Description of Our 3D MHD Computations
Our final prediction was run on a 3D mesh
with 201 x 191 x 432 mesh
points (16.5 million cells) in spherical coordinates
It was run on the new
massively parallel supercomputer at the
Computing Center (TACC). This is a very high performance
with 62,976 CPUs and a theoretical peak speed of 580 teraflops.
In June 2008 it was the
fourth fastest supercomputer in the
Ranger is a Sun Constellation Linux Cluster that uses quad-core AMD
(Barcelona) 2.3 GHz processors with an Infiniband interconnect.
(In layman's terms, it is a very fast machine!) The staff at TACC
graciously agreed to give us dedicated time to run our
simulations without interruption in order to make a timely prediction
for the eclipse, and were very helpful in making this happen.
We used our spherical 3D (magnetohydrodynamic) MHD
code MAS, which integrates
the MHD equations using semi-implicit (Alfvén and sound waves),
fully implicit (diffusive terms), and explicit (flow terms)
We solve the very large sparse matrix equations generated by these
algorithms using a preconditioned iterative conjugate gradient
solver. We set as a boundary condition the radial component of
field at the base of the corona. This field is deduced from MDI magnetograms
aboard the SOHO spacecraft,
which measure the line
of sight component of the photospheric magnetic field from space.
Our code is written in Fortran
90 and uses the Message
Interface (MPI) for interprocessor communication. Our code
very well on many high-performance computer systems. We have
essentially linear scaling with processor number up to
about 4096 processors.
Our calculation ran for about 75,000 time steps,
relaxing the corona
in time (for about 3.4 days of solar time) towards a steady state,
thereby approximating the state of the solar corona. Our time
step in the computation was about 4.5 seconds. For our
final eclipse prediction we used 4368 processors on Ranger
and ran continuously for about 3.6 days.