Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical investigation of the conditioning for plane wave discontinuous
  Galerkin methods   We present a numerical study to investigate the conditioning of the plane
wave discontinuous Galerkin discretization of the Helmholtz problem. We provide
empirical evidence that the spectral condition number of the plane wave basis
on a single element depends algebraically on the mesh size and the wave number,
and exponentially on the number of plane wave directions; we also test its
dependence on the element shape. We show that the conditioning of the global
system can be improved by orthogonalization of the local basis functions with
the modified Gram-Schmidt algorithm, which results in significantly fewer GMRES
iterations for solving the discrete problem iteratively.

30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an