mwang@watmath.UUCP (mwang) (03/12/84)
_D_E_P_A_R_T_M_E_N_T _O_F _C_O_M_P_U_T_E_R _S_C_I_E_N_C_E
_U_N_I_V_E_R_S_I_T_Y _O_F _W_A_T_E_R_L_O_O
_S_E_M_I_N_A_R _A_C_T_I_V_I_T_I_E_S
_N_U_M_E_R_I_C_A_L _A_N_A_L_Y_S_I_S _S_E_M_I_N_A_R
- Thursday, March 22, 1984.
Dr. W. Liniger of IBM Thomas J. Watson Research Center
will speak on ``Fast Finite Difference Algorithms for
Solving Poisson's Equation on General Two-dimensional
Regions''.
TIME: 3:30 PM
ROOM: MC 6091A
ABSTRACT
Fast finite difference algorithms are proposed for
solving Poisson's equation on general two-dimensional
regions. These algorithms are based on a variant of
the marching method but are intrinsically much more
stable than the latter and thus can be applied on rela-
tively large grids without resorting to multiple shoot-
ing. The algorithms are associated with a one-
parameter family of factored second-order complex
discretizations of the Laplace operator and the gain in
stability is due to solving initial value problems for
two first-order difference equations, rather than one
second-order equation as in the conventional marching
method. These initial value problems represent back-
solves in a sparse Choleski decomposition. The stabil-
ity and accuracy of the method can be further con-
trolled by the choice of the parameter on which the
discretization depends. The factored discretization
lends itself well to an iterative implementation by
means of the preconditioned conjugate gradient method,
as well as for a direct implementation. The algorithms
were tested successfully on regions with complicated
geometries, including multiply connected ones.
March 12, 1984