9503997 Weare The purpose of this proposal is to develop adaptive numerical methods and the accompanying software infrastructure for the solution of the LDA equations in materials science. Current solution methods, based on Fast Fourier Transform techniques, cannot accurately resolve the short length scales present in many materials of technological importance. Our adaptive numerical methods will integrate adaptive mesh refinement techniques with advanced multilevel numerical eigenvalue algorithms. The implementation of adaptive numerical methods on high performance parallel platforms is difficult because the programmer must manage irregularly distributed, dynamically changing data. The use of adaptive numerical techniques will enable theoretical material scientists to model complex materials which cannot be treated using existing methods. Furthermore, because adaptive methods can be applied to a number of scientific and engineering disciplines, this research will impact other fields, including computational fluid dynamics, semiconductor modeling, and geophysical modeling.
