1,720,986 research outputs found
The local discontinuous Galerkin method for contaminant transport
No full textAizinger, Vadym; Dawson, Clint; Cockburn, Bernardo; Castillo, Paul. (1999). The local discontinuous Galerkin method for contaminant transport. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/3382
FESTUNG: A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method. Part III: Hybridized discontinuous Galerkin (HDG) formulation
No full textThe third paper in our series on open source MATLAB / GNU Octave implementation of the discontinuous Galerkin (DG) method(s) focuses on a hybridized formulation. The main aim of this ongoing work is to develop rapid prototyping techniques covering a range of standard DG methodologies and suitable for small to medium sized applications. Our FESTUNG package relies on fully vectorized matrix / vector operations throughout, and all details of the implementation are fully documented. Once again, great care is taken to maintain a direct mapping between discretization terms
and code routines as well as to ensure full compatibility to GNU Octave. The current work formulates a hybridized DG scheme for a linear advection problem, describes hybrid approximation spaces on the mesh skeleton, and compares the performance of this discretization to the standard (element-based) DG method for different polynomial orders.The stay of A. Jaust at the University of Erlangen-Nurnberg was supported by the Research Foundation - Flanders (FWO) with a grant for a short study visit abroad and by the Special Research Fund (BOF) of Hasselt University
Bathymetry reconstruction via a time-dependent intrinsic shallow water model
Full text linkIn this thesis, we firstly give a presentation of the state of the art of the bathymetry reconstruction problem. Secondly we introduce, in a geometrical setting, the Shallow water model, known for its many applications (dynamics of the athmosphere, geophysical phenomena and more). Furthermore, we use the SW model to derive a novel intrinsic model for the bathymetry reconstruction. More specifically, we find a second order approximation of the Navier-Stokes equations based on the SW model. Finally, employing the Discontinuous Galerkin method, we perform the first steps towards the experimental validation of our model.ope
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A discontinuous Galerkin method for two- and three-dimensional shallow-water equations
Full text linkThe shallow-water equations (SWE), derived from the incompressible Navier-Stokes equations using the hydrostatic assumption and the Boussinesq approximation, are a standard mathematical representation valid for most types of
flow encountered in coastal sea, river, and ocean modeling. They can be utilized to predict storm surges, tsunamis, floods, and, augmented by additional
equations (e.g., transport, reaction), to model oil slicks, contaminant plume
propagation, temperature and salinity transport, among other problems. An
analytical solution of these equations is possible for only a handful of particular cases. However, their numerical solution is made challenging by a number
of factors.
The SWE are a system of coupled nonlinear partial differential equations
defined on complex physical domains arising, for example, from irregular land boundaries. The bottom sea bed (bathymetry) is also often very irregular.
Shallow-water systems are subjected to a wide range of external forces, such
as the Coriolis force, surface wind stress, atmospheric pressure gradient, and
tidal potential forces. As a result, flow regimes can vary greatly throughout the
domain, from very smooth to high gradients and shock waves. The solution
of the system is further complicated by the difficulties connected with the
mathematical nature of the SWE. Most important is the coupling between the
gravity forcing and the horizontal velocity field, which could lead to spurious
spatial oscillations if the numerical algorithms are not chosen with care.
One has to note, though, that most existing numerical methods for
the SWE have serious drawbacks with regard to stability, local conservation,
and ability to accommodate parallel implementation and hp-adaptivity. These
problems become even more evident if we try to simulate problems involving
discontinuities, shock waves, etc.
The discontinuous Galerkin (DG) methods are an attempt to marry
the most favorable features of the continuous finite element and finite volume
schemes. On the one hand, they can employ approximating spaces of any order
(not necessarily polynomial), and, on the other, the numerical fluxes on the
inter-element boundaries are evaluated exactly as in the finite volume method
– by solving a Riemann problem. As a result, these numerical schemes enjoy
the same stability properties as the finite volume method. In addition, most
DG methods guarantee local conservation of mass and momentum, which is,
in many cases, a highly desirable quality reflecting the physical nature of the
processes we are trying to model.
In this thesis, we formulate the local discontinuous Galerkin method
for the 2- and 3D shallow-water equations and derive stability and a priori error estimates for a simplified form of the 2D shallow-water equations and
conduct stability analysis of our 3D scheme. In a series of numerical studies, we
test both formulations using problems with discontinuous solutions as well as
typical tidal flow problems. In addition, we demonstrate adaptive capabilities
of the method using a shock-detection algorithm as an error indicator.Computational Science, Engineering, and MathematicsComputational and Applied Mathematic
A hierarchical scale separation approach for the hybridized discontinuous Galerkin method
No full textIn this work, the hierarchical scale separation (HSS) method developed for linear systems resulting from discontinuous Galerkin (DG) discretizations has been extended to hybridized discontinuous Galerkin (HDG) schemes. The HSS method is related to p-multigrid techniques for DG systems but is conceptually much simpler. Our extension of the HSS scheme to the HDG method tested using a convection–diffusion equation for a range of benchmark problems demonstrated excellent performance on a par with that of the HSS method for a non-hybridized DG approximation. In the limiting case of a pure convection equation, the measured convergence rate of the HSS scheme was significantly better than the rates demonstrated in the non-hybridized case
A hierarchical scale separation approach for the hybridized discontinuous Galerkin method
No full text
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
p-adaptive discontinuous Galerkin method for the shallow water equations with a parameter-free error indicator
Full text linkWe propose a p-adaptive quadrature-free discontinuous Galerkin method for the shallow water equations based on a computationally efficient adaptivity indicator which works without any problem-dependent parameters. The error and smoothness of the solution are detected using the information collected for slope limiting and, for piecewise constant discretizations, by carrying out a reconstruction procedure. The accuracy and robustness of the new scheme are evaluated using several benchmarks and compared to other adaptivity indicators. Our results indicate that the proposed indicator finds a good balance between solution quality and computational overhead.Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/50110000165
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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