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