GAMER: a GPU-Accelerated Adaptive Mesh Refinement Code for Astrophysics

We present the newly developed code, GAMER (GPU-accelerated Adaptive MEsh Refinement code), which has adopted a novel approach to improve the performance of adaptive mesh refinement (AMR) astrophysical simulations by a large factor with the use of the graphic processing unit (GPU). The AMR implementation is based on a hierarchy of grid patches with an oct-tree data structure. We adopt a three-dimensional relaxing TVD scheme for the hydrodynamic solver, and a multi-level relaxation scheme for the Poisson solver. Both solvers have been implemented in GPU, by which hundreds of patches can be advanced in parallel. The computational overhead associated with the data transfer between CPU and GPU is carefully reduced by utilizing the capability of asynchronous memory copies in GPU, and the computing time of the ghost-zone values for each patch is made to diminish by overlapping it with the GPU computations. We demonstrate the accuracy of the code by performing several standard test problems in astrophysics. GAMER is a parallel code that can be run in a multi-GPU cluster system. We measure the performance of the code by performing purely-baryonic cosmological simulations in different hardware implementations, in which detailed timing analyses provide comparison between the computations with and without GPU(s) acceleration. Maximum speed-up factors of 12.19 and 10.47 are demonstrated using 1 GPU with 4096^3 effective resolution and 16 GPUs with 8192^3 effective resolution, respectively.Comment: 60 pages, 22 figures, 3 tables. More accuracy tests are included. Accepted for publication in ApJ

Computational Physics on Graphics Processing Units

The use of graphics processing units for scientific computations is an emerging strategy that can significantly speed up various different algorithms. In this review, we discuss advances made in the field of computational physics, focusing on classical molecular dynamics, and on quantum simulations for electronic structure calculations using the density functional theory, wave function techniques, and quantum field theory.Comment: Proceedings of the 11th International Conference, PARA 2012, Helsinki, Finland, June 10-13, 201

Optimization Techniques for Mapping Algorithms and Applications onto CUDA GPU Platforms and CPU-GPU Heterogeneous Platforms

An emerging trend in processor architecture seems to indicate the doubling of the number of cores per chip every two years with same or decreased clock speed. Of particular interest to this thesis is the class of many-core processors, which are becoming more attractive due to their high performance, low cost, and low power consumption. The main goal of this dissertation is to develop optimization techniques for mapping algorithms and applications onto CUDA GPUs and CPU-GPU heterogeneous platforms. The Fast Fourier transform (FFT) constitutes a fundamental tool in computational science and engineering, and hence a GPU-optimized implementation is of paramount importance. We first study the mapping of the 3D FFT onto the recent, CUDA GPUs and develop a new approach that minimizes the number of global memory accesses and overlaps the computations along the different dimensions. We obtain some of the fastest known implementations for the computation of multi-dimensional FFT. We then present a highly multithreaded FFT-based direct Poisson solver that is optimized for the recent NVIDIA GPUs. In addition to the massive multithreading, our algorithm carefully manages the multiple layers of the memory hierarchy so that all global memory accesses are coalesced into 128-bytes device memory transactions. As a result, we have achieved up to 375GFLOPS with a bandwidth of 120GB/s on the GTX 480. We further extend our methodology to deal with CPU-GPU based heterogeneous platforms for the case when the input is too large to fit on the GPU global memory. We develop optimization techniques for memory-bound, and computation-bound application. The main challenge here is to minimize data transfer between the CPU memory and the device memory and to overlap as much as possible these transfers with kernel execution. For memory-bounded applications, we achieve a near-peak effective PCIe bus bandwidth, 9-10GB/s and performance as high as 145 GFLOPS for multi-dimensional FFT computations and for solving the Poisson equation. We extend our CPU-GPU based software pipeline to a computation-bound application-DGEMM, and achieve the illusion of a memory of the CPU memory size and a computation throughput similar to a pure GPU

Fast finite difference Poisson solvers on heterogeneous architectures

In this paper we propose and evaluate a set of new strategies for the solution of three dimensional separable elliptic problems on CPU–GPU platforms. The numerical solution of the system of linear equations arising when discretizing those operators often represents the most time consuming part of larger simulation codes tackling a variety of physical situations. Incompressible fluid flows, electromagnetic problems, heat transfer and solid mechanic simulations are just a few examples of application areas that require efficient solution strategies for this class of problems. GPU computing has emerged as an attractive alternative to conventional CPUs for many scientific applications. High speedups over CPU implementations have been reported and this trend is expected to continue in the future with improved programming support and tighter CPU–GPU integration. These speedups by no means imply that CPU performance is no longer critical. The conventional CPU-control–GPU-compute pattern used in many applications wastes much of CPU’s computational power. Our proposed parallel implementation of a classical cyclic reduction algorithm to tackle the large linear systems arising from the discretized form of the elliptic problem at hand, schedules computing on both the GPU and the CPUs in a cooperative way. The experimental result demonstrates the effectiveness of this approach