PARALLELIZED IMPLICIT PROPAGATORS FOR THE FINITE-DIFFERENCE SCHRODINGER-EQUATION

Jonathan Parker

doi:10.1016/0010-4655(95)00036-F

PARALLELIZED IMPLICIT PROPAGATORS FOR THE FINITE-DIFFERENCE SCHRODINGER-EQUATION

1995-08-01

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DOI：10.1016/0010-4655(95)00036-F

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We describe the application of block Gauss-Seidel and block Jacobi iterative methods to the design of implicit propagators for finite-difference models of the time-dependent Schrodinger equation. The block-wise iterative methods discussed here are mixed direct-iterative methods for solving simultaneous equations, in the sense that direct methods (e.g. LU decomposition) are used to invert certain block sub-matrices, and iterative methods are used to complete the solution. We describe parallel variants of the basic algorithm that are well suited to the medium- to coarse-grained parallelism of work-station clusters, and MIMD supercomputers, and we show that under a wide range of conditions, fine-grained parallelism of the computation can be achieved. Numerical tests are conducted on a typical one-electron atom Hamiltonian. The methods converge robustly to machine precision (15 significant figures), in some cases in as few as 6 or 7 iterations. The rate of convergence is nearly independent of the finite-difference grid-point separations.

PARALLELIZED IMPLICIT PROPAGATORS FOR THE FINITE-DIFFERENCE SCHRODINGER-EQUATION

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