Simulation Of Reaction-diffusion Processes Research Articles

Grouping techniques for large-scale cluster dynamics simulations of reaction diffusion processes

Cluster dynamics is a powerful, high fidelity, mesoscale method for modeling the kinetic evolution of point defects, impurities, and their clusters in materials and is commonly used in studying radiation damage. These methods excel at modeling nucleation, but often require too many equations to successfully model the long term growth and coarsening that govern microstructural evolution. One solution to this problem is to group equations into a coarser approximation of the cluster size distribution function which can reduce the cost of solution by many orders of magnitude. While such grouping methods have been advanced for a limited class of problems, no reliable method currently exists for the general case. This paper advances a framework for grouping arbitrary cluster dynamics problems, and develops several competing schemes based on that framework. These schemes are each evaluated against a variety of test problems designed to assess their accuracy, robustness, and efficiency.

Simulation of reaction diffusion processes over biologically relevant size and time scales using multi-GPU workstations.

Simulation of in vivo cellular processes with the reaction-diffusion master equation (RDME) is a computationally expensive task. Our previous software enabled simulation of inhomogeneous biochemical systems for small bacteria over long time scales using the MPD-RDME method on a single GPU. Simulations of larger eukaryotic systems exceed the on-board memory capacity of individual GPUs, and long time simulations of modest-sized cells such as yeast are impractical on a single GPU. We present a new multi-GPU parallel implementation of the MPD-RDME method based on a spatial decomposition approach that supports dynamic load balancing for workstations containing GPUs of varying performance and memory capacity. We take advantage of high-performance features of CUDA for peer-to-peer GPU memory transfers and evaluate the performance of our algorithms on state-of-the-art GPU devices. We present parallel e ciency and performance results for simulations using multiple GPUs as system size, particle counts, and number of reactions grow. We also demonstrate multi-GPU performance in simulations of the Min protein system in E. coli. Moreover, our multi-GPU decomposition and load balancing approach can be generalized to other lattice-based problems.

Parallel solutions for voxel-based simulations of reaction-diffusion systems.

There is an increasing awareness of the pivotal role of noise in biochemical processes and of the effect of molecular crowding on the dynamics of biochemical systems. This necessity has given rise to a strong need for suitable and sophisticated algorithms for the simulation of biological phenomena taking into account both spatial effects and noise. However, the high computational effort characterizing simulation approaches, coupled with the necessity to simulate the models several times to achieve statistically relevant information on the model behaviours, makes such kind of algorithms very time-consuming for studying real systems. So far, different parallelization approaches have been deployed to reduce the computational time required to simulate the temporal dynamics of biochemical systems using stochastic algorithms. In this work we discuss these aspects for the spatial TAU-leaping in crowded compartments (STAUCC) simulator, a voxel-based method for the stochastic simulation of reaction-diffusion processes which relies on the Sτ-DPP algorithm. In particular we present how the characteristics of the algorithm can be exploited for an effective parallelization on the present heterogeneous HPC architectures.