DIFFUSION PROBLEMS

THE APPLICATION OF SPECTRAL METHODS TO THE SOLUTION OF HIGHLY-VARIABLE-COEFFICIENT DIFFUSION PROBLEMS IS STUDIED FOR APPLICATIONS TO MULTI-DIMENSIONAL FLUID DYNAMICS AND HEAT TRANSFER PROBLEMS OF INTEREST TO NASA. THE UTILITY OF THESE METHODS FOR THE DESIGN OF EXPERIMENTS FOR MATERIALSPROCESSING IN SPACE APPLICATIONS IS CONSIDERED. THE MAJOR ADVANTAGE OF SPECTRAL METHODS IS THAT THEY REQUIRE AT LEAST AN ORDER OF MAGNITUDE FEWER DEGREES OF FREEDOM TO ACHIEVE GIVEN ACCURACY THAN CONVENTIONAL FINITE DIFFERENCE OR FINITEELEMENT METHODS. FOR MULTI-DIMENSIONAL DIFFUSION PROBLEMS, THIS ACCURACY ADVANTAGE TRANSLATES INTO A SPEED ADVANTAGE OFSEVERAL ORDERS OF MAGNITUDE, PERMITTING THE SOLUTION OF DIFFICULT PROBLEMS WHOSE SOLUTION WOULD OTHERWISE BE BEYOND THE STATE OF THE ART.