Visualization of Finite Elements and Tools for Numerical Analysis

Abstract

A visualization approach for finite elements including numerical algorithms based on an object oriented environment is presented. Starting from examples of numerical analysis of partial differential equations the requirements and specifications for a toolbox offering highly interactive rendering facilities for continuum mechanical as well as geometrical problems in 2D and 3D are explained. After a short description of object oriented programming our concept of interactive geometric modeling is introduced. Applications include the rendering of isoline, color scaled maps, vector and tensor fields on 2D domains, surfaces of intersections in 3D bodies (bars under stress or containers with fluid flow), particle traces, moved hyper surf aces, and the 2D levels of a function on a 3D finite element domain. Our concept has been implemented in the object oriented programming environment GRAPE at the graphics laboratory of the SFB 256. The appendix contains the definition of the specific classes and a description of all methods.