Numerical optimization of the Dirichlet boundary condition in the phase field model with an application to pure substance solidification

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F23%3A00368408" target="_blank" >RIV/68407700:21340/23:00368408 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.camwa.2023.06.007" target="_blank" >https://doi.org/10.1016/j.camwa.2023.06.007</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.camwa.2023.06.007" target="_blank" >10.1016/j.camwa.2023.06.007</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Numerical optimization of the Dirichlet boundary condition in the phase field model with an application to pure substance solidification

Popis výsledku v původním jazyce

As opposed to the distributed control of parabolic PDE's, very few contributions currently exist pertaining to the Dirichlet boundary condition control for parabolic PDE's. This motivates our interest in the Dirichlet boundary condition control for the phase field model describing the solidification of a pure substance from a supercooled melt. In particular, our aim is to control the time evolution of the temperature field on the boundary of the computational domain in order to achieve the prescribed shape of the crystal at the given time. To obtain efficient means of computing the gradient of the cost functional, we derive the adjoint problem formally. The gradient is then used to perform gradient descent. The viability of the proposed optimization method is supported by several numerical experiments performed in one and two spatial dimensions. Among other things, these experiments show that a reaction term with simple linear dependence on supercooling in the phase field equation proves to be insufficient in certain scenarios. An alternative reaction term is considered to improve the models behavior.

Název v anglickém jazyce

Numerical optimization of the Dirichlet boundary condition in the phase field model with an application to pure substance solidification

Popis výsledku anglicky

As opposed to the distributed control of parabolic PDE's, very few contributions currently exist pertaining to the Dirichlet boundary condition control for parabolic PDE's. This motivates our interest in the Dirichlet boundary condition control for the phase field model describing the solidification of a pure substance from a supercooled melt. In particular, our aim is to control the time evolution of the temperature field on the boundary of the computational domain in order to achieve the prescribed shape of the crystal at the given time. To obtain efficient means of computing the gradient of the cost functional, we derive the adjoint problem formally. The gradient is then used to perform gradient descent. The viability of the proposed optimization method is supported by several numerical experiments performed in one and two spatial dimensions. Among other things, these experiments show that a reaction term with simple linear dependence on supercooling in the phase field equation proves to be insufficient in certain scenarios. An alternative reaction term is considered to improve the models behavior.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Computers and Mathematics with Applications

ISSN

0898-1221

e-ISSN

1873-7668

Svazek periodika

145

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

16

Strana od-do

90-105

Kód UT WoS článku

001033436600001

EID výsledku v databázi Scopus

2-s2.0-85163881714