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Recent developments and applications of the real-space multigrid method...

by Jerzy Bernholc, Miroslav Hodak, Wenchang Lu
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Journal Name
Journal of Physics: Condensed Matter
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The salient features of the real-space multigrid method and its recent applications are described.
This method is suitable for very large scale, massively parallel calculations of atomic and
electronic structure, as well as quantum molecular dynamics. Its nearly O(N) implementation
provides a compact, variationally optimized basis that is also very useful for fully O(N)
calculations of quantum transport. Recently, we also developed a hybrid method for simulating
biomolecules in solution, in which most of the solvent is inexpensively treated using an
approximate density-functional method, while the biomolecule and its first solvation shells are
described at the full Kohn–Sham level. Our calculations show excellent parallel efficiency and
scaling on massively parallel supercomputers.