Hypercubic storage layout and transforms in arbitrary dimensions using GPUs and CUDA

Abstract

SUMMARYMany simulations in the physical sciences are expressed in terms of rectilinear arrays of variables. It is attractive to develop such simulations for use in 1-, 2-, 3-or arbitrary physical dimensions and also in a manner that supports exploitation of data-parallelism on fast modern processing devices. We report on data layouts and transformation algorithms that support both conventional and data-parallel memory layouts. We present our implementations expressed in both conventional serial C code as well as in NVIDIA's Compute Unified Device Architecture concurrent programming language for use on general purpose graphical processing units. We discuss: general memory layouts; specific optimizations possible for dimensions that are powers-of-two and common transformations, such as inverting, shifting and crinkling. We present performance data for some illustrative scientific applications of these layouts and transforms using several current GPU devices and discuss the code and speed scalability of this approach.

Regular Lattice and Small-World Spin Model Simulations Using CUDA and GPUs

“…To overcome this issue we use a method known as crinkling to re-order the bits in the mesh. Crinkling was pioneered for distributed array processors like the DAP by [23] and the same process is described for GPU architectures in [24]. The process of crinkling a mesh involves relocating the red and black spins of the mesh into separate parts of the array or into separate arrays.…”

“…The implementation can either take an existing Ising system or randomly initialise one. The Crinkle and Uncrinkle operators are performed on the GPU and described in [24]. One thread is created for each element in the crinkled arrays, these threads will perform the algorithm described above for a single element from one array and write the results to the same array.…”

Well-Mixed Systems and the Approach to Equilibria in Spatial Hawk and Dove Game Simulations

“…We developed a customised simulation code in the C++ programming language for this work. This uses a pre- viously developed and tested library of geometry generating algorithms [7] and allows us to experiment with hexagonal, triangular and hyper-cubic lattice systems in arbitrary dimensions and also to experiment with different sizes of neighbourhoods, including simple nearest neighbour (eg 4 in 2D, 6 in 3D); Moore neighbourhoods (eg 8 in 2D, 26 in 3D) and generalised spherical inclusion parameterised by a radius. The procedure for the computational experiments is outlined in Algorithm 1.…”

Engineering Software for d-Dimensional Simulations with Hyper-Cubic Neighbours

“…Hyperbrick of the Ising model simulated on a 64 3 lattice, rendered with a cut-away octant to allow viewing of the interior structure. approach also lends itself well to using data-parallelism [4,31,34] and other tile -oriented [3,28] parallel computing solutions [29,32] such as special purpose processing accelerators [22] such as Graphical Processing Units (GPUs) [27] that have special purpose hardware for manipulating regular arrays of cells [1] that can be easily mapped to a multi dimensional simulation model [16].…”