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   COLLOQUIUM OF THE LABORATORY FOR COMPUTER DESIGN OF MATERIALS        
        Institute for Computational Sciences and Informatics	
                           (CSI 898-Sec 001) 
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         Real-Space, Finite-Element Approach to Large-Scale 
                  Electronic-Structure Calculations

                            J.E. Pask
          Center for Computational Materials Science 
        Naval Research Laboratory, Washington, DC 20375

Over the course of the past few decades the Density Functional Theory
(DFT) of Hohenberg, Kohn, and Sham has proven to be an accurate and
reliable basis for the ab initio (from first principles) understanding and
prediction of a wide variety of materials properties. Through DFT, the
calculation of many basic materials properties can be reduced to the
self-consistent solution of the Schroedinger and Poisson equations.
However, since the potentials and charge densities in a typical solid are
so highly inhomogeneous, the solution of these equations is formidable
task and this has severely limited the range of systems which can be
considered -- to systems with unit cells of no more than a few hundred
atoms in the case of planewave (Fourier-based) methods of solution, for
example. I will discuss a new approach to solid-state electronic-structure
calculations based on the finite-element (FE) method, which promises to
extend the range of systems which can be considered. Like the planewave
method, the FE method is an expansion method. In FE method, however, the
basis functions are strictly local, piecewise polynomials. Because the
basis is composed of polynomials, the method is completely general and its
convergence can be controlled systematically. Because the basis functions
are strictly local in real space, the method allows for variable
resolution in real space; produces sparse, structured matrices, enabling
the effective use of iterative solution methods; and is well suited to
parallel implementation. The method thus combines the significant
advantages of both real-space-grid and basis-oriented approaches and so
promises to be particularly well suited for large, accurate ab initio
calculations. I'll begin with a discussion of the physical problem to be
solved and its reduction via DFT to the solution of the Schroedinger and
Poisson equations. I'll then go on to discuss our approach to the solution
of the relevant equations, advantages and disadvantages, and some initial
results, including electronic band structures, positron distributions and
lifetimes, and details of the convergence of the method.

                         Monday , February 21, 2000
                                  4:30 pm
                        Room 206, Science & Tech. I

Refreshments will be served.
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Find the schedule at http://csi.gmu.edu/lcdm/seminar/schedule.html