κ-compatible tessellations

Abstract

The vast majority of visualization algorithms for finite element (FE) simulations assume that linear constitutive relationships are used to interpolate values over an element, because the polynomial order of the FE basis functions used in practice has traditionally been low - linear or quadratic. However, higher order FE solvers, which become increasingly popular, pose a significant challenge to visualization systems as the assumptions of the visualization algorithms are violated by higher order solutions. This paper presents a method for adapting linear visualization algorithms to higher order data through a careful examination of a linear algorithm's properties and the assumptions it makes. This method subdivides higher order finite elements into regions where these assumptions hold (κ-compatibility). Because it is arguably one of the most useful visualization tools, isosurfacing is used as an example to illustrate our methodology.