Parallelization of the Algorithm WHAM with NVIDIA CUDA

Nicolo’ Savioli
Universita di Bologna, Corso di Studio in Ingegneria biomedica [LM-DM270] – Cesena
Universita di Bologna, 2013


   title={Parallelization of the Algorithm WHAM with NVIDIA CUDA},

   author={e Cellulare, Bioingegneria Molecolare and Severi, Stefano and Furini, Simone and Savioli, Nicolo and Sessione, II},



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The aim of my thesis is to parallelize the Weighting Histogram Analysis Method (WHAM), which is a popular algorithm used to calculate the Free Energy of a molecular system in Molecular Dynamics simulations. WHAM works in post processing in cooperation with another algorithm called Umbrella Sampling. Umbrella Sampling has the purpose to add a biasing in the potential energy of the system in order to force the system to sample a specific region in the configurational space. Several N independent simulations are performed in order to sample all the region of interest. Subsequently, the WHAM algorithm is used to estimate the original system energy starting from the N atomic trajectories. The parallelization of WHAM has been performed through CUDA, a language that allows to work in GPUs of NVIDIA graphic cards, which have a parallel architecture. The parallel implementation may sensibly speed up the WHAM execution compared to previous serial CPU implementations. However, the WHAM CPU code presents some temporal criticalities to very high numbers of interactions. The algorithm has been written in C++ and executed in UNIX systems provided with NVIDIA graphic cards. The results were satisfying obtaining an increase of performances when the model was executed on graphics cards with compute capability greater. Nonetheless, the GPUs used to test the algorithm is quite old and not designated for scientific calculations. It is likely that a further performance increase will be obtained if the algorithm would be executed in clusters of GPU at high level of computational efficiency. The thesis is organized in the following way: I will first describe the mathematical formulation of Umbrella Sampling and WHAM algorithm with their applications in the study of ionic channels and in Molecular Docking (Chapter 1); then, I will present the CUDA architectures used to implement the model (Chapter 2); and finally, the results obtained on model systems will be presented (Chapter 3).
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