Recent developments and applications of the real-space multigrid method

• Published in: Journal of physics. Condensed matter Vol. 20; no. 29; pp. 294205 - 294205 (8)
• Main Authors: Bernholc, J, Hodak, Miroslav, Lu, Wenchang
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Bristol IOP Publishing 23.07.2008; Institute of Physics
• Subjects: Condensed matter: electronic structure, electrical, magnetic, and optical properties; Cross-disciplinary physics: materials science; rheology; Electron states; Exact sciences and technology; Materials science; Methods of electronic structure calculations; Nanoscale materials and structures: fabrication and characterization; Physics; Quantum wells; Electronic structure; Approximate method; Multigrid; Quantum wells; Scaling laws; Molecular dynamics method; Density functional method; Atomic structure; Implementation; Optimization; Quantum theory; Quantum transport
• ISSN: 0953-8984; 1361-648X
• DOI: 10.1088/0953-8984/20/29/294205

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.