Petascale computing on the TeraGrid: Novel Scalable Algorithms in Density Functional Theory Calculations

Note: After ten years of service to the national science and engineering community, the TeraGrid project has ended. It is succeeded by a new National Science Foundation (NSF) program, the Extreme Science and Engineering Discovery Environment (XSEDE). You should move any data stored on TeraGrid systems to an alternate storage resource. If you have leftover service units on your TeraGrid allocation, or if your research requires further use of high performance computational, visualization, storage, and network resources, consider applying for an allocation on one or more XSEDE digital services.

Note: The project described in this document is funded by the National Science Foundation (NSF) Office of Cyberinfrastructure (OCI) to use TeraGrid's petascale environments for highly advanced scientific analysis and simulations that advance the frontiers of scientific and engineering research. For more, see Petascale computing on the TeraGrid.

Density functional theory (DFT) is one of the great scientific achievements of the 20th century. The fundamental importance of DFT originates from its much simplified description of the law of the fundamental building blocks of materials over the Schrodinger equation. DFT has had significant impact in a broad range of fields, including condensed matter physics, quantum chemistry, and materials science. However, first principals DFT calculations for complex materials often lead to computational problems of enormous dimension. Without efficient scalable algorithms, the sheer size of the problems can easily overwhelm even the most powerful supercomputers.

One major computational bottleneck in DFT calculations is the repeated solution of large scale eigenproblems inside a self-consistent loop.

Novel algorithms are needed in order to significantly reduce the computational cost without scarifying accuracy. This project is investigating filtering approaches based on the recently developed Chebyshev filtered subspace iteration (CheFSI) method.

CheFSI method utilizes Chebyshev polynomials for adaptive subspace filtering, and is close to an eigenvector-free approach except that the first step of the self-consistent loop requires a diagonalization. This research will further investigate and develop novel eigenvector-free algorithms based on polynomial filtering and preconditioning techniques for the nonlinear eigenvalue problems in DFT calculations. Emphasis is placed on extending the nonlinear subspace filtering techniques developed in the real-space setting to the widely used plane-wave setting. The goal is to make first principals DFT calculations more efficient and feasible for the study of increasingly more complex materials.

For more, see award abstract #0749074 on the National Science Foundation (NSF) web site.

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