Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Role of PDE-Based Parameterization Techniques in Gradient-Based IGA
  Shape Optimization Applications   This paper proposes a shape optimization algorithm based on the principles of
Isogeometric Analysis (IGA) in which the parameterization of the geometry
enters the problem formulation as an additional PDE-constraint. Inspired by the
isoparametric principle of IGA, the parameterization and the governing state
equation are treated using the same numerical technique. This leads to a scheme
that is comparatively easy to differentiate, allowing for a fully symbolic
derivation of the gradient and subsequent gradient-based optimization. To
improve the efficiency and robustness of the scheme, the basis is re-selected
during each optimization iteration and adjusted to the current needs. The
scheme is validated in two test cases.

29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph