Details
| Original language | English |
|---|---|
| Pages (from-to) | 2271-2288 |
| Number of pages | 18 |
| Journal | SIAM Journal on Control and Optimization |
| Volume | 55 |
| Issue number | 4 |
| Publication status | Published - 2017 |
| Externally published | Yes |
Abstract
This paper is concerned with an optimal control problem governed by a regularized fracture model using a phase-field technique. To avoid the nondifferentiability due to the irreversibility constraint on the fracture growth, the phase-field fracture model is relaxed using a penalization approach. The existence of a solution to the penalized fracture model is shown, and the existence of at least one solution for the regularized optimal control problem is established. Moreover, the linearized fracture model is considered and used to establish first order necessary conditions as well as to discuss QP-approximations to the nonlinear optimization problem. A numerical example suggests that these can be used to obtain a fast convergent algorithm.
Keywords
- Existence of solutions, Optimal control, Phase-field, Regularized fracture model
ASJC Scopus subject areas
- Mathematics(all)
- Control and Optimization
- Mathematics(all)
- Applied Mathematics
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In: SIAM Journal on Control and Optimization, Vol. 55, No. 4, 2017, p. 2271-2288.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - An optimal control problem governed by a regularized phase-field fracture propagation model
AU - Neitzel, I.
AU - Wick, T.
AU - Wollner, W.
N1 - Publisher Copyright: © 2017 Society for Industrial and Applied Mathematics. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2017
Y1 - 2017
N2 - This paper is concerned with an optimal control problem governed by a regularized fracture model using a phase-field technique. To avoid the nondifferentiability due to the irreversibility constraint on the fracture growth, the phase-field fracture model is relaxed using a penalization approach. The existence of a solution to the penalized fracture model is shown, and the existence of at least one solution for the regularized optimal control problem is established. Moreover, the linearized fracture model is considered and used to establish first order necessary conditions as well as to discuss QP-approximations to the nonlinear optimization problem. A numerical example suggests that these can be used to obtain a fast convergent algorithm.
AB - This paper is concerned with an optimal control problem governed by a regularized fracture model using a phase-field technique. To avoid the nondifferentiability due to the irreversibility constraint on the fracture growth, the phase-field fracture model is relaxed using a penalization approach. The existence of a solution to the penalized fracture model is shown, and the existence of at least one solution for the regularized optimal control problem is established. Moreover, the linearized fracture model is considered and used to establish first order necessary conditions as well as to discuss QP-approximations to the nonlinear optimization problem. A numerical example suggests that these can be used to obtain a fast convergent algorithm.
KW - Existence of solutions
KW - Optimal control
KW - Phase-field
KW - Regularized fracture model
UR - http://www.scopus.com/inward/record.url?scp=85027717797&partnerID=8YFLogxK
U2 - 10.1137/16m1062375
DO - 10.1137/16m1062375
M3 - Article
AN - SCOPUS:85027717797
VL - 55
SP - 2271
EP - 2288
JO - SIAM Journal on Control and Optimization
JF - SIAM Journal on Control and Optimization
SN - 0363-0129
IS - 4
ER -