Pre-conditioning

  To improve the condition of our equation system it is feasible to apply a pre-conditioning algorithm. Thereby faster convergence of an iterative solver is observed. The best results are obtained by using an incomplete LU factorization with threshold pivoting (ILUT) algorithm [Saa88]. Thereby the system matrix is split into an upper matrix U and lower matrix L during factorization. This factorization generates off-diagonal entries in the system matrix. To preserve the sparse structure of the system matrix and for efficient memory management not all elements are taken into account for factorization. The fill-in per row and a given tolerance determines which elements are kept for pre-conditioning. The success of pre-conditioning strongly depends on the number of matrix entries, because more fill-in during pre-conditioning causes higher memory consumption and increases the time used by the iterative solver.