Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Schwarz waveform relaxation method for one dimensional Schr{\"o}dinger
  equation with general potential   In this paper, we apply the Schwarz Waveform Relaxation (SWR) method to the
one dimensional Schr{\"o}dinger equation with a general linear or a nonlinear
potential. We propose a new algorithm for the Schr{\"o}dinger equation with
time independent linear potential, which is robust and scalable up to 500
subdo-mains. It reduces significantly computation time compared with the
classical algorithms. Concerning the case of time dependent linear potential or
the non-linear potential, we use a preprocessed linear operator for the zero
potential case as preconditioner which lead to a preconditioned algorithm. This
ensures high scalability. Besides, some newly constructed absorbing boundary
conditions are used as the transmission condition and compared numerically.

35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas