Keywords: discrete element method, parallel computing, domain decomposition, general purpose graphic processing unit, FDEM, GPU.

The DEM is a promising algorithm which is widely used in many practical fields especially by civil and mechanical engineers. However, the usage of this method is limited by its high computational cost and it is difficult to provide real time solution directly on desktop PCs. This situation becomes even worse when triangular shaped particles are involved.

Fine-grained parallel computation techniques are well fitted to the nature of the DEM and can greatly accelerate the computation of the DEM using reconfigurable hardware as a co-processor. GPUs are used to handle complex graphic rendering task on modern PCs. Benefitting from the combination of built-in support for floating point operations and parallel processing, GPUs can provide an accessible and highly efficient solution to dealing with problems requiring a high volume of arithmetic data-parallel computations.

A common flow for the DEM method is described. It is divided into three major steps: contact detection, contact interaction and position update. The direct area method is been used in the contact detection process. The combined finite-discrete element concept is used to obtain the contact force resulting from the contact interaction.

A two dimensional DEM implementation on a GPU is given. This approach achieved a speed up of about 240 times on a consumer level GPU, GeForce 8600M GT, compared to a similar algorithm run on a fast desktop PC. This design can also be used on faster GPUs with more stream processors and higher core clock rate to achieve even greater levels of speed up.

Practical problem involving large number of particles cannot be solved using a single domain. A two-dimensional domain decomposition technique is presented. The basic idea behind this method is to dynamically modify the boundaries of the sub-domains to maintain a stable number of particles in each sub-domain. To reduce the complexity of the solution, a simplified domain decomposition method has been used by setting the number of sub-domains in the y direction to 1, so only the borders of the sub-domains in the x direction need be changed during program execution.

As an overall conclusion, the GPU is a desirable platform for problems with data-parallel computations with a high ratio of arithmetic operations to memory operations, such as the DEM. It can achieve a very large speed up for the two-dimensional triangular shaped discrete element method compared to a similar algorithm run on a standard CPU.

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A. Munjiza, "Processing of Contact Interaction in the Combined Finite Discrete Element Method", in "The Combined Finite-Discrete Element Method", 35-72, 2004. doi:10.1002/0470020180.ch2

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