We evaluate the computational performance of the Bernstein-Bezier basis for discontinuous Galerkin (DG) discretizations and show how to exploit properties of derivative and lift operators specific to Bernstein polynomials. Issues of efficiency and numerical stability are discussed in the context of a model wave propagation problem. We compare the performance of Bernstein-Bezier kernels to both […]

December 22, 2015 by hgpu

We present a parallel algorithm for finding the shortest path whose total weight is smaller than a pre-determined value. The passage times over the edges are assumed to be positive integers. In each step the processing elements are not analyzing the entire graph. Instead they are focusing on a subset of vertices called active vertices. […]

November 24, 2015 by hgpu

We present a time-explicit discontinuous Galerkin (DG) solver for the time-domain acoustic wave equation on hybrid meshes containing vertex-mapped hexahedral, wedge, pyramidal and tetrahedral elements. Discretely energy-stable formulations are presented for both Gauss-Legendre and Gauss-Legendre-Lobatto (Spectral Element) nodal bases for the hexahedron. Stable timestep restrictions for hybrid meshes are derived by bounding the spectral radius […]

July 13, 2015 by hgpu

This report shows that significant reduction in fuel use could be achieved by the adoption of `free flight’ type of trajectories in the Terminal Manoeuvring Area (TMA) of an airport, under the control of an algorithm which optimises the trajectories of all the aircraft within the TMA simultaneously while maintaining safe separation. We propose the […]

June 10, 2015 by hgpu

Finite Element Methods are techniques for estimating solutions to boundary value problems for partial differential equations from an approximating subspace. These methods are based on weak or variational forms of the BVP that require less of the problem functions than what the original PDE would suggest in terms of order of differentiability and continuity. In […]

June 7, 2015 by hgpu

The Radon transform and its adjoint, the back-projection operator, can both be expressed as convolutions in log-polar coordinates. Hence, fast algorithms for the application of the operators can be constructed by using FFT, if data is resampled at log-polar coordinates. Radon data is typically measured on an equally spaced grid in polar coordinates, and reconstructions […]

June 5, 2015 by hgpu

Polynomial systems occur in many areas of science and engineering. Unlike general nonlinear systems, the algebraic structure enables to compute all solutions of a polynomial system. We describe our massive parallel predictor-corrector algorithms to track many solution paths of a polynomial homotopy. The data parallelism that provides the speedups stems from the evaluation and differentiation […]

May 10, 2015 by hgpu

In non-linear systems, where explicit analytic solutions usually can’t be found, visualisation is a powerful approach which can give insights into the dynamical behaviour of models; it is also crucial for teaching this area of mathematics. In this paper we present new software, Fireflies, which exploits the power of graphical processing unit (GPU) computing to […]

May 7, 2015 by hgpu

In this paper, we propose a new very simple numerical method for solving liquid-gas compressible flows on two dimensional cartesian meshes. For achieving high performance, the scheme is tested on recent multi-core processors and Graphics Processing Units (GPU), using the OpenCL environment. We describe how to install and to run the code CLBUBBLE for computing […]

April 25, 2015 by hgpu

In a recent paper, Parikh and Boyd describe a method for solving a convex optimization problem, where each iteration involves evaluating a proximal operator and projection onto a subspace. In this paper we address the critical practical issues of how to select the proximal parameter in each iteration, and how to scale the original problem […]

April 1, 2015 by hgpu

This document describes an implementation in C of a set of randomized algorithms for computing partial Singular Value Decompositions (SVDs). The techniques largely follow the prescriptions in the article "Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions," N. Halko, P.G. Martinsson, J. Tropp, SIAM Review, 53(2), 2011, pp. 217-288, but with some […]

February 22, 2015 by hgpu

In this thesis we present the first, to our knowledge, implementation and performance analysis of Hermite methods on GPU accelerated systems. We give analytic background for Hermite methods; give implementations of the Hermite methods on traditional CPU systems as well as on GPUs; give the reader background on basic CUDA programming for GPUs; discuss performance […]

February 2, 2015 by hgpu