Parallel Approaches in Molecular Dynamics Simulations

In this contribution we will present the survey of our past and current endeavor on parallel approaches in molecular modeling algorithm development, for example, molecular dynamics (MD) simulation. In particular, we will describe the new split integration symplectic method for the numerical solution of molecular dynamics equations and methods for the determination of vibrational frequencies and normal modes of large systems, and the distributed diagonal force decomposition method, a parallel method for MD simulation. Parallel computer programs are used to speed up the calculation of computationally demanding scientific problems such as MD simulations. Parallel MD methods distribute calculations to the processors of a parallel computer but the efficiency of parallel computation decreases due to inter processor communication. Calculating the interactions among all atoms of the simulated system is the most computationally demanding part of an MD simulation. Parallel methods differ in their distribution of these calculations among the processors, while the distribution dictates the method’s communication requirements. We have developed a computer program for molecular dynamics simulation that implements the split integration symplectic method and is designed to run on specialized parallel computers. The molecular dynamics integration is performed by the new integration method, which analytically treats high-frequency vibrational motion and thus enables the use of longer simulation time steps. The low-frequency motion Dušanka Janežič National Institute of Chemistry, Hajdrihova 19, 1000 Ljubljana, Slovenia, e-mail: [email protected] Urban Borštnik National Institute of Chemistry, Hajdrihova 19, 1000 Ljubljana, Slovenia, e-mail: [email protected] Matej Praprotnik National Institute of Chemistry, Hajdrihova 19, 1000 Ljubljana, Slovenia, e-mail: [email protected] R. Trobec et al. (eds.), Parallel Computing, DOI 10.1007/978-1-84882-409-6_10, 281 c © Springer-Verlag London Limited 2009 282 Dušanka Janežič, Urban Borštnik and Matej Praprotnik is treated numerically on specially designed parallel computers, which decreases the computational time of each simulation time step. We study the computational performance of simulation on specialized computers and provide a comparison to standard personal computers. The combination of the new integration method with two specialized parallel computers is an effective way to significantly increase the speed of molecular dynamics simulations. We have also developed a parallel method for MD simulation, the distributeddiagonal force decomposition method. Compared to other methods its communication requirements are lower and it features dynamic load balancing, which increase the parallel efficiency. We have designed a cluster of personal computers featuring a topology based on the new method. Its lower communication time in comparison to standard topologies enables an even greater parallel efficiency. 10.1 Split Integration Symplectic Method The standard integrators for solving the classical equations of motion are the secondorder symplectic leap-frog Verlet (LFV) algorithm [1] and its variants. Their power lies in their simplicity since the only required information about the studied physical system are its interacting potential and the timescale of the fastest motion in the system, which determines the integration time step size. Therefore they are employed for solving dynamics problems in a variety of scientific fields, for example, molecular dynamics (MD) simulation [2, 3], celestial mechanics [4–6], and accelerator physics [7]. However, in the case of MD integration, the integration time step size is severely limited due to the numerical treatment of the high-frequency molecular vibrations, which represent the fastest motion in the system [8]. Therefore, a huge number of integration steps is usually required to accurately sample the phase space composed of all the coordinates and momenta of all the particles. This is a timeconsuming task and is often too demanding for the capabilities of contemporary computers. One way of overcoming the limitation of the standard methods’ integration time step size is to analytically treat high-frequency molecular vibrations. This requires the standard theory of molecular vibrations [9] to be built into the integration method. In this way the fast degrees of freedom are rigorously treated and not removed, as in case of rigid-body dynamics [10–12], where small molecules are treated as rigid bodies. Such semi-analytical second-order symplectic integrators were developed by combining MD integration and the standard theory of molecular vibrations [13–16]. The unique feature of these MD integrators is that the standard theory of molecular vibrations, which is a very efficient tool to analyze the dynamics of the studied system from computed trajectories [17–23], is used not to analyze, but to compute trajectories of molecular systems. Information about the energy distribution of normal modes and the energy transfer between them is obtained without 10 Parallel Approaches in Molecular Dynamics Simulations 283 additional calculations. The analytical description of coupled molecular vibrations can be employed only when using the normal coordinates [9, 13–15] and a translating and rotating internal coordinate system of each molecule [24,25]. The dynamics of an Eckart frame has to be adopted to be used within the second-order generalized leap-frog scheme [26, 27] for MD integration. This assures the time reversibility of the methods [13,16]. In the following we shortly summarize technical details of the method. In MD simulations for each atom of the system the Hamilton equations are solved