The application of spectral methods to the solution of highly-variable-coefficient diffusionproblems is studied for applications to multi-dimensional fluiddynamics and heat transfer problems of interest to NASA. Theutility of these methods for the design of experiments formaterials processing in space applications is considered. Themajor advantage of spectral methods is that they require at leastan order of magnitude fewer degrees of freedom to achieve givenaccuracy than conventional finite difference or finite elementmethods. For multidimensional diffusion problems, this accuracyadvantage translates into a speed advantage of several orders ofmagnitude, permitting the solution of difficult problems whosesolution would otherwise be beyond the state-of-the-art.
