Revisiting Molecular Dynamics on a CPU/GPU system: Water Kernel and SHAKE Parallelization.

We report Graphics Processing Unit (GPU) and Open-MP parallel implementations of water-specific force calculations and of bond constraints for use in Molecular Dynamics simulations. We focus on a typical laboratory computing-environment in which a CPU with a few cores is attached to a GPU. We discuss in detail the design of the code and we illustrate performance comparable to highly optimized codes such as GROMACS. Beside speed our code shows excellent energy conservation. Utilization of water-specific lists allows the efficient calculations of non-bonded interactions that include water molecules and results in a speed-up factor of more than 40 on the GPU compared to code optimized on a single CPU core for systems larger than 20,000 atoms. This is up four-fold from a factor of 10 reported in our initial GPU implementation that did not include a water-specific code. Another optimization is the implementation of constrained dynamics entirely on the GPU. The routine, which enforces constraints of all bonds, runs in parallel on multiple Open-MP cores or entirely on the GPU. It is based on Conjugate Gradient solution of the Lagrange multipliers (CG SHAKE). The GPU implementation is partially in double precision and requires no communication with the CPU during the execution of the SHAKE algorithm. The (parallel) implementation of SHAKE allows an increase of the time step to 2.0fs while maintaining excellent energy conservation. Interestingly, CG SHAKE is faster than the usual bond relaxation algorithm even on a single core if high accuracy is expected. The significant speedup of the optimized components transfers the computational bottleneck of the MD calculation to the reciprocal part of Particle Mesh Ewald (PME).

MOIL-opt: Energy-Conserving Molecular Dynamics on a GPU/CPU system.

We report an optimized version of the molecular dynamics program MOIL that runs on a shared memory system with OpenMP and exploits the power of a Graphics Processing Unit (GPU). The model is of heterogeneous computing system on a single node with several cores sharing the same memory and a GPU. This is a typical laboratory tool, which provides excellent performance at minimal cost. Besides performance, emphasis is made on accuracy and stability of the algorithm probed by energy conservation for explicit-solvent atomically-detailed-models. Especially for long simulations energy conservation is critical due to the phenomenon known as "energy drift" in which energy errors accumulate linearly as a function of simulation time. To achieve long time dynamics with acceptable accuracy the drift must be particularly small. We identify several means of controlling long-time numerical accuracy while maintaining excellent speedup. To maintain a high level of energy conservation SHAKE and the Ewald reciprocal summation are run in double precision. Double precision summation of real-space non-bonded interactions improves energy conservation. In our best option, the energy drift using 1fs for a time step while constraining the distances of all bonds, is undetectable in 10ns simulation of solvated DHFR (Dihydrofolate reductase). Faster options, shaking only bonds with hydrogen atoms, are also very well behaved and have drifts of less than 1kcal/mol per nanosecond of the same system. CPU/GPU implementations require changes in programming models. We consider the use of a list of neighbors and quadratic versus linear interpolation in lookup tables of different sizes. Quadratic interpolation with a smaller number of grid points is faster than linear lookup tables (with finer representation) without loss of accuracy. Atomic neighbor lists were found most efficient. Typical speedups are about a factor of 10 compared to a single-core single-precision code.

SHAKE parallelization.

SHAKE is a widely used algorithm to impose general holonomic constraints during molecular simulations. By imposing constraints on stiff degrees of freedom that require integration with small time steps (without the constraints) we are able to calculate trajectories with time steps larger by approximately a factor of two. The larger time step makes it possible to run longer simulations. Another approach to extend the scope of Molecular Dynamics is parallelization. Parallelization speeds up the calculation of the forces between the atoms and makes it possible to compute longer trajectories with better statistics for thermodynamic and kinetic averages. A combination of SHAKE and parallelism is therefore highly desired. Unfortunately, the most widely used SHAKE algorithm (of bond relaxation) is inappropriate for parallelization and alternatives are needed. The alternatives must minimize communication, lead to good load balancing, and offer significantly better performance than the bond relaxation approach. The algorithm should also scale with the number of processors. We describe the theory behind different implementations of constrained dynamics on parallel systems, and their implementation on common architectures.