Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Toward a Consistent Framework for High Order Mesh Refinement Schemes in
  Numerical Relativity   It has now become customary in the field of numerical relativity to couple
high order finite difference schemes to mesh refinement algorithms. To this
end, different modifications to the standard Berger-Oliger adaptive mesh
refinement algorithm have been proposed. In this work we present a fourth order
stable mesh refinement scheme with sub-cycling in time for numerical
relativity. We do not use buffer zones to deal with refinement boundaries but
explicitly specify boundary data for refined grids. We argue that the
incompatibility of the standard mesh refinement algorithm with higher order
Runge Kutta methods is a manifestation of order reduction phenomena, caused by
inconsistent application of boundary data in the refined grids. Our scheme also
addresses the problem of spurious reflections that are generated when
propagating waves cross mesh refinement boundaries. We introduce a transition
zone on refined levels within which the phase velocity of propagating modes is
allowed to decelerate in order to smoothly match the phase velocity of coarser
grids. We apply the method to test problems involving propagating waves and
show a significant reduction in spurious reflections.

30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn