Astrophysics is the field where radiative transfer plays
an extremely
important, even sometimes crucial, role. Radiation is
almost
exclusively the only information about a distant object we
have.
Yet, the radiation is not only a passive probe of the
physical state
of the object, but in many cases an active energy and
momentum balance
agent. However, a treatment of radiation involves a highly
non-linear,
highly coupled, highly non-local, multi-dimensional, and
sometimes even
time-dependent problem, which poses enormous numerical
challenges.
In this review, I will summarize various numerical
techniques used to
deal with a non-local and non-linear coupling of radiation
and matter.
Efficient methods can either be constructed purely
mathematically,
by formulating the problem essentially exactly, and using
various
pre-conditioners to invert resulting huge matrices
The methods can also be developed using our physical
insight,
by realizing that some parts of the coupling are more
important than
others, which leads to techniques in which an important
part of
the coupling in treated directly, while the rest is
treated iteratively.
In fact, the most successful techniques are those which
combine both
approaches, and which can be generically called
physics-based
pre-conditioning techniques. The group of methods
developed in
astrophysics called the Accelerated Lambda Iteration (ALI)
method,
are a typical example of such techniques. In this paper, I
will
discuss the method in a general context, and show its
various
applications.
Copyright. All Rights Reserved.