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The Development of WARP  A Framework for Continuous Energy Monte Carlo Neutron Transport in General 3D Geometries on GPUs
 Bergmann, Ryan Mitchell
 Advisor(s): Vujic, Jasmina
Abstract
Graphics processing units, or GPUs, have gradually increased in computational power from the small, jobspecific boards of the early 1990s to the programmable powerhouses of today. Compared to more common central processing units, or CPUs, GPUs have a higher aggregate memory bandwidth, much higher floatingpoint operations per second (FLOPS), and lower energy consumption per FLOP. Because one of the main obstacles in exascale computing is power consumption, many new supercomputing platforms are gaining much of their computational capacity by incorporating GPUs into their compute nodes. Since CPUoptimized parallel algorithms are not directly portable to GPU architectures (or at least not without losing substantial performance), transport codes need to be rewritten to execute efficiently on GPUs. Unless this is done, reactor simulations cannot take full advantage of these new supercomputers.
WARP, which can stand for ``Weaving All the Random Particles,'' is a threedimensional (3D) continuous energy Monte Carlo neutron transport code developed in this work as to efficiently implement a continuous energy Monte Carlo neutron transport algorithm on a GPU. WARP accelerates Monte Carlo simulations while preserving the benefits of using the Monte Carlo Method, namely, very few physical and geometrical simplifications. WARP is able to calculate multiplication factors, flux tallies, and fission source distributions for timeindependent problems, and can run in both criticality or fixed source modes. WARP can transport neutrons in unrestricted arrangements of parallelepipeds, hexagonal prisms, cylinders, and spheres.
WARP uses an eventbased algorithm, but with some important differences. Moving data is expensive, so WARP uses a remapping vector of pointer/index pairs to direct GPU threads to the data they need to access. The remapping vector is sorted by reaction type after every transport iteration using a highefficiency parallel radix sort, which serves to keep the reaction types as contiguous as possible and removes completed histories from the transport cycle. The sort reduces the amount of divergence in GPU ``thread blocks,'' keeps the SIMD units as full as possible, and eliminates using memory bandwidth to check if a neutron in the batch has been terminated or not. Using a remapping vector means the data access pattern is irregular, but this is mitigated by using large batch sizes where the GPU can effectively eliminate the high cost of irregular global memory access.
WARP modifies the standard unionized energy grid implementation to reduce memory traffic. Instead of storing a matrix of pointers indexed by reaction type and energy, WARP stores three matrices. The first contains cross section values, the second contains pointers to angular distributions, and a third contains pointers to energy distributions. This linked list type of layout increases memory usage, but lowers the number of data loads that are needed to determine a reaction by eliminating a pointer load to find a cross section value.
Optimized, highperformance GPU code libraries are also used by WARP wherever possible. The CUDA performance primitives (CUDPP) library is used to perform the parallel reductions, sorts and sums, the CURAND library is used to seed the linear congruential random number generators, and the OptiX ray tracing framework is used for geometry representation. OptiX is a highlyoptimized library developed by NVIDIA that automatically builds hierarchical acceleration structures around userinput geometry so only surfaces along a ray line need to be queried in ray tracing. WARP also performs material and cell number queries with OptiX by using a pointinpolygon like algorithm.
In the initial testing where 10^6 source neutrons per criticality batch are used, WARP is capable of delivering results that are anywhere from 4 to 800 pcm away from MCNP 6.1 and Serpent 2.1.18, but with run times that are 1182 times lower, depending on problem geometry and materials. On average, WARP's performance on a NIVIDIA K20 is equivalent to approximately 45 AMD Opteron 6172 CPU cores. Larger batches are typically perform better on the GPU, but memory limitations of the K20 card restricted batch size to $10^6$ source neutrons.
WARP has shown that GPUs are an effective platform for performing Monte Carlo neutron transport with continuous energy cross sections. Currently, WARP is the most detailed and featurerich program in existence for performing continuous energy Monte Carlo neutron transport in general 3D geometries on GPUs, but compared to production codes like Serpent and MCNP, WARP has limited capabilities. Despite WARP's lack of features, its novel algorithm implementations show that high performance can be achieved on a GPU despite the inherently divergent program flow and sparse data access patterns. WARP is not ready for everyday nuclear reactor calculations, but is a good platform for further development of GPUaccelerated Monte Carlo neutron transport. In it's current state, it may be a useful tool for multiplication factor searches, i.e. determining reactivity coefficients by perturbing material densities or temperatures, since these types of calculations typically do not require many flux tallies.
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