Real-space numerical grid methods: The next generation of electronic structure codes*

Two physical ingredients, pseudopotentials and density functional theory, are widely used in electronic structure computations for a variety of materials applications. If we wish to address large, complex systems, the implementation of these ingredients on high performance computational platforms is vital. Real space grid methods offer a compelling vehicle for such computations. These methods are mathematically robust, very accurate and well suited for modern, massively parallel computing resources [1]. I will illustrate the utility of these methods as implemented in the PARSEC code [2]. Key algorithms in this code include subspace filtering based on Chebyshev polynomials for an accelerated eigenvalue solution, spectrum slicing for an added level of parallelism, Cholesky QR algorithms to improve the performance of orthogonalization, and a 2D partition of the wave functions for efficient matrix-vector operations. Applications will be illustrated for nanostructures containing tens of thousands of atoms.

[1] L. Frediani and D. Sundholm, Phys. Chem. Chem. Phys. 17, 31357 (2015).
[2] http://parsec.ices.utexas.edu