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Visualizing Higher-Order Finite Element Surfaces
Posted Tue November 03, 2020 @03:07PM
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Post Processing Tecplot's foray into visualizing higher-order finite element geometry and solutions continues with a blog post on Visualizing Higher-Order Finite-Element Surfaces.

For higher-order finite-element surfaces, the geometry (x,y,z coordinates of any point on the surface) is defined for each element by polynomials in terms of the local surface coordinates (r,s).

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If the same polynomial type and order is used for the solution and the geometry, it is called isoparametric. If a lower order polynomial is used for the geometry than compared to the solution, it is call subparametric. If higher, it is superparametric. In any case, if the same type of polynomial functions are used for geometry and solution, and then similar visualization techniques can be used as well.

Our technique for visualizing higher-order surface elements is very similar to our technique for higher-order volume elements. We use hierarchical subdivision of the surface elements. On each level of subdivision, triangles are subdivided into four sub-triangles and quadrilaterals are subdivided into four sub-quadrilaterals. The hierarchical subdivision of the surface elements continues until the resulting set of linear elements is a good representation of the curved polynomial surface.

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