Scaling

  Equation systems resulting from diffusion problems can vary over several orders of magnitude in the main diagonal. Therefore, each row of the whole system has to be scaled to the largest entry within the row. The main-diagonal is scaled to unity. This scaling operation affects the pre-conditioner in a strong manner because the off-diagonal values are determing the new main-diagonal entries during Gauß elimination. It is also possible to scale the off-diagonals while simultaneously conserving the main diagonals with advanced schemes [Fis94].