Accurate contour plotting using 6-node triangular elements in 2D

Singh, Chandan Deep; Singh, Jaswinder Pal

doi:10.1016/j.finel.2008.07.011

Cited by 9 publications

(2 citation statements)

References 22 publications

(44 reference statements)

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“…Another approach steps along a direction orthogonal to the field's gradient [3], where each step is controlled by a user-defined step size. A method for generating contour lines over quadrilateral elements by determining the shape of the contour in reference space and then generating a polyline to approximate it was developed in [28] and later extended to linear and quadratic triangles in [29].…”

Section: Related Workmentioning

confidence: 99%

Stochastic Collocation for Optimal Control Problems with Stochastic PDE Constraints

Tiesler

Kirby

Xiu

et al. 2012

SIAM J. Control Optim.

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Fig. 1. Pressure field on the ONERA M6 Wing (Section 5.1.2), rendered using ElVis and illustrating the application of color maps and contour lines on curved and planar surfaces.Abstract-This paper presents the Element Visualizer (ElVis), a new, open-source scientific visualization system for use with highorder finite element solutions to PDEs in three dimensions. This system is designed to minimize visualization errors of these types of fields by querying the underlying finite element basis functions (e.g., high-order polynomials) directly, leading to pixel-exact representations of solutions and geometry. The system interacts with simulation data through runtime plugins, which only require users to implement a handful of operations fundamental to finite element solvers. The data in turn can be visualized through the use of cut surfaces, contours, isosurfaces, and volume rendering. These visualization algorithms are implemented using NVIDIA's OptiX GPU-based ray-tracing engine, which provides accelerated ray traversal of the high-order geometry, and CUDA, which allows for effective parallel evaluation of the visualization algorithms. The direct interface between ElVis and the underlying data differentiates it from existing visualization tools. Current tools assume the underlying data is composed of linear primitives; high-order data must be interpolated with linear functions as a result. In this work, examples drawn from aerodynamic simulations-high-order discontinuous Galerkin finite element solutions of aerodynamic flows in particular-will demonstrate the superiority of ElVis' pixel-exact approach when compared with traditional linear-interpolation methods. Such methods can introduce a number of inaccuracies in the resulting visualization, making it unclear if visual artifacts are genuine to the solution data or if these artifacts are the result of interpolation errors. Linear methods additionally cannot properly visualize curved geometries (elements or boundaries) which can greatly inhibit developers' debugging efforts. As we will show, pixel-exact visualization exhibits none of these issues, removing the visualization scheme as a source of uncertainty for engineers using ElVis.

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Section: Related Workmentioning

confidence: 99%

Stochastic Collocation for Optimal Control Problems with Stochastic PDE Constraints

Tiesler

Kirby

Xiu

et al. 2012

SIAM J. Control Optim.

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“…Therefore, several attempts are made to use the higher order element for tracing of contours to maintain the accuracy of contour tracing. A review of such methods can be found in Singh and Singh [5]. Singh and Saini [6] develops a fast algorithm for plotting of contours using eight-node quadrilateral elements.…”

Section: Introductionmentioning

confidence: 99%

Algorithms for Accurate and Fast Plotting of Contour Surfaces in 3D Using Hexahedral Elements

Singh

Saini

2016

J. Inst. Eng. India Ser. C

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In the present study, Fast and accurate algorithms for the generation of contour surfaces in 3D are described using hexahedral elements which are popular in finite element analysis. The contour surfaces are described in the form of groups of boundaries of contour segments and their interior points are derived using the contour equation. The locations of contour boundaries and the interior points on contour surfaces are as accurate as the interpolation results obtained by hexahedral elements and thus there are no discrepancies between the analysis and visualization results.

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Accurate and Fast Algorithm for the Plotting of Contours Using Eight Node Quadrilateral Meshes

Singh

Saini

2014

J. Inst. Eng. India Ser. B

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Accurate contour plotting using 6-node triangular elements in 2D

Cited by 9 publications

References 22 publications

Stochastic Collocation for Optimal Control Problems with Stochastic PDE Constraints

Stochastic Collocation for Optimal Control Problems with Stochastic PDE Constraints

Algorithms for Accurate and Fast Plotting of Contour Surfaces in 3D Using Hexahedral Elements

Accurate and Fast Algorithm for the Plotting of Contours Using Eight Node Quadrilateral Meshes

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