Laplacian-Isoparametric Grid Generation Scheme

Herrmann, Leonard R.

doi:10.1061/jmcea3.0002158

Cited by 164 publications

(22 citation statements)

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“…In order to avoid nonphysical solutions from the ionospheric solver due to large gradients (spikiness) in the conductance values, a smoothing filter was applied on the coefficients. The filter was based on a Laplacian mesh smoothing algorithm (e.g., Herrmann, 1976), commonly used in image processing (Yagou et al, 2002) and mesh refinement (Sorkine et al, 2004). The filter is applied such that at each node i,…”

Section: Cmeementioning

confidence: 99%

Conductance Model for Extreme Events : Impact of Auroral Conductance on Space Weather Forecasts

Mukhopadhyay

Welling

Liemohn

et al. 2020

Preprint

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Ionospheric conductance is a crucial factor in regulating the closure of magnetospheric field-aligned currents through the ionosphere as Hall and Pedersen currents. Despite its importance in predictive investigations of the magnetosphere-ionosphere coupling, the estimation of ionospheric conductance in the auroral region is precarious in most global first-principles-based models. This impreciseness in estimating the auroral conductance impedes both our understanding and predictive capabilities of the magnetosphere-ionosphere system during extreme space weather events. In this article, we address this concern, with the development of an advanced Conductance Model for Extreme Events (CMEE) that estimates the auroral conductance from field-aligned current values. CMEE has been developed using nonlinear regression over a year's worth of 1-min resolution output from assimilative maps, specifically including times of extreme driving of the solar wind-magnetosphere-ionosphere system. The model also includes provisions to enhance the conductance in the aurora using additional adjustments to refine the auroral oval. CMEE has been incorporated within the Ridley Ionosphere Model (RIM) of the Space Weather Modeling Framework (SWMF) for usage in space weather simulations. This paper compares performance of CMEE against the existing conductance model in RIM, through a validation process for six space weather events. The performance analysis indicates overall improvement in the ionospheric feedback to ground-based space weather forecasts. Specifically, the model is able to improve the prediction of ionospheric currents, which impact the simulated dB/dt and ΔB, resulting in substantial improvements in dB/dt predictive skill.Plain Language Summary Electric currents generated in the Earth's space environment due to its magnetic interaction with the Sun leads to charged particle deposition and closure of these currents in the terrestrial upper atmosphere, especially in the high-latitude auroral region. The enhancement in the electrical charge-carrying capacity as a result of this process in the Earth's upper atmosphere, also known as the ionosphere, is challenging to estimate in most numerical simulations attempting to study the interactive dynamic and chemical processes in the near-Earth region. The inability to accurately estimate this quantity leads to underprediction of severe space weather events that can have adverse impacts on man-made technology like electrical power grids, railway, and oil pipelines. In this study, we present a novel modeling approach to address this problem and provide global simulations with a more accurate estimate on the electrical conductivity of the ionosphere. Through this investigation, we show that the accurate measurement of the charge carriers in the ionosphere using the new model causes substantial improvements in the prediction of space weather on the ground, and significantly advances our understanding of global dynamics causing ground-based space weather.

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Section: Cmeementioning

confidence: 99%

Conductance Model for Extreme Events : Impact of Auroral Conductance on Space Weather Forecasts

Mukhopadhyay

Welling

Liemohn

et al. 2020

Preprint

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“…After the point mesh generation steps are completed, the domain will be covered by points with node spacing compatible with the user specifications. Just similar to the automatic mesh generation, it is found that the grading of the final the mesh can be improved by applying a Laplacian smoothing [26] procedure to the point mesh. However, for a point mesh, no fix connectivity relationship exists among the interior nodes.…”

Section: Point Mesh Quality Measurement and Enhancementmentioning

confidence: 99%

A new finite point generation scheme using metric specifications

Lee

2000

Int. J. Numer. Meth. Engng.

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A new approach to generate finite point meshes on 2D flat surface and any bi‐variate parametric surfaces is suggested. It can be used to generate boundary‐conforming anisotropic point meshes with node spacing compatible with the metric specifications defined in a background point mesh. In contrast to many automatic mesh generation schemes, the advancing front concept is abandoned in the present method. A few simple basic operations including boundary offsetting, node insertion and node deletion are used instead. The point mesh generation schemeis initialized by a boundary offsetting procedure. The point mesh quality is then improved by node insertion and deletion such that optimally spaced nodes will fill up the entire problem domain. In addition to the point mesh generation scheme, a new way to define the connectivity of a point mesh is also suggested. Furthermore, based on the connectivity information, a new scheme to perform smoothing for a point mesh is proposed toimprove the node spacing quality of the mesh. Timing shows thatdue to the simple node insertion and deletion operations, the generation speed of the new scheme is nearly 10 times faster than a similar advancing front mesh generator. Copyright © 2000 John Wiley & Sons, Ltd.

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“…In order to improve the general shape of the mesh elements, an iterative Laplacian smoothing procedure based on Herrmann [9] is applied in which the position of each internal node is defined to be an average of that of its contiguous neighbours, being the ones connected to the given node by a single element segment: (1) where i ranges over all nodes, j ranges from 1 to K i , the number of nodes contiguous to the ith node, and n is the iteration counter. Convergence is evaluated according to: (2) where M is the total number of nodes and δ is a small value (0.001).…”

Section: Mesh Smoothingmentioning

confidence: 99%

A metal‐forming approach to automatic generation of graded initial quadrilateral finite element meshes

Petersen¹,

Gouveia

Rodrigues

et al. 1998

Engineering Computations

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This paper presents an algorithm for automatic generation of graded initial quadrilateral meshes targeted for the finite element analysis of metal‐forming processes. Meshing the domain geometry deals with a universe of shapes, and the procedure therefore takes into account the initial geometry of the billet. A grid‐based approach is utilised for generating an initial coarse mesh with well‐shaped (internal) elements, and in cases where non‐rectangular shapes are to be discretized, linking with the boundary is performed on the basis of constrained Delaunay triangulation. By analysing the contact situation between dies and mesh, an attempt is made to identify regions where plastic deformation is likely to be concentrated during the early stages of processing, and accordingly refinement of the mesh is performed locally by elemental subdivision. Simulation examples for closed‐die forging, forward rod and backward can extrusion substantiate the feasibility of this approach in terms of lowering the overall calculation error and limiting the interference between mesh and die.

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Laplacian-Isoparametric Grid Generation Scheme

Cited by 164 publications

References 0 publications

Conductance Model for Extreme Events : Impact of Auroral Conductance on Space Weather Forecasts

Conductance Model for Extreme Events : Impact of Auroral Conductance on Space Weather Forecasts

A new finite point generation scheme using metric specifications

A metal‐forming approach to automatic generation of graded initial quadrilateral finite element meshes

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