Date of Award


Document Type


Degree Name

Master of Science in Aeronautical Engineering


Department of Aeronautics and Astronautics

First Advisor

Philip S. Beran, PhD


The timely visualization of three-dimensional data sets and the advantages of using a spectral method solution versus a finite-difference method solution in rendering isosurfaces is described. The Beam-Warming numerical algorithm, which uses implicit-approximate-factorization, is used to generate the steady-state solutions for a model diffusion-convection problem. The Chebyshev collocation operator is used to evaluate the right-hand side of the Beam-Warming algorithm for the spectral solution. Comparing the model problem results with the exact solution, the spectral series solution is truncated to the same degree of accuracy as the finite-difference for comparison of rendering times. The rendering algorithm employs octrees to efficiently traverse the data set to fit the isosurfaces. The actual fitting of polygons to the isosurface uses the marching cubes table look up algorithm. With the spectral series solution, interval math is investigated for guaranteed detection of isosurfaces during the initial octree traversal(s).

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DTIC Accession Number



The author's Vita page is omitted.