Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Calculating initial data for the conformal Einstein equations by
  pseudo-spectral methods   We present a numerical scheme for determining hyperboloidal initial data sets
for the conformal field equations by using pseudo-spectral methods. This
problem is split into two parts. The first step is the determination of a
suitable conformal factor which transforms from an initial data set in physical
space-time to a hyperboloidal hypersurface in the ambient conformal manifold.
This is achieved by solving the Yamabe equation, a non-linear second order
equation. The second step is a division by the conformal factor of certain
fields which vanish on $\scri$, the zero set of the conformal factor. The
challenge there is to numerically obtain a smooth quotient. Both parts are
treated by pseudo-spectral methods. The non-linear equation is solved
iteratively while the division problem is treated by transforming the problem
to the coefficient space, solving it there by the QR-factorisation of a
suitable matrix, and then transforming back. These hyperboloidal initial data
can be used to generate general relativistic space-times by evolution with the
conformal field equations.

20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg