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 (r,theta,phi).  It was run on the new Ranger massively parallel supercomputer at the Texas Advanced Computing Center (TACC).  This is a very high performance computer with 62,976 CPUs and a theoretical peak speed of 580 teraflops.  In June 2008 it was the fourth fastest supercomputer in the world.  Ranger is a Sun Constellation Linux Cluster that uses quad-core AMD Opteron (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) schemes.  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 the magnetic 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 Passing Interface (MPI) for interprocessor communication.  Our code scales very well on many high-performance computer systems.  We have shown 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.