Post-processing and visualization techniques for isogeometric analysis results

Abstract

Isogeometric Analysis (IGA) introduced in 2005 by Hughes et al. (2005) [1] exploits one mathematical basis representation for computer aided design (CAD), geometry and analysis during the entire engineering process. In this paper we extend this concept also for visualization. The presented post-processing and visualization techniques thereby strengthen the relation between geometry, analysis and visualization. This is achieved by facilitating the same mathematical function space used for geometry and analysis also for post-processing and visualization purposes. During non-linear analysis derivatives are incrementally computed and stored with different basis function representations. We introduce and investigate projection methods to be able to use the same function space for both displacements and stresses without loss of accuracy. To obtain a common representation for structured and unstructured meshes like hierarchical spline, locally refined B-spline (LR B-spline) and T-spline techniques we exploit Bézier decomposition in a post-processing step resulting in a Bézier element representation and constitute it as generalized representation. The typically used unrelated (fictitious) finite element mesh representation for visualization purposes are easily replaced without changing the underlying geometry as well as the algorithmic data structure. One further benefit of the used Bézier decomposition lies in the fact that it facilitates a natural parallel implementation on Graphics Processor Units (GPUs) exploiting shader programming. In this paper we have developed and investigated an accurate, efficient and practical post-processing pipeline for visualization of isogeometric analysis results. The proposed IGA visualization pipeline consists of three steps: (1) Projection, (2) Bézier decomposition and (3) Pixel-accurate rendering. We have tested four different projection methods. A description on how to perform Bézier decomposition of LR B-splines are given (whereas for hierarchical and T-splines this has been done before). Furthermore, the use of GPU shader programming to enable efficient and pixel-accurate visualization is detailed. The performance of the four different projection techniques has been tested on manufactured problems as well as on realistic benchmark problems. Furthermore, the IGA visualization pipeline has been demonstrated on a number of real-world applications.