Complex generalized minimal residual algorithm for iterative solution of quantum-mechanical reactive scattering equations Article

Chatfield, DC, Reeves, MS, Truhlar, DG et al. (1992). Complex generalized minimal residual algorithm for iterative solution of quantum-mechanical reactive scattering equations . JOURNAL OF CHEMICAL PHYSICS, 97(11), 8322-8333. 10.1063/1.463402

cited authors

  • Chatfield, DC; Reeves, MS; Truhlar, DG; Duneczky, C; Schwenke, DW

authors

abstract

  • A complex GMRes (generalized minimum residual) algorithm is presented and used to solve dense systems of linear equations arising in variational basis-set approaches to quantum-mechanical reactive scattering. The examples presented correspond to physical solutions of the Schrödinger equation for the reactions O+HD→OH+D, D+H2→HD+H, and H+H2→ H2 +H. It is shown that the computational effort for solution with GMRes depends upon both the dimension of the linear system and the total energy of the reaction. In several cases with dimensions in the range 1110-5632, GMRes outperforms the LAPACK direct solver, with speedups for the linear equation solution as large as a factor of 23. In other cases, the iterative algorithm does not converge within a reasonable time. These convergence differences can be correlated with "indices of diagonal dominance," which we define in detail and which are relatively easy to compute. Furthermore, we find that for a given energy, the computational effort for GMRes can vary with dimension as favorably as M1.7, where M is the dimension of the linear system, whereas the computer time for a direct method is approximately proportional to the cube of the dimension of the linear system. © 1992 American Institute of Physics.

publication date

  • January 1, 1992

published in

Digital Object Identifier (DOI)

start page

  • 8322

end page

  • 8333

volume

  • 97

issue

  • 11