Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fast integral equation methods for the heat equation and the modified
  Helmholtz equation in two dimensions   We present an efficient integral equation approach to solve the heat
equation, $u_t (\x) - \Delta u(\x) = F(\x,t)$, in a two-dimensional, multiply
connected domain, and with Dirichlet boundary conditions. Instead of using
integral equations based on the heat kernel, we take the approach of
discretizing in time, first. This leads to a non-homogeneous modified Helmholtz
equation that is solved at each time step. The solution to this equation is
formulated as a volume potential plus a double layer potential.The volume
potential is evaluated using a fast multipole-accelerated solver. The boundary
conditions are then satisfied by solving an integral equation for the
homogeneous modified Helmholtz equation. The integral equation solver is also
accelerated by the fast multipole method (FMM). For a total of $N$ points in
the discretization of the boundary and the domain, the total computational cost
per time step is $O(N)$ or $O(N\log N)$.

23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci