Frenzel, David ; Lang, Jens (2021)
A third-order weighted essentially non-oscillatory scheme in optimal control problems governed by nonlinear hyperbolic conservation laws.
In: Computational Optimization and Applications, 80 (1)
doi: 10.1007/s10589-021-00295-2
Artikel, Bibliographie
Dies ist die neueste Version dieses Eintrags.
Kurzbeschreibung (Abstract)
The weighted essentially non-oscillatory (WENO) methods are popular and effective spatial discretization methods for nonlinear hyperbolic partial differential equations. Although these methods are formally first-order accurate when a shock is present, they still have uniform high-order accuracy right up to the shock location. In this paper, we propose a novel third-order numerical method for solving optimal control problems subject to scalar nonlinear hyperbolic conservation laws. It is based on the first-disretize-then-optimize approach and combines a discrete adjoint WENO scheme of third order with the classical strong stability preserving three-stage third-order Runge–Kutta method SSPRK3. We analyze its approximation properties and apply it to optimal control problems of tracking-type with non-smooth target states. Comparisons to common first-order methods such as the Lax–Friedrichs and Engquist–Osher method show its great potential to achieve a higher accuracy along with good resolution around discontinuities.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2021 |
| Autor(en): | Frenzel, David ; Lang, Jens |
| Art des Eintrags: | Bibliographie |
| Titel: | A third-order weighted essentially non-oscillatory scheme in optimal control problems governed by nonlinear hyperbolic conservation laws |
| Sprache: | Englisch |
| Publikationsjahr: | 2 Juli 2021 |
| Verlag: | Springer |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Computational Optimization and Applications |
| Jahrgang/Volume einer Zeitschrift: | 80 |
| (Heft-)Nummer: | 1 |
| DOI: | 10.1007/s10589-021-00295-2 |
| Zugehörige Links: | |
| Kurzbeschreibung (Abstract): | The weighted essentially non-oscillatory (WENO) methods are popular and effective spatial discretization methods for nonlinear hyperbolic partial differential equations. Although these methods are formally first-order accurate when a shock is present, they still have uniform high-order accuracy right up to the shock location. In this paper, we propose a novel third-order numerical method for solving optimal control problems subject to scalar nonlinear hyperbolic conservation laws. It is based on the first-disretize-then-optimize approach and combines a discrete adjoint WENO scheme of third order with the classical strong stability preserving three-stage third-order Runge–Kutta method SSPRK3. We analyze its approximation properties and apply it to optimal control problems of tracking-type with non-smooth target states. Comparisons to common first-order methods such as the Lax–Friedrichs and Engquist–Osher method show its great potential to achieve a higher accuracy along with good resolution around discontinuities. |
| Freie Schlagworte: | Nonlinear optimal control, Discrete adjoints, Hyperbolic conservation laws, WENO schemes, Strong stability preserving Runge–Kutta methods |
| Zusätzliche Informationen: | Erstveröffentlichung; Mathematics Subject Classifcation 34H05, 49M25, 65L06, 65M22 |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Numerik und wissenschaftliches Rechnen |
| Hinterlegungsdatum: | 17 Dez 2024 12:01 |
| Letzte Änderung: | 17 Dez 2024 12:01 |
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Verfügbare Versionen dieses Eintrags
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A third-order weighted essentially non-oscillatory scheme in optimal control problems governed by nonlinear hyperbolic conservation laws. (deposited 10 Dez 2024 12:53)
- A third-order weighted essentially non-oscillatory scheme in optimal control problems governed by nonlinear hyperbolic conservation laws. (deposited 17 Dez 2024 12:01) [Gegenwärtig angezeigt]
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