Separated Representation for Computational Materials Science
Abstract
Our goal was to develop novel multiparticle computational tools for materials science based on representing operators and functions of many variables as short sums of separable functions. We have extended multiresolution separated representation of free-space Green's functions to those periodic or satisfying boundary conditions, making fast algorithms available for solving integral equations. The problem of incorporating inter-electron cusps within two-particle methods led us to the problem of approximating multivariable functions by sums of products of Gaussians. We have developed and tested a new (suboptimal) algorithm, sufficient for many practical purposes. Using this algorithm we constructed novel separated representations of non-convolutional Green's functions and spectral projectors for operators with potentials from the Rollnik class. Such potentials include all physically significant potentials considered within a finite domain. For optimal representations, we have developed an algorithm in the case of two variables; extensions to higher dimensions need to be worked on further. We started work on moving preliminary implementations of these algorithms into the Python environment where they can be used for practical computations. We have developed the algorithmic framework for a size-extensive/consistent method for the multiparticle Schrodinger equation. The central computation involved has revealed a center-of-mass principle for electrons, which gives hope for the construction of an analogue of the Fast Multipole Method for quantum mechanical systems.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 31, 2005
- Accession Number
- ADA447344
Entities
People
- Gregory Beylkin
- Lucas Monzon
- Martin J. Mohlenkamp
Organizations
- University of Colorado Boulder