Efficient solution of liquid state integral equations using the Newton-GMRES algorithm

Abstract

We present examples of the accurate, robust and efficient solution of Ornstein-Zernike type integral equations which describe the structure of both homogeneous and inhomogeneous fluids. In this work we use the Newton-GMRES algorithm as implemented in the public-domain nonlinear Krylov solvers NKSOL [ P. Brown, Y. Saad, SIAM J. Sci. Stat. Comput. 11 (1990) 450] and NITSOL [ M. Pernice, H.F. Walker, SIAM J. Sci. Comput. 19 (1998) 302]. We compare and contrast this method with more traditional approaches in the literature, using Picard iteration (successive-substitution) and hybrid Newton-Raphson and Picard methods, and a recent vector extrapolation method [ H.H.H. Homeier, S. Rast, H. Krienke, Comput. Phys. Commun. 92 (1995) 188]. We find that both the performance and ease of implementation of these nonlinear solvers recommend them for the solution of this class of problem.