Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topology optimization on two-dimensional manifolds   This paper implements topology optimization on two-dimensional manifolds. In
this paper, the material interpolation is implemented on a material parameter
in the partial differential equation used to describe a physical field, when
this physical field is defined on a two-dimensional manifold; the material
density is used to formulate a mixed boundary condition of the physical field
and implement the penalization between two different types of boundary
conditions, when this physical field is defined on a three-dimensional domain
with its boundary conditions defined on the two-dimensional manifold
corresponding a surface or an interface of this three-dimensional domain. Based
on the homeomorphic property of two-dimensional manifolds, typical
two-dimensional manifolds, e.g., sphere, torus, M\"{o}bius strip and Klein
bottle, are included in the numerical tests, which are provided for the
problems on fluidic mechanics, heat transfer and electromagnetics.

6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn