Abstract

A Finite-Element Approach for Electronic Structure Calculations

Philip Sterne
Lawrence Livermore National Laboratory
Physics

This talk discusses the development of a finite-element (FE) method for
large-scale ab initio electronic-structure calculations in solids.
Conventional density-functional-based electronic structure calculations
involve the solution of two differential equations - the Schrodinger
equation and Poisson's equation. The FE method is used routinely to
solve differential equations in a vast range of engineering
applications, and as a result has an extensive set of algorithms and
codes for a wide range of problems. We have formulated a FE Galerkin
approach to solve the Schrodinger equation and Poisson's equation for
the Bloch-periodic boundary conditions that arise in electronic
structure calculations on solids. This variational approach can be
understood as an expansion method that uses a strictly local,
piecewise-polynomial basis. The FE method combines the significant
advantages of both basis-oriented and grid-based approaches: the
polynomial nature of the basis leads to a completely general approach in
which convergence can be controlled systematically, while the local
nature of the basis results in sparse, structured matrices that are
amenable to efficient iterative solution methods. The result is a
variational real-space method that requires no Fourier transforms and is
well suited for parallelization.

We will present recent results from calculations of positron
distributions and lifetimes in systems consisting of several thousand
atoms. We will also discuss the development of a fully self-consistent
density-functional program based on this approach.

This work was performed under the auspices of the U.S. Department of
Energy by the University of California, Lawrence Livermore National
Laboratory under contract No. W-7405-Eng-48.