The goal of this project is to develop and apply scalable numerical methods and a software infrastructure for the first principles prediction of the properties of materials. These materials typically have complex structures and compositions, a large number of atoms (n>100) and little or no symmetry. For many important examples reliable theoretical predictions are not possible using present day approaches. Here a new method is being tested; preliminary results show that it promises to remove a major roadblock to the wider application of first principle calculations to real materials, thereby greatly expanding the problems that can be treated. As part of the project this new method will be applied to an important problem, the oxidation of carbon based materials. The project builds on a novel computational approach to solving the LAD equations based on a parallel, real-space, adaptive multigrid eigenvalue solver. Unlike Fourier methods, this adaptive method locally refines the solution to capture the short length scales in the problem; for example, the short length in near oxygen region in the carbon oxygen system. The investigators' preliminary calculations are currently limited to model problems with structures similar to the real materials Schrodinger eigenvalue equation. However, the new computational method shows promising improvements in convergence and efficiency over present algorithms. The purpose of this program is to enhance the proposed solver to enable application of an adaptive method to real materials.
