Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An accelerated Poisson solver based on multidomain spectral
  discretization   This paper presents a numerical method for variable coefficient elliptic PDEs
with mostly smooth solutions on two dimensional domains. The PDE is discretized
via a multi-domain spectral collocation method of high local order (order 30
and higher have been tested and work well). Local mesh refinement results in
highly accurate solutions even in the presence of local irregular behavior due
to corner singularities, localized loads, etc. The system of linear equations
attained upon discretization is solved using a direct (as opposed to iterative)
solver with $O(N^{1.5})$ complexity for the factorization stage and $O(N \log
N)$ complexity for the solve. The scheme is ideally suited for executing the
elliptic solve required when parabolic problems are discretized via
time-implicit techniques. In situations where the geometry remains unchanged
between time-steps, very fast execution speeds are obtained since the solution
operator for each implicit solve can be pre-computed.

1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int