Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On an interior-exterior nonoverlapping domain decomposition method for
  the Poisson--Boltzmann equation   A nonoverlapping domain decomposition method is studied for the linearized
Poisson--Boltzmann equation, which is essentially an interior-exterior
transmission problem with bounded interior and unbounded exterior. This problem
is different from the classical Schwarz alternating method for bounded
nonoverlapping subdomains well studied by Lions in 1990, and is challenging due
to the existence of unbounded subdomain. To obtain the convergence, a new
concept of interior-exterior Sobolev constant is introduced and a spectral
equivalence of related Dirichlet-to-Neumann operators is established
afterwards. We prove rigorously that the spectral equivalence results in the
convergence of interior-exterior iteration. Some numerical simulations are
provided to investigate the optimal stepping parameter of iteration and to
verify our convergence analysis.

31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph