Asymptotic preserving time-discretization of optimal control problems for the Goldstein–Taylor model

Giacomo Albi; Michael Herty; Christian Jörres; Lorenzo Pareschi

doi:10.1002/num.21877

Asymptotic preserving time-discretization of optimal control problems for the Goldstein–Taylor model

Giacomo Albi, Michael Herty, Christian Jörres^*, Lorenzo Pareschi

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We consider the development of implicit-explicit time integration schemes for optimal control problems governed by the Goldstein–Taylor model. In the diffusive scaling, this model is a hyperbolic approximation to the heat equation.We investigate the relation of time integration schemes and the formal Chapman–Enskogtype limiting procedure. For the class of stiffly accurate implicit–explicit Runge–Kutta methods, the discrete optimality system also provides a stable numerical method for optimal control problems governed by the heat equation. Numerical examples illustrate the expected behavior.

Original language	English
Pages (from-to)	1770-1784
Number of pages	15
Journal	Numerical Methods for Partial Differential Equations
Volume	30
Issue number	6
DOIs	https://doi.org/10.1002/num.21877
Publication status	Published - Nov 2014

Keywords

Asymptotic-preserving schemes
Hyperbolic conservation laws
Implicit–explicit Runge–Kutta methods
Kinetic equations
Optimal boundary control

ASJC Scopus subject areas

Analysis
Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1002/num.21877

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@article{bece5b4835f740d09641cb428df551fb,

title = "Asymptotic preserving time-discretization of optimal control problems for the Goldstein–Taylor model",

abstract = "We consider the development of implicit-explicit time integration schemes for optimal control problems governed by the Goldstein–Taylor model. In the diffusive scaling, this model is a hyperbolic approximation to the heat equation.We investigate the relation of time integration schemes and the formal Chapman–Enskogtype limiting procedure. For the class of stiffly accurate implicit–explicit Runge–Kutta methods, the discrete optimality system also provides a stable numerical method for optimal control problems governed by the heat equation. Numerical examples illustrate the expected behavior.",

keywords = "Asymptotic-preserving schemes, Hyperbolic conservation laws, Implicit–explicit Runge–Kutta methods, Kinetic equations, Optimal boundary control",

author = "Giacomo Albi and Michael Herty and Christian J{\"o}rres and Lorenzo Pareschi",

note = "Publisher Copyright: {\textcopyright} 2014 Wiley Periodicals, Inc.",

year = "2014",

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doi = "10.1002/num.21877",

language = "English",

volume = "30",

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journal = "Numerical Methods for Partial Differential Equations",

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TY - JOUR

T1 - Asymptotic preserving time-discretization of optimal control problems for the Goldstein–Taylor model

AU - Albi, Giacomo

AU - Herty, Michael

AU - Jörres, Christian

AU - Pareschi, Lorenzo

PY - 2014/11

Y1 - 2014/11

N2 - We consider the development of implicit-explicit time integration schemes for optimal control problems governed by the Goldstein–Taylor model. In the diffusive scaling, this model is a hyperbolic approximation to the heat equation.We investigate the relation of time integration schemes and the formal Chapman–Enskogtype limiting procedure. For the class of stiffly accurate implicit–explicit Runge–Kutta methods, the discrete optimality system also provides a stable numerical method for optimal control problems governed by the heat equation. Numerical examples illustrate the expected behavior.

AB - We consider the development of implicit-explicit time integration schemes for optimal control problems governed by the Goldstein–Taylor model. In the diffusive scaling, this model is a hyperbolic approximation to the heat equation.We investigate the relation of time integration schemes and the formal Chapman–Enskogtype limiting procedure. For the class of stiffly accurate implicit–explicit Runge–Kutta methods, the discrete optimality system also provides a stable numerical method for optimal control problems governed by the heat equation. Numerical examples illustrate the expected behavior.

KW - Asymptotic-preserving schemes

KW - Hyperbolic conservation laws

KW - Implicit–explicit Runge–Kutta methods

KW - Kinetic equations

KW - Optimal boundary control

UR - https://www.scopus.com/pages/publications/85045291138

U2 - 10.1002/num.21877

DO - 10.1002/num.21877

M3 - Article

AN - SCOPUS:85045291138

SN - 0749-159X

VL - 30

SP - 1770

EP - 1784

JO - Numerical Methods for Partial Differential Equations

JF - Numerical Methods for Partial Differential Equations

IS - 6

ER -

Asymptotic preserving time-discretization of optimal control problems for the Goldstein–Taylor model

Abstract

Keywords

ASJC Scopus subject areas

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