Applications of Multigrid Methods in Chemistry, Biophysics, and Materials Nanoscience

APPLICATIONS OF MULTIGRID METHODS IN CHEMISTRY, BIOPHYSICS, AND MATERIALS NANOSCIENCE 

In this section, we discuss recent progress in algorithms and some case studies of the application of real-space and MG methods in computational 

After initial testing on small systems, Chelikowsky s group extended their real-space code (now called PARSEC) for a wide range of challenging applications.The applications include quantum dots, semiconductors, nanowires, spin polarization, and molecular dynamics to determine photoelectron spectra, metal clusters, and time-dependent DFT (TDDFT) calculations for excited-state properties. PARSEC calculations have been performed on systems with more than 10,000 atoms. The PARSEC code does not utilize MG methods but rather employs Chebyshev-filtered subspace acceleration and other efficient techniques during the iterative solution process. When possible, symmetries may be exploited to reduce the numbers of atoms treated explicitly. 

Two of the first efforts to adapt MG methods for DFT calculations were made by the groups of Bernholc and The method 

An ambitious goal is to model materials at the all-electron level. Typically, for large-scale materials calculations in DFT, the core electrons are removed and replaced by a nonlocal pseuodopotential. Mortensen, Hansen, and Jacobsen ° have taken the first steps to perform all-electron DFT calculations with FD difference representations and MG acceleration. They employ the projection augmented wave method in the frozen-core approximation. 

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