Application of GPU computing to upper bound rigid block analysis

Upper bound rigid block analysis involves the minimisation of a function describing the stability of a structure based upon a specific mechanism that is defined a priori. Minimisation of this function can be performed using local search algorithms, such as the Hooke and Jeeves algorithm, or by using global optimisation methods such as a multi-dimensional grid search. However, for complex mechanisms grid search methods are extremely inefficient as the dimensionality of the solution space increases with each additional optimisable variable, motivating the use of simplified grid searches, such as the univariate grid search, and computationally efficient implementations. Modern graphics cards are extremely powerful and are now being used for applications beyond graphical processing. The high performance of graphics processing units (GPUs) results from the many cores that process data in parallel. These cores all perform the same computations concurrently, albeit on different data; this allows the operations being performed to remain synchronised, minimising the required overhead. In this paper, a GPU implementation of the univariate search is proposed to calculate the stability of shallow circular tunnels in cohesive-frictional material using upper bound rigid block analysis. The GPU implementation allows the univariate search to evaluate many of the 'grid points' in parallel. Results will be presented to demonstrate the performance ofGPU univariate grid search in upper bound rigid block analysis.