11796
Brendan M McLaughlin, Connor P Ballance
Petaflop architectures are currently being utilized efficiently to perform large scale computations in Atomic, Molecular and Optical Collisions. We solve the Schroedinger or Dirac equation for the appropriate collision problem using the R-matrix or R-matrix with pseudo-states approach. We briefly outline the parallel methodology used and implemented for the current suite of Breit-Pauli and DARC […]
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Andres More
This work reviews the experience of implementing different versions of the SSPR rank-one update operation of the BLAS library. The main objective was to contrast CPU versus GPU implementation effort and complexity of an optimized BLAS routine, not considering performance. This work contributes with a sample procedure to compare BLAS kernel implementations, how to start […]
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Mauro Blanco, Pablo Perdomo, Pablo Ezzatti, Alberto Pardo, Marcos Viera
We investigate the use of functional programming to develop a numerical linear algebra run-time; i.e. a framework where the solvers can be adapted easily to different contexts and task parallelism can be attained (semi-) automatically. We follow a bottom up strategy, where the first step is the design and implementation of a framework layer, composed […]
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Jiri Filipovic, Matus Madzin, Jan Fousek, Ludek Matyska
Modern GPUs are able to perform significantly more arithmetic operations than transfers of a single word to or from global memory. Hence, many GPU kernels are limited by memory bandwidth and cannot exploit the arithmetic power of GPUs. However, the memory locality can be often improved by kernel fusion when a sequence of kernels is […]
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Matthew Badin, Paolo D'Alberto, Lubomir Bic, Michael Dillencourt, Alexandru Nicolau
Scientific computing is only bound by the limits of Moore’s Law and the scalability of high performance mathematical library implementations. Most mathematical libraries however tend to focus only on general inputs, limiting their potential performance and scalability by not tailoring their implementation to specific inputs, such as non-negative inputs. By removing this limitation it is […]
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Chetan Jhurani
We describe an interface and an implementation for performing Kronecker product actions on NVIDIA GPUs for multiple small 2-D matrices and 3-D arrays processed in parallel as a batch. This method is suited to cases where the Kronecker product component matrices are identical but the operands in a matrix-free application vary in the batch. Any […]
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Chetan Jhurani, Paul Mullowney
We present an interface and an implementation of the General Matrix Multiply (GEMM) routine for multiple small matrices processed simultaneously on NVIDIA graphics processing units (GPUs). We focus on matrix sizes under 16. The implementation can be easily extended to larger sizes. For single precision matrices, our implementation is 30% to 600% faster than the […]
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Hans Henrik Brandenborg Sorensen
In this paper, we consider the automatic performance tuning of dense vector and matrix-vector operations on GPUs. Such operations form the backbone of level 1 and level 2 routines in the Basic Linear Algebra Subroutines (BLAS) library and are therefore of great importance in many scientific applications. As examples, we develop single-precision CUDA kernels for […]
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Hans Henrik Brandenborg Sorensen
In this paper, we develop a high-performance GPU kernel for one of the most popular dense linear algebra operations, the matrix-vector multiplication. The target hardware is the most recent Nvidia Tesla 20-series (Fermi architecture), which is designed from the ground up for scientific computing. We show that it is essentially a matter of fully utilizing […]
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Hans Henrik Brandenborg Sorensen
The use of high performance libraries for dense linear algebra operations is of great importance in many numerical scientific applications. The most common operations form the backbone of the Basic Linear Algebra Subroutines (BLAS) library. In this paper, we consider the performance and auto-tuning of level 1 and level 2 BLAS routines on GPUs. As […]
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Filippo Spiga, Ivan Girotto
GPU computing has revolutionized HPC by bringing the performance of the supercomputer to the desktop. Attractive price, performance, and power characteristics allow multiple GPUs to be plugged into both desktop machines as well as supercomputer nodes for increased performance. Excellent performance and scalability can be achieved for some problems using hybrid combinations of multiple GPUs […]
Jakub Kurzak, Stanimire Tomov, Jack Dongarra
In recent years, the use of graphics chips has been recognized as a viable way of accelerating scientific and engineering applications, even more so since the introduction of the Fermi architecture by NVIDIA, with features essential to numerical computing, such as fast double precision arithmetic and memory protected with error correction codes. Being the crucial […]
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