For the Newton algorithm we need to solve repeatedly a large sparse system of linear equations (3.5-13).
As mentioned above the coefficient matrix, i.e. the Jacobian matrix
, has a nine block-diagonal structure. Only the nine block-diagonals
(Figure 3.5-1) of the matrix have non-zero elements and are
therefore stored. Considerable effort has been made in house by
Heinreichsberger and Stiftinger [Hei92] on iterative methods, so we
omit the discussion of the algorithms. In PROMIS two linear
solvers are usually provided, a direct GAUSS solver and an
iterative SOR (Successive Over-Relaxation) solver. Both
are highly customized to the matrix structure.
