Design and Implementation of New Scalable Algorithms in Nano-Scale Materials Science

Southern Methodist University, Dallas TX

Investigators

Abstract

Large scale eigenvalue-related problems constitute the computational bottlenecks in a wide range of science and engineering disciplines. The central goal of this project is to design and implement novel, scalable algorithms for one of these bottleneck problems: the nonlinear eigenvalue problems from first principles density functional theory (DFT) calculations. DFT is one of the most significant scientific achievements, it has revolutionized approaches used in studying electronic structures of atoms and molecules and has been an indispensable tool in fields such as condensed matter physics and materials science. Tremendous progress has been made in DFT applications/calculations. However, the full power of DFT is still severely limited by computational constraints. One major bottleneck is the repeated solution of large scale eigenvalue problems that can be of unprecedented dimension in the self-consistent-field (SCF) loop. By exploiting adaptive polynomial filters, we recently developed the nonlinear Chebyshev filtered subspace iteration (CheFSI) method which is almost eigenvector-free. This method significantly alleviates the computational burden for SCF calculations. The proposed research will (1) further improve the efficiency of the CheFSI method, especially the algorithm used for the initial diagonalization at the first SCF step; (2) continue improving and utilizing our own DFT package called PARSEC, which uses CheFSI, to perform challenging DFT simulations on materials of scientific and technological significance; (3) extend the filtering ideas used in CheFSI to significantly improve the diagonalization methods in the plane-wave package called PWscf; (4) explore and develop novel filtering and preconditioning techniques for the nonlinear eigenvalues in DFT calculations. DFT is of fundamental importance because it describes the law of the fundamental building blocks of materials. Advances in making DFT more computationally feasible for complex materials will have far-reaching intellectual impact. The two targeted packages PARSEC and PWscf are both open source software with large user group, being able to improve the solver efficiency for the bottleneck eigenproblems will benefit a large number of researchers and facilitate applying DFT to explore properties of larger and more complex materials that have not been studied before. Furthermore, the filtering and preconditioning techniques to be explored are closely related to calculating principal eigensubspaces, they have potentially broad range of applications in areas such as model reduction, data mining and information retrieval of massive data sets.