical Quadrature Procedure With Constraint Reduction for Large-Scale Parameterized Nonlinear Problems.
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500 $a Advisor: Yano, Masayuki.
502 $a Thesis (M.A.S.)--University of Toronto (Canada), 2023.
504 $a Includes bibliographical references
520 $a Many engineering applications require rapid and reliable approximations of parameterized nonlinear partial differential equations. Model order reduction (MOR) constructs a low-dimensional model in the offline stage such that we can rapidly calculate outputs for any parameter value in the online stage. For equations with general nonlinearities, MOR requires hyperreduction, which can be computationally expensive. In this work, we improve the offline-efficiency of empirical quadrature procedure (EQP) used for hyperreduction. EQP involves solving a constrained minimization problem, often with a large set of constraints. We propose four modifications to EQP. First, we consider second-order error contributions to achieve smaller error tolerances. Second, we propose a rounding-error stable constraint residual calculation method, reducing offline cost. Third, and most importantly, we develop a constraint reduction method, employing QR factorization to reduce the number of constraints and thus improve offline-efficiency. Fourth, we develop an efficient sampling procedure for problems with high-dimensional parameter spaces.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
650 4 $a Aerospace engineering. $3 686400
653 $a Constraint reduction
653 $a Empirical quadrature procedure
653 $a Hyperreduction
653 $a Parameter sampling
653 $a Reduced order modeling
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