This paper presents initial experiments in implementing two notable matrix multiplication algorithms – the DNS algorithm and Cannon’s algorithm – using NVIDIA’s general-purpose graphics processing units (GPGPUs) and CUDA development platform. We demonstrate that these implementations are comparable with traditional methods in terms of computational expense and may scale better than traditional techniques.

April 3, 2014 by hgpu

This report gives a brief introduction to the interpolation with radial basis functions and it’s application to the deformation of computational grids. The FGP algorithm is quoted as an iterative method for the calculation of the interpolation coefficients. A multipole method is described for the efficient approximation of the required matrix-vector product. Results are presented […]

March 25, 2014 by hgpu

Massively parallel processors, such as graphical processing units (GPUs), have in recent years proven to be effective for a vast amount of scientific appli- cations. Today, most desktop computers are equipped with one or more pow- erful GPUs, offering heterogeneous high-performance computing to a broad range of scientific researchers and software developers. Though GPUs are […]

March 12, 2014 by apek

We discuss the development, verification, and performance of a GPU accelerated discontinuous Galerkin method for the solutions of two dimensional nonlinear shallow water equations. The shallow water equations are hyperbolic partial differential equations and are widely used in the simulation of tsunami wave propagations. Our algorithms are tailored to take advantage of the single instruction […]

March 10, 2014 by hgpu

We present an efficient, robust and fully GPU-accelerated aggregation-based algebraic multigrid preconditioning technique for the solution of large sparse linear systems. These linear systems arise from the discretization of elliptic PDEs. The method involves two stages, setup and solve. In the setup stage, hierarchical coarse grids are constructed through aggregation of the fine grid nodes. […]

March 10, 2014 by hgpu

The turbulent transport of a passive scalar is an important and challenging problem in many applications in fluid mechanics. It involves different range of scales in the fluid and in the scalar and requires important computational resources. In this work we show how hybrid numerical methods, combining Eulerian and Lagrangian schemes, are natural tools to […]

March 3, 2014 by hgpu

Great strides have been made in recent years in the search for ever larger prime Generalized Fermat Numbers (GFN). We briefly review the history of the GFN prime search, and describe new implementations of the ‘Genefer’ software (now available as open source) using CUDA and optimised CPU assembler which have underpinned this unprecedented progress. The […]

February 27, 2014 by hgpu

Wavelets and their associated transforms are highly efficient when approximating and analyzing one-dimensional signals. However, multivariate signals such as images or videos typically exhibit curvilinear singularities, which wavelets are provably deficient of sparsely approximating and also of analyzing in the sense of, for instance, detecting their direction. Shearlets are a directional representation system extending the […]

February 26, 2014 by hgpu

In order to compensate for the higher cost of double double and quad double arithmetic when solving large polynomial systems, we investigate the application of NVIDIA Tesla C2050, K20C, and K40 general purpose graphics processing units. As the dimension equals several thousands, the cost to compute one QR decomposition is sufficiently large so that the […]

January 26, 2014 by hgpu

The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. We propose a principled and practical technique to linearize and evaluate arbitrary continuous nonlinear functions using polygonal (continuous piecewise linear) models under the L1 norm. A thorough error analysis is developed to guide an optimal design of two […]

January 2, 2014 by hgpu

It is time-consuming and error-prone to implement inference procedures for each new probabilistic model. Probabilistic programming addresses this problem by allowing a user to specify the model and having a compiler automatically generate an inference procedure for it. For this approach to be practical, it is important to generate inference code that has reasonable performance. […]

December 13, 2013 by hgpu

How do we build maintainable, robust, and performance-portable scientific applications? This thesis argues that the answer to this software engineering question in the context of the finite element method is through the use of layers of Domain-Specific Languages (DSLs) to separate the various concerns in the engineering of such codes. Performance-portable software achieves high performance […]

December 11, 2013 by hgpu