Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Domain decomposition algorithms for two dimensional linear Schr\"odinger
  equation   This paper deals with two domain decomposition methods for two dimensional
linear Schr{\"o}dinger equation, the Schwarz waveform relaxation method and the
domain decomposition in space method. After presenting the classical
algorithms, we propose a new algorithm for the free Schr{\"o}dinger equation
and a preconditioned algorithm for the general Schr{\"o}dinger equation. These
algorithms are studied numerically, which shows that the two new algorithms
could accelerate the convergence and reduce the computation time. Besides the
traditional Robin transmission condition, we also propose to use a newly
constructed absorbing condition as the transmission condition.

25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an