ITR: New Algorithms for Scalable Modeling in Materials Science

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)One of the most significant achievements of the last century has been the development of accurate methods to predict the electronic and structural properties of matter. These methods, based on density functional theory and pseudopotentials, allow us to explore the properties of materials without resort to experiments. We can now predict new materials and their properties based on numerical calculations. The only inherent limitations of these methods are computational constraints; current electronic structures methods have a very high computational cost. While the use of modern high-performance computers has enabled tremendous progress in raw computational power for these problems, gains on the algorithms side are also necessary to accommodate more complex materials.This project will introduce new methods, based on efficient algorithms, for bypassing the computational limitations mentioned above. It will seek novel solution methodologies that improve efficiency without sacrificing accuracy and functionality. In particular, one goal will be to avoid the use of eigenvectors, the primary cost for both computation and memory. The project will do this by examining the fundamental physics of the problem, which reveals that a different basis for the subspace spanned by the same eigenvectors can be computed and used instead. The project will find efficient and robust methods for computing these bases, find efficient solutions to the time-dependent and self-consistent Kohn-Sham equations, develop effective out-of-core parallel methods for solving these very large systems, and use these methods to perform pioneering calculations of real materials.