A. van der Ploeg
Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands
R. Keppens
FOM-Institute for Plasma-Physics Rijnhuizen, The Netherlands
G. Tóth
Astronomical Institute, Utrecht Univ., Utrecht, The Netherlands
Proceedings of HPCN'97, Vienna, Austria
Lecture Notes in Computer Science, 1225, 421-430
In many astrophysical hydrodynamical and magnetohydrodynamical problems
explicit time integration is inefficient due to the disparate time scales, or
because we are looking for a steady-state. Implicit schemes can offer a
viable alternative, which requires efficient solution of large linear
systems. In multi-dimensional flows these linear systems
cannot be solved with a direct method, so that iterative
methods must be used. Since the physical problems are often advection
dominated, the matrix is approximately anti-symmetric and non-diagonally
dominant, thus preconditioning is necessary.
We describe a new approach, in which a GMRES type iterative method is
combined with an Eisenstat implementation of a relaxed form of
a modified Block Incomplete LU-decomposition as preconditioner.
Parallelisation aspects of the algorithm are also discussed.