Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kernel-based collocation methods for heat transport on evolving surfaces   We propose algorithms for solving convective-diffusion partial differential
equations (PDEs), which model surfactant concentration and heat transport on
evolving surfaces, based on intrinsic kernel-based meshless collocation
methods. The algorithms can be classified into two categories: one collocates
PDEs directly and analytically, and the other approximates surface differential
operators by meshless pseudospectral approaches. The former is specifically
designed to handle PDEs on evolving surfaces defined by parametric equations,
and the latter works on surface evolutions based on point clouds. After some
convergence studies and comparisons, we demonstrate that the proposed method
can solve challenging PDEs posed on surfaces with high curvatures with
discontinuous initial conditions with correct physics.

25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat