The integration of different variants of the (I)LU algorithm in the LINSOL program package Original Research Article

LINSOL [H. Häfner, W. Schönauer, R. Weiss, in: H. Lederer, F. Hertwick (Eds.), Proceedings of the Fourth European SGI/Cray MPP Workshop, IPP R/46, Max-Planck-Institut für Plasmaphysik, 1998, pp. 242–251], [W. Schönauer, H. Häfner, R. Weiss, in: M. Heath et al. (Eds.), Proceedings of the 8th SIAM Conference on Parallel Processing for Scientific Computing, SIAM, 1997] is an iterative linear solver package (solving Ax=b) with optional direct solvers as preconditioners. The program package is adapted to the application of sparse matrices, but can be efficiently applied to full matrices, too. It contains presently fourteen iterative methods and nine polyalgorithms of generalized Conjugate Gradient (CG) methods. Eight different data structures are supported by LINSOL to ease the embedding of LINSOL into an application as well as the mapping of arbitrary sparse matrices to storage patterns. The direct solver for (I)LU preconditioning is the Gauss algorithm operating within the skyline of the matrix of the linear system. It can be used as an “emergency exit”, i.e., the complete LU factorization is performed for the preconditioning (which means that the system is solved by Gauss elimination and the iterative method will normally converge in one step), or as Incomplete LU preconditioner. Three variants of preconditioning have been integrated into the program package LINSOL and are investigated in this paper.