14,982 research outputs found
An adaptive, hanging-node, discontinuous isogeometric analysis method for the first-order form of the neutron transport equation with discrete ordinate (SN) angular discretisation
In this paper a discontinuous, hanging-node, isogeometric analysis (IGA) method is developed and applied to the first-order form of the neutron transport equation with a discrete ordinate (SN) angular discretisation in two-dimensional space. The complexities involved in upwinding across curved element boundaries that contain hanging-nodes have been addressed to ensure that the scheme remains conservative. A robust algorithm for cycle-breaking has also been introduced in order to develop a unique sweep ordering of the elements for each discrete ordinates direction. The convergence rate of the scheme has been verified using the method of manufactured solutions (MMS) with a smooth solution. Heuristic error indicators have been used to drive an adaptive mesh refinement (AMR) algorithm to take advantage of the hanging-node discretisation. The effectiveness of this method is demonstrated for three test cases. The first is a homogeneous square in a vacuum with varying mean free path and a prescribed extraneous unit source. The second test case is a radiation shielding problem and the third is a 3×3 “supercell” featuring a burnable absorber. In the final test case, comparisons are made to the discontinuous Galerkin finite element method (DGFEM) using both straight-sided and curved quadratic finite elements
Redefining A in RGBA: Towards a Standard for Graphical 3D Printing
Advances in multimaterial 3D printing have the potential to reproduce various
visual appearance attributes of an object in addition to its shape. Since many
existing 3D file formats encode color and translucency by RGBA textures mapped
to 3D shapes, RGBA information is particularly important for practical
applications. In contrast to color (encoded by RGB), which is specified by the
object's reflectance, selected viewing conditions and a standard observer,
translucency (encoded by A) is neither linked to any measurable physical nor
perceptual quantity. Thus, reproducing translucency encoded by A is open for
interpretation.
In this paper, we propose a rigorous definition for A suitable for use in
graphical 3D printing, which is independent of the 3D printing hardware and
software, and which links both optical material properties and perceptual
uniformity for human observers. By deriving our definition from the absorption
and scattering coefficients of virtual homogeneous reference materials with an
isotropic phase function, we achieve two important properties. First, a simple
adjustment of A is possible, which preserves the translucency appearance if an
object is re-scaled for printing. Second, determining the value of A for a real
(potentially non-homogeneous) material, can be achieved by minimizing a
distance function between light transport measurements of this material and
simulated measurements of the reference materials. Such measurements can be
conducted by commercial spectrophotometers used in graphic arts.
Finally, we conduct visual experiments employing the method of constant
stimuli, and derive from them an embedding of A into a nearly perceptually
uniform scale of translucency for the reference materials.Comment: 20 pages (incl. appendices), 20 figures. Version with higher quality
images: https://cloud-ext.igd.fraunhofer.de/s/pAMH67XjstaNcrF (main article)
and https://cloud-ext.igd.fraunhofer.de/s/4rR5bH3FMfNsS5q (appendix).
Supplemental material including code:
https://cloud-ext.igd.fraunhofer.de/s/9BrZaj5Uh5d0cOU/downloa
DISPATCH: A Numerical Simulation Framework for the Exa-scale Era. I. Fundamentals
We introduce a high-performance simulation framework that permits the
semi-independent, task-based solution of sets of partial differential
equations, typically manifesting as updates to a collection of `patches' in
space-time. A hybrid MPI/OpenMP execution model is adopted, where work tasks
are controlled by a rank-local `dispatcher' which selects, from a set of tasks
generally much larger than the number of physical cores (or hardware threads),
tasks that are ready for updating. The definition of a task can vary, for
example, with some solving the equations of ideal magnetohydrodynamics (MHD),
others non-ideal MHD, radiative transfer, or particle motion, and yet others
applying particle-in-cell (PIC) methods. Tasks do not have to be grid-based,
while tasks that are, may use either Cartesian or orthogonal curvilinear
meshes. Patches may be stationary or moving. Mesh refinement can be static or
dynamic. A feature of decisive importance for the overall performance of the
framework is that time steps are determined and applied locally; this allows
potentially large reductions in the total number of updates required in cases
when the signal speed varies greatly across the computational domain, and
therefore a corresponding reduction in computing time. Another feature is a
load balancing algorithm that operates `locally' and aims to simultaneously
minimise load and communication imbalance. The framework generally relies on
already existing solvers, whose performance is augmented when run under the
framework, due to more efficient cache usage, vectorisation, local
time-stepping, plus near-linear and, in principle, unlimited OpenMP and MPI
scaling.Comment: 17 pages, 8 figures. Accepted by MNRA
Pushing the Limits of 3D Color Printing: Error Diffusion with Translucent Materials
Accurate color reproduction is important in many applications of 3D printing,
from design prototypes to 3D color copies or portraits. Although full color is
available via other technologies, multi-jet printers have greater potential for
graphical 3D printing, in terms of reproducing complex appearance properties.
However, to date these printers cannot produce full color, and doing so poses
substantial technical challenges, from the shear amount of data to the
translucency of the available color materials. In this paper, we propose an
error diffusion halftoning approach to achieve full color with multi-jet
printers, which operates on multiple isosurfaces or layers within the object.
We propose a novel traversal algorithm for voxel surfaces, which allows the
transfer of existing error diffusion algorithms from 2D printing. The resulting
prints faithfully reproduce colors, color gradients and fine-scale details.Comment: 15 pages, 14 figures; includes supplemental figure
Population growth and persistence in a heterogeneous environment: the role of diffusion and advection
The spatio-temporal dynamics of a population present one of the most
fascinating aspects and challenges for ecological modelling. In this article we
review some simple mathematical models, based on one dimensional
reaction-diffusion-advection equations, for the growth of a population on a
heterogeneous habitat. Considering a number of models of increasing complexity
we investigate the often contrary roles of advection and diffusion for the
persistence of the population. When it is possible we demonstrate basic
mathematical techniques and give the critical conditions providing the survival
of a population, in simple systems and in more complex resource-consumer models
which describe the dynamics of phytoplankton in a water column.Comment: Introductory review of simple conceptual models. 45 pages, 15 figures
v2: minor change
The role of mesoscale eddies time and length scales on phytoplankton production
Horizontal mixing has been found to play a crucial role in the development of spatial plankton structures in the ocean. We study the influence of time and length scales of two different horizontal two-dimensional (2-D) flows on the growth of a single phytoplankton patch. To that end, we use a coupled model consisting of a standard three component ecological NPZ model and a flow model able to mimic the mesoscale structures observed in the ocean. Two hydrodynamic flow models are used: a flow based on Gaussian correlated noise, for which the Eulerian length and time scales can be easily controlled, and a multiscale velocity field derived from altimetry data in the North Atlantic ocean. We find the optimal time and length scales for the Gaussian flow model favouring the plankton spread. These results are used for an analysis of a more realistic altimetry flow. We discuss the findings in terms of the time scale of the NPZ model, the qualitative interaction of the flow with the reaction front and a Finite-Time Lyapunov Exponent analysis
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