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Particle Systems for Efficient and Accurate High-Order Finite Element Visualization

The use of high-order finite element methods for solving science and engineering problems has increased over the last 20 years as researchers have attempted to capitalize upon the accuracy these methods can provide without compromising meshing flexibility. SCI research concerning the development and implementation of high-order finite element methods not only increases the efficiency of the simulation component of the simulation science pipeline, but also provides interesting opportunities for interaction with the pipeline’s visualization component. Simulations making use of the high-order finite element method for spatial subdivision present a challenge to conventional isosurface visualization techniques. As a case study, consider the following example: finite element isosurfaces are often defined by basis functions in reference space, which give rise to a world space solution through a coordinate transformation. Because these high-order transformations do not generally have a closed-form inverse, they require isosurface rendering methods such as marching cubes and raytracing to perform a nested root-finding computation – an expensive algorithm. In current research at SCI, we propose visualizing these isosurfaces with a particle system. We have developed a framework that allows particles to sample an isosurface in reference space, avoiding the costly inverse mapping of positions from world space when evaluating the basis functions. The distribution of particles across the reference space isosurface is controlled, however, by geometric information from the world space isosurface, such as the surface gradient and curvature. The resulting particle distributions provide compact, efficient, and accurate isosurface representations of these challenging data sets.