Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computational performance studies for space-time phase-field fracture
  optimal control problems   The purpose of this work are computational demonstations for a newly
developed space-time phase-field fracture optimal control framework. The
optimal control solution algorithm is a Newton algorithm, which is obtained
with the reduced approach by eliminating the state constraint. Due to the crack
irreversibility constraint, a rate-independent problem arises, which is treated
by penalization and for which we utilize a space-time approach. Therein, we
deal with the state, adjoint, tangent, and adjoint Hessian equations. Our fully
discretized space-time optimization algorithm is presented and extensively
tested with various numerical experiments.

27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th