After the development of the well-known iterative methods for solving systems of linear equations resulting from the finite difference approximations to elliptic partial differential equations the last decade some new iterative methods have been proposed. In this report we apply the fastests of these methods to the relatively simple problem of solving the Poison equation with Dirichlet boundary conditions on an octagon. Moreover we pay some attention
to stop criteria for iterative procedures. Experiments are given comparing the number of iterations for different stop criteria and also the iteration time ratio with respect to the point SOR method.
S.J. Bijlsma and R.J. Hoogendoorn. Experiments with interactive methods for solving the discrete Poisson equation
KNMI number: WR-79-01, Year: 1979, Pages: 45