Optimizing the Dimensional Method for Performing Multidimensional, Multiprocessor, Out-of-Core FFTs

We present an improved version of the Dimensional Method for computing multidimensional Fast Fourier Transforms (FFTs) on a multiprocessor system when the data consist of too many records to fit into memory. Data are spread across parallel disks and processed in sections. We use the Parallel Disk Model for analysis. The simple Dimensional Method performs the 1-dimensional FFTs for each dimension in term. Between each dimension, an out-of-core permutation is used to rearrange the data to contiguous locations. The improved Dimensional Method processes multiple dimensions at a time. We show that determining an optimal sequence and groupings of dimensions is NP-complete. We then analyze the effects of two modifications to the Dimensional Method independently: processing multiple dimensions at one time, and processing single dimensions in a different order. Finally, we show a lower bound on the I/O complexity of the Dimensional Method and present an algorithm that is approximately asymptotically optimal

The inherent overlapping in the parallel calculation of the Laplacian

Producción CientíficaA new approach for the parallel computation of the Laplacian in the Fourier domain is presented. This numerical problem inherits the intrinsic sequencing involved in the calculation of any multidimensional Fast Fourier Transform (FFT) where blocking communications assure that its computation is strictly carried out dimension by dimension. Such data dependency vanishes when one considers the Laplacian as the sum of n independent one-dimensional kernels, so that computation and communication can be naturally overlapped with nonblocking communications. Overlapping is demonstrated to be responsible for the speedup figures we obtain when our approach is compared to state-of-the-art parallel multidimensional FFTs.Junta de Castilla León (grant number VA296P18

General Purpose Computation on Graphics Processing Units Using OpenCL

Computational Science has emerged as a third pillar of science along with theory and experiment, where the parallelization for scientific computing is promised by different shared and distributed memory architectures such as, super-computer systems, grid and cluster based systems, multi-core and multiprocessor systems etc. In the recent years the use of GPUs (Graphic Processing Units) for General purpose computing commonly known as GPGPU made it an exciting addition to high performance computing systems (HPC) with respect to price and performance ratio. Current GPUs consist of several hundred computing cores arranged in streaming multi-processors so the degree of parallelism is promising. Moreover with the development of new and easy to use interfacing tools and programming languages such as OpenCL and CUDA made the GPUs suitable for different computation demanding applications such as micromagnetic simulations. In micromagnetic simulations, the study of magnetic behavior at very small time and space scale demands a huge computation time, where the calculation of magnetostatic field with complexity of O(Nlog(N)) using FFT algorithm for discrete convolution is the main contribution towards the whole simulation time, and it is computed many times at each time step interval. This study and observation of magnetization behavior at sub-nanosecond time-scales is crucial to a number of areas such as magnetic sensors, non volatile storage devices and magnetic nanowires etc. Since micromagnetic codes in general are suitable for parallel programming as it can be easily divided into independent parts which can run in parallel, therefore current trend for micromagnetic code concerns shifting the computationally intensive parts to GPUs. My PhD work mainly focuses on the development of highly parallel magnetostatic field solver for micromagnetic simulators on GPUs. I am using OpenCL for GPU implementation, with consideration that it is an open standard for parallel programming of heterogeneous systems for cross platform. The magnetostatic field calculation is dominated by the multidimensional FFTs (Fast Fourier Transform) computation. Therefore i have developed the specialized OpenCL based 3D-FFT library for magnetostatic field calculation which made it possible to fully exploit the zero padded input data with out transposition and symmetries inherent in the field calculation. Moreover it also provides a common interface for different vendors' GPUs. In order to fully utilize the GPUs parallel architecture the code needs to handle many hardware specific technicalities such as coalesced memory access, data transfer overhead between GPU and CPU, GPU global memory utilization, arithmetic computation, batch execution etc. In the second step to further increase the level of parallelism and performance, I have developed a parallel magnetostatic field solver on multiple GPUs. Utilizing multiple GPUs avoids dealing with many of the limitations of GPUs (e.g., on-chip memory resources) by exploiting the combined resources of multiple on board GPUs. The GPU implementation have shown an impressive speedup against equivalent OpenMp based parallel implementation on CPU, which means the micromagnetic simulations which require weeks of computation on CPU now can be performed very fast in hours or even in minutes on GPUs. In parallel I also worked on ordered queue management on GPUs. Ordered queue management is used in many applications including real-time systems, operating systems, and discrete event simulations. In most cases, the efficiency of an application itself depends on usage of a sorting algorithm for priority queues. Lately, the usage of graphic cards for general purpose computing has again revisited sorting algorithms. In this work i have presented the analysis of different sorting algorithms with respect to sorting time, sorting rate and speedup on different GPU and CPU architectures and provided a new sorting technique on GPU

Department of Computer Science Activity 1998-2004

This report summarizes much of the research and teaching activity of the Department of Computer Science at Dartmouth College between late 1998 and late 2004. The material for this report was collected as part of the final report for NSF Institutional Infrastructure award EIA-9802068, which funded equipment and technical staff during that six-year period. This equipment and staff supported essentially all of the department\u27s research activity during that period

GPU Fast Convolution via the Overlap-and-Save Method in Shared Memory

We present an implementation of the overlap-and-save method, a method for the convolution of very long signals with short response functions, which is tailored to GPUs. We have implemented several FFT algorithms (using the CUDA programming language), which exploit GPU shared memory, allowing for GPU accelerated convolution. We compare our implementation with an implementation of the overlap-and-save algorithm utilizing the NVIDIA FFT library (cuFFT). We demonstrate that by using a shared-memory-based FFT, we can achieved significant speed-ups for certain problem sizes and lower the memory requirements of the overlap-and-save method on GPUs