Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A spectral approach to numerical simulations of the ADM equations   We present a numerical study of the Einstein equations, according to the
Arnowitt-Deser-Misner (ADM) formalism, in order to simulate the dynamics of
gravitational fields. We took in consideration the original $3+1$ decomposition
of the ADM equations, in vacuum conditions, in simplified geometries. The
numerical code is based on spectral methods, making use of filtering
(de-aliasing) techniques. The algorithm has been stabilized via an adaptive
time-refinement, based on a procedure that checks self-consistently the
regularity of the solutions. The accuracy of our numerical model has been
validated through a series of standard tests. Finally, we present also a new
kind of initial data that can be used for testing numerical codes.

31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph