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Tor Gillberg, Are Magnus Bruaset, Oyvind Hjelle, Mohammed Sourouri
Two new algorithms for numerical solution of static Hamilton-Jacobi equations are presented. These algorithms are designed to work efficiently on different parallel computing architectures, and numerical results for multicore CPU and GPU implementations are reported and discussed. The numerical experiments show that the proposed solution strategies scale well with the computational power of the hardware. […]
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Hasse Lovgren
CONTEXT: Reinforcement Learning (RL) is a time consuming effort that requires a lot of computational power as well. There are mainly two approaches to improving RL efficiency, the theoretical mathematics and algorithmic approach or the practical implementation approach. In this study, the approaches are combined in an attempt to reduce time consumption. OBJECTIVES: We investigate […]
Anastasia Kruchinina
Parallel computing is a topic that became very popular in the last few decades. Parallel computers are being used in many different areas of science such as astrophysics, climate modelling, quantum chemistry, fluid dynamics and medicine. Parallel programming is a type of programming where computations can be performed concurrently on different processors or devices. There […]
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Matthias Bartelt, Michael Gross
This paper deals with a Galerkin-based multi-scale time integration of a viscoelastic rope model. Using Hamilton’s dynamical formulation, Newton’s equation of motion as a second-order partial differential equation is transformed into two coupled first order partial differential equations in time. The considered finite viscoelastic deformations are described by means of a deformation-like internal variable determined […]
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T. W. O’Neil
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.
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D. Martin, G. Haase
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 […]
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Stefan Lemvig Glimberg, Allan Peter Engsig-Karup, Allan S. Nielsen, Bernd Dammann
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 […]
R. Gandham, D. S. Medina, T. Warburton
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 […]
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Rajesh Gandham, Ken Esler, Yongpeng Zhang
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. […]
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Guillaume Balarac, Georges-Henri Cottet, Jean-Mathieu Etancelin, Jean-Baptiste Lagaert, Franck Perignon, Christophe Picard
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 […]
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Iain Bethune, Michael Goetz
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 […]
Gitta Kutyniok, Wang-Q Lim, Rafael Reisenhofer
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 […]
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