A modified balanced POD model reduction algorithm for parabolic PDEs with unbounded inputs

Weiwei Hu; John R. Singler

doi:10.1109/ACC.2014.6859087

A modified balanced POD model reduction algorithm for parabolic PDEs with unbounded inputs

Weiwei Hu, John R. Singler

Institute for Mathematics and its Applications

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We develop an algorithm to approximate the balanced reduced order model for linear parabolic PDE systems with an unbounded input operator and a bounded output operator. We use balanced POD, a widely used simulation-based algorithm for balanced truncation, however we modify the algorithm to avoid unusual and challenging simulations due to the unbounded input operator. We develop the modified algorithm for two classes of unbounded input operators; the first class includes Neumann boundary input operators, and the second class includes Dirichlet boundary input operators. We present numerical results for a convection diffusion equation.

Original language	English (US)
Title of host publication	2014 American Control Conference, ACC 2014
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1680-1685
Number of pages	6
ISBN (Print)	9781479932726
DOIs	https://doi.org/10.1109/ACC.2014.6859087
State	Published - Jan 1 2014
Event	2014 American Control Conference, ACC 2014 - Portland, OR, United States Duration: Jun 4 2014 → Jun 6 2014

Publication series

Name	Proceedings of the American Control Conference
ISSN (Print)	0743-1619

Other

Other	2014 American Control Conference, ACC 2014
Country/Territory	United States
City	Portland, OR
Period	6/4/14 → 6/6/14

Keywords

Computational methods
Distributed parameter systems
Reduced order modeling

Publisher link

10.1109/ACC.2014.6859087

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A modified balanced POD model reduction algorithm for parabolic PDEs with unbounded inputs. / Hu, Weiwei; Singler, John R.
2014 American Control Conference, ACC 2014. Institute of Electrical and Electronics Engineers Inc., 2014. p. 1680-1685 6859087 (Proceedings of the American Control Conference).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Hu, W & Singler, JR 2014, A modified balanced POD model reduction algorithm for parabolic PDEs with unbounded inputs. in 2014 American Control Conference, ACC 2014., 6859087, Proceedings of the American Control Conference, Institute of Electrical and Electronics Engineers Inc., pp. 1680-1685, 2014 American Control Conference, ACC 2014, Portland, OR, United States, 6/4/14. https://doi.org/10.1109/ACC.2014.6859087

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abstract = "We develop an algorithm to approximate the balanced reduced order model for linear parabolic PDE systems with an unbounded input operator and a bounded output operator. We use balanced POD, a widely used simulation-based algorithm for balanced truncation, however we modify the algorithm to avoid unusual and challenging simulations due to the unbounded input operator. We develop the modified algorithm for two classes of unbounded input operators; the first class includes Neumann boundary input operators, and the second class includes Dirichlet boundary input operators. We present numerical results for a convection diffusion equation.",

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N2 - We develop an algorithm to approximate the balanced reduced order model for linear parabolic PDE systems with an unbounded input operator and a bounded output operator. We use balanced POD, a widely used simulation-based algorithm for balanced truncation, however we modify the algorithm to avoid unusual and challenging simulations due to the unbounded input operator. We develop the modified algorithm for two classes of unbounded input operators; the first class includes Neumann boundary input operators, and the second class includes Dirichlet boundary input operators. We present numerical results for a convection diffusion equation.

AB - We develop an algorithm to approximate the balanced reduced order model for linear parabolic PDE systems with an unbounded input operator and a bounded output operator. We use balanced POD, a widely used simulation-based algorithm for balanced truncation, however we modify the algorithm to avoid unusual and challenging simulations due to the unbounded input operator. We develop the modified algorithm for two classes of unbounded input operators; the first class includes Neumann boundary input operators, and the second class includes Dirichlet boundary input operators. We present numerical results for a convection diffusion equation.

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A modified balanced POD model reduction algorithm for parabolic PDEs with unbounded inputs

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