TY - UNPB

T1 - Space-time formulation and time discretization of phase-field fracture optimal control problems

AU - Khimin, Denis

AU - Steinbach, Marc C.

AU - Wick, Thomas

N1 - 17 pages

PY - 2021/10/21

Y1 - 2021/10/21

N2 - The purpose of this work is the development of space-time discretization schemes for phase-field optimal control problems. First, a time discretization of the forward problem is derived using a discontinuous Galerkin formulation. Here, a challenge is to include regularization terms and the crack irreversibility constraint. The optimal control setting is formulated by means of the Lagrangian approach from which the primal part, adjoint, tangent and adjoint Hessian are derived. Herein the overall Newton algorithm is based on a reduced approach by eliminating the state constraint. From the low-order discontinuous Galerkin discretization, adjoint time-stepping schemes are finally obtained.

AB - The purpose of this work is the development of space-time discretization schemes for phase-field optimal control problems. First, a time discretization of the forward problem is derived using a discontinuous Galerkin formulation. Here, a challenge is to include regularization terms and the crack irreversibility constraint. The optimal control setting is formulated by means of the Lagrangian approach from which the primal part, adjoint, tangent and adjoint Hessian are derived. Herein the overall Newton algorithm is based on a reduced approach by eliminating the state constraint. From the low-order discontinuous Galerkin discretization, adjoint time-stepping schemes are finally obtained.

KW - math.OC

KW - cs.NA

KW - math.NA

KW - 74R10, 65N30, 49M15, 49K20, 35Q74

M3 - Preprint

BT - Space-time formulation and time discretization of phase-field fracture optimal control problems

ER -