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Istvan Zoltan Reguly
The last decade saw the long tradition of frequency scaling of processing units grind to a halt, and efforts were re-focused on maintaining computational growth by other means; such as increased parallelism, deep memory hierarchies and complex execution logic. After a long period of "boring productivity", a host of new architectures, accelerators, programming languages and […]
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Fabio Luporini, Ana Lucia Varbanescu, Florian Rathgeber, Gheorghe-Teodor Bercea, J. Ramanujam, David A. Ham, Paul H.J. Kelly
The numerical solution of partial differential equations using the finite element method is one of the key applications of high performance computing. Local assembly is its characteristic operation. This entails the execution of a problem-specific kernel to numerically evaluate an integral for each element in the discretized problem domain. Since the domain size can be […]
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Harald Koestler, Christian Schmitt, Sebastian Kuckuk, Frank Hannig, Juergen Teich, Ulrich Ruede
Many problems in computational science and engineering involve partial differential equations and thus require the numerical solution of large, sparse (non)linear systems of equations. Multigrid is known to be one of the most efficient methods for this purpose. However, the concrete multigrid algorithm and its implementation highly depend on the underlying problem and hardware. Therefore, […]
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P. Yang
This tutorial is written for beginners as an introduction to basic wave propagation using nite di erence method, from acoustic and elastic wave modeling, to reverse time migration and full waveform inversion. Most of the theoretical delineations summarized in this tutorial have been implemented in Madagascar with Matlab, C and CUDA programming, which will bene t readers’ […]
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Steffen Muthing, Dirk Ribbrock, Dominik Goddeke
A major challenge in PDE software is the balance between user-level flexibility and performance on heterogeneous hardware. We discuss our ideas on how this challenge can be tackled, exemplarily for the DUNE framework and in particular its linear algebra and solver components. We demonstrate how the former MPI-only implementation is modified to support MPI+[CPU/GPU] threading […]
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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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Zheng Xia
Scientific computation is the field of study that uses computers to implement mathematical models of physical phenomena such as FEM in deformation measurement in virtual reality. Scientific and engineering problems that would be almost impossible to solve by hand whereas on a computer, it can be handled properly. A numerical algorithm calculating for different fields […]
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R. Pethiyagoda, S. W. McCue, T. J. Moroney, J. M. Back
The nonlinear problem of steady free-surface flow past a submerged source is considered as a case study for three-dimensional ship wave problems. Of particular interest is the distinctive wedge-shaped wave pattern that forms on the surface of the fluid. By reformulating the governing equations with a standard boundary-integral method, we derive a system of nonlinear […]
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S. Stella, R. Chignola, E. Milotti
We have developed a numerical model that simulates the growth of small avascular solid tumors. At its core lies a set of partial differential equations that describe diffusion processes as well as transport and reaction mechanisms of a selected number of nutrients. Although the model relies on a restricted subset of molecular pathways, it compares […]
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Gabor Janos Tornai, Gyorgy Cserey
In this paper, we investigated the effect of adding more small curves to the initial condition which determines the required number of iterations of a fast level set (LS) evolution. As a result, we discovered two new theorems and developed a proof on the worst case of the required number of iterations. Furthermore, we found […]
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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