On the Treatment of Field Quantities and Elemental Continuity in FEM Solutions

Abstract

Fig. 1. 3D NACA wing example of vorticity before (left of the dashed line) and after (right) the application of our proposed approach.Abstract-As the finite element method (FEM) and the finite volume method (FVM), both traditional and high-order variants, continue their proliferation into various applied engineering disciplines, it is important that the visualization techniques and corresponding data analysis tools that act on the results produced by these methods faithfully represent the underlying data. To state this in another way: the interpretation of data generated by simulation needs to be consistent with the numerical schemes that underpin the specific solver technology. As the verifiable visualization literature has demonstrated: visual artifacts produced by the introduction of either explicit or implicit data transformations, such as data resampling, can sometimes distort or even obfuscate key scientific features in the data. In this paper, we focus on the handling of elemental continuity, which is often only C 0 continuous or piecewise discontinuous, when visualizing primary or derived fields from FEM or FVM simulations. We demonstrate that traditional data handling and visualization of these fields introduce visual errors. In addition, we show how the use of the recently proposed line-SIAC filter provides a way of handling elemental continuity issues in an accuracy-conserving manner with the added benefit of casting the data in a smooth context even if the representation is element discontinuous.

The Effect of Data Transformations on Scalar Field Topological Analysis of High-Order FEM Solutions

“…Later, Docampo-Sánchez et al proved that the Line-SIAC filter (L-SIAC), when applied to 2D and 3D simulation data, has all the properties of the SIAC filter [21], but is more computationally efficient than the traditional tensor-product-based SIAC filter in multiple dimensions. Jallepalli et al compared the commonly used data transformation methodologies to the L-SIAC filter and showed that the L-SIAC filter is a better tool for creating continuous visualization data [37]. This work, in part, motivates us to study its effect on downstream analysis with topological tools.…”

“…For example, one can use topology to study vortex breakdown patterns [69], vortex merging [3], and shedding patterns. These techniques are built with the assumption of continuity in the data, but as presented in [37], one of the challenges associated with the visualization, and in this case the topological analysis, of HO-FEM fields (and their corresponding derived fields) is their lack of continuity at element interfaces. Fundamentally, topological analysis is based on extracting properties in a continuum: these properties are designed to be invariant to deformation but sensitive to topological events such as cutting or splitting.…”

“…Two of the methodologies we consider are sampling the data on a regular grid (avoiding discontinuities) and subdividing the elements on the simulation mesh (avoiding discontinuities and judiciously producing low-order elements). These methodologies are commonly used due to their ease of implementation and lower computational cost, but they have the disadvantage of creating undesirable artifacts [37]. We use these methodologies to provide baselines to discuss the interplay between the sampling parameter and its effect on the intensity of the discontinuities and interpolation artifacts.…”

Point Movement in a DSL for Higher-Order FEM Visualization

“…There is no prior work extracting ridge surfaces from FEM data, but Pagot et al find ridge lines on affine meshes via PVO and new seed finding and streamline routines [31]. Jallepalli et al's smoothing of finite element data could usefully complement the visualization methods we target [18].…”

“…We present preliminary work on extending the open-source compiler for a scientific visualization DSL [8,19,20], previously limited to regular grids, to also work on higher-order FEM data. Our long-term goal is to connect previous FEM visualization methods [11,18,25,[27][28][29][30][31][32] by simplifying how they can be expressed and combined in working code. Our current focus is just two kinds of visualizations, both involving computations on a discrete set of points: streamlines [11], and particle systems sampling surface features [25].…”