Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Construction of analysis-suitable $G^1$ planar multi-patch
  parameterizations   Isogeometric analysis allows to define shape functions of global $C^{1}$
continuity (or of higher continuity) over multi-patch geometries. The
construction of such $C^{1}$-smooth isogeometric functions is a non-trivial
task and requires particular multi-patch parameterizations, so-called
analysis-suitable $G^{1}$ (in short, AS-$G^{1}$) parameterizations, to ensure
that the resulting $C^{1}$ isogeometric spaces possess optimal approximation
properties, cf. [7]. In this work, we show through examples that it is possible
to construct AS-$G^{1}$ multi-patch parameterizations of planar domains, given
their boundary. More precisely, given a generic multi-patch geometry, we
generate an AS-$G^{1}$ multi-patch parameterization possessing the same
boundary, the same vertices and the same first derivatives at the vertices, and
which is as close as possible to this initial geometry. Our algorithm is based
on a quadratic optimization problem with linear side constraints. Numerical
tests also confirm that $C^{1}$ isogeometric spaces over AS-$G^{1}$ multi-patch
parameterized domains converge optimally under mesh refinement, while for
generic parameterizations the convergence order is severely reduced.

21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn