Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fast Adaptive Algorithms in the Non-Standard Form for Multidimensional
  Problems   We present a fast, adaptive multiresolution algorithm for applying integral
operators with a wide class of radially symmetric kernels in dimensions one,
two and three. This algorithm is made efficient by the use of separated
representations of the kernel. We discuss operators of the class
$(-\Delta+\mu^{2}I)^{-\alpha}$, where $\mu\geq0$ and $0<\alpha<3/2$, and
illustrate the algorithm for the Poisson and Schr\"{o}dinger equations in
dimension three. The same algorithm may be used for all operators with radially
symmetric kernels approximated as a weighted sum of Gaussians, making it
applicable across multiple fields by reusing a single implementation.
  This fast algorithm provides controllable accuracy at a reasonable cost,
comparable to that of the Fast Multipole Method (FMM). It differs from the FMM
by the type of approximation used to represent kernels and has an advantage of
being easily extendable to higher dimensions.

34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an