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

## TL;DR

This paper evaluates how different data transformation methods, including the L-SIAC filter, impact topological analysis of high-order FEM simulation data, providing guidance for effective pipeline design.

## Contribution

It offers an empirical comparison of transformation techniques for high-order FEM data to improve topological analysis accuracy and applicability.

## Key findings

- Transformations significantly affect topological analysis results.
- L-SIAC filter provides distinct advantages in data smoothing.
- Guidelines for pipeline design in topological analysis of HO-FEM data.

## Abstract

High-order finite element methods (HO-FEM) are gaining popularity in the simulation community due to their success in solving complex flow dynamics. There is an increasing need to analyze the data produced as output by these simulations. Simultaneously, topological analysis tools are emerging as powerful methods for investigating simulation data. However, most of the current approaches to topological analysis have had limited application to HO-FEM simulation data for two reasons. First, the current topological tools are designed for linear data (polynomial degree one), but the polynomial degree of the data output by these simulations is typically higher (routinely up to polynomial degree six). Second, the simulation data and derived quantities of the simulation data have discontinuities at element boundaries, and these discontinuities do not match the input requirements for the topological tools. One solution to both issues is to transform the high-order data to achieve low-order, continuous inputs for topological analysis. Nevertheless, there has been little work evaluating the possible transformation choices and their downstream effect on the topological analysis. We perform an empirical study to evaluate two commonly used data transformation methodologies along with the recently introduced L-SIAC filter for processing high-order simulation data. Our results show diverse behaviors are possible. We offer some guidance about how best to consider a pipeline of topological analysis of HO-FEM simulations with the currently available implementations of topological analysis.