PSHAKE: A quadratically convergent SHAKE in O(n^{2})
Abstract
An algorithm for solving arbitrary linear constraints in molecular dynamics simulations of rigid and semirigid molecules is presented. The algorithm  PSHAKE  is a modified version of the SHAKE [J.P. Ryckaert, G. Ciccotti, H.J.C. Berendsen, Numerical integration of the cartesian equations of motion of a system with constraints: Molecular dynamics of nalkanes, J. Comput. Phys. 23 (1977) 327341.] algorithm with a preconditioner applied which effectively decouples the constraint equations. It achieves quadratic convergence, as does MSHAKE [V. Kräutler, W.F. van Gunsteren, P.H. Hünenberger, A fast SHAKE algorithm to solve distance constraint equations for small molecules in molecular dynamics simulations. J. Comput. Chem. 22 (5) (2001) 501508.], yet at a cost of only O(n^{2}) operations per iteration, as opposed to O(n^{3}) per iteration for MSHAKE. The algorithm is applied to simulations of rigid water, DMSO, chlorophorm and nonrigid ethane and cyclohexane and is shown to be faster than MSHAKE by up to a factor of three for relatively small error tolerances.
 Publication:

Journal of Computational Physics
 Pub Date:
 January 2007
 DOI:
 10.1016/j.jcp.2006.05.032
 Bibcode:
 2007JCoPh.220..740G