@inbook{5786,
  author = {A. van der Ploeg and R. Keppens and G. Toth and B. Hertzberger and P. Sloot},
  title = {Block incomplete LU-preconditioners for implicit solution of advection dominated problems},
  abstract = {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.},
  year = {1997},
  journal = {High-Performance Computing and Networking},
  volume = {1225},
  pages = {421-430},
  isbn = {0302-97433-540-62898-3},
  language = {eng},
}