Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Fast Semi-implicit Method for Anisotropic Diffusion   Simple finite differencing of the anisotropic diffusion equation, where
diffusion is only along a given direction, does not ensure that the numerically
calculated heat fluxes are in the correct direction. This can lead to negative
temperatures for the anisotropic thermal diffusion equation. In a previous
paper we proposed a monotonicity-preserving explicit method which uses limiters
(analogous to those used in the solution of hyperbolic equations) to
interpolate the temperature gradients at cell faces. However, being explicit,
this method was limited by a restrictive Courant-Friedrichs-Lewy (CFL)
stability timestep. Here we propose a fast, conservative, directionally-split,
semi-implicit method which is second order accurate in space, is stable for
large timesteps, and is easy to implement in parallel. Although not strictly
monotonicity-preserving, our method gives only small amplitude temperature
oscillations at large temperature gradients, and the oscillations are damped in
time. With numerical experiments we show that our semi-implicit method can
achieve large speed-ups compared to the explicit method, without seriously
violating the monotonicity constraint. This method can also be applied to
isotropic diffusion, both on regular and distorted meshes.

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The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ