Comparison of two methods for solving linear equations occurring in molecular dynamics applications Original Research Article

Consider molecular dynamics simulations of systems containing large molecules such as proteins, where all fast bond vibrations are frozen. An important part of the computational overhead then comes from solving a large set of linear equations for determining the bonded forces (constraint forces). The corresponding matrix is symmetric, positive definite and has a very sparse nature. In this article we compare efficient implementations of the Conjugate Gradient method and an improved version of Cholesky Factorization for solving such types of linear equations. Based on both theoretical predictions and practical simulation tests on three different proteins, we show that the improved Cholesky method is a factor 15 faster than the Conjugate Gradient method.