ElVis: A System for the Accurate and Interactive Visualization of High-Order Finite Element Solutions

Abstract

Fig. 1. Pressure field on the ONERA M6 Wing (Section 5.1.2), rendered using ElVis and illustrating the application of color maps and contour lines on curved and planar surfaces.Abstract-This paper presents the Element Visualizer (ElVis), a new, open-source scientific visualization system for use with highorder finite element solutions to PDEs in three dimensions. This system is designed to minimize visualization errors of these types of fields by querying the underlying finite element basis functions (e.g., high-order polynomials) directly, leading to pixel-exact representations of solutions and geometry. The system interacts with simulation data through runtime plugins, which only require users to implement a handful of operations fundamental to finite element solvers. The data in turn can be visualized through the use of cut surfaces, contours, isosurfaces, and volume rendering. These visualization algorithms are implemented using NVIDIA's OptiX GPU-based ray-tracing engine, which provides accelerated ray traversal of the high-order geometry, and CUDA, which allows for effective parallel evaluation of the visualization algorithms. The direct interface between ElVis and the underlying data differentiates it from existing visualization tools. Current tools assume the underlying data is composed of linear primitives; high-order data must be interpolated with linear functions as a result. In this work, examples drawn from aerodynamic simulations-high-order discontinuous Galerkin finite element solutions of aerodynamic flows in particular-will demonstrate the superiority of ElVis' pixel-exact approach when compared with traditional linear-interpolation methods. Such methods can introduce a number of inaccuracies in the resulting visualization, making it unclear if visual artifacts are genuine to the solution data or if these artifacts are the result of interpolation errors. Linear methods additionally cannot properly visualize curved geometries (elements or boundaries) which can greatly inhibit developers' debugging efforts. As we will show, pixel-exact visualization exhibits none of these issues, removing the visualization scheme as a source of uncertainty for engineers using ElVis.

High-Order Visualization with ElVis

“…The delta-wing geometry is linear and the computational mesh consists of 19410 quadratic tetrahedral elements with straight edges. The numerical solution has been obtained via a discontinuous Galerkin solver 3 . Figure 1 depicts a linear visualization of the solution on a plane cut located at the trailing edge of the wing.…”

“…The purpose of this chapter is to give a brief overview of the Element Visualiser (ElVis) [7], which aims to address these issues through a novel approach that provides interactive and accurate visualization of high-order simulations 1 . The simulations are represented by spectral/hp finite element fields that are produced by the continuous or discontinuous Galerkin methods.…”

“…ElVis was originally created by B.W. Nelson, as part of his PhD at the University of Utah [3]. Currently ElVis is actively maintained by R.M.…”

Visualização De Seções De Corte Arbitrárias De Malhas Não Estruturadas

“…Após calcular a equação da reta de interseção para cada uma das faces do elemento, calculamos o ponto mais próximo do fragmento em cada uma das retas. O ponto da reta mais próximo ao fragmentoé calculado como: (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) onde b ié a coordenada baricêntrica de p m em relação ao vértice i do triângulo e v rié a coordenada do vértice i no espaço da superfície renderizada.…”

“…Em (4), a visualizaçãoé restrita a cortes planares, uma aproximação da interseção entre o plano de corte e o modeló e calculada na CPU eé feito no shader de fragmentos o cálculo do valor do campo escalar na posição de cada fragmento. Em (16,17), a renderização de superfícies arbitrárias de corte (superfícies implícitas e paramétricas)é feita através de um algoritmo de traçado de raio em GPU. A implmentação utiliza o framework de traçado de raio OptiX da Nvidia e o modeloé estruturado em GPU na forma de um grafo.…”