Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A fast spectral method for the Boltzmann collision operator with general
  collision kernels   We propose a simple fast spectral method for the Boltzmann collision operator
with general collision kernels. In contrast to the direct spectral method
\cite{PR00, GT09} which requires $O(N^6)$ memory to store precomputed weights
and has $O(N^6)$ numerical complexity, the new method has complexity
$O(MN^4\log N)$, where $N$ is the number of discretization points in each of
the three velocity dimensions and $M$ is the total number of discretization
points on the sphere and $M\ll N^2$. Furthermore, it requires no precomputation
for the variable hard sphere (VHS) model and only $O(MN^4)$ memory to store
precomputed functions for more general collision kernels. Although a faster
spectral method is available \cite{MP06} (with complexity $O(MN^3\log N)$), it
works only for hard sphere molecules, thus limiting its use for practical
problems. Our new method, on the other hand, can apply to arbitrary collision
kernels. A series of numerical tests is performed to illustrate the efficiency
and accuracy of the proposed method.

37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph