✦ LIBER ✦

Exploring Sparsity in Three-Dimensional Integration for Density-Functional Calculations

✍ Scribed by L. Lou

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 105 KB
Volume: 157
Category: Article
ISSN: 0021-9991
DOI: 10.1006/jcph.1999.6388

No coin nor oath required. For personal study only.

✦ Synopsis

The cost of a density-functional calculation with three-dimensional integration remains to be order N 3 , although a large portion of the integration grid may have negligible effects on the generation of a matrix element, due to rapid decay of atomcentered basis functions with distance. This type of integration sparsity is exploited by prescreening for insignificant contributions based on a direct estimate of their magnitudes. The result is a substantial reduction in cost without sacrificing numerical precision. Timing on compact molecules shows that a near order N 2 scaling with system size can be obtained for N տ 300 basis functions. The overhead of prescreening is moderate and may be characterized by a break-even size N ≈ 200.

📜 SIMILAR VOLUMES

An algorithm to delineate and integrate

An algorithm to delineate and integrate topological basins in a three-dimensional quantum mechanical density function

✍ Nathaniel O. J. Malcolm; Paul L. A. Popelier 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 190 KB

## Abstract The growing activity in the area of Quantum Chemical Topology warrants a new algorithm to delineate topological basins in 3D scalar fields other than the electron density. A method based on the “octal tree search algorithm” of computer graphics is proposed to reach this goal. We illustr

Three-dimensional elastic-plastic j-inte

Three-dimensional elastic-plastic j-integral calculations for semielliptical surface cracks in a tensile plate

✍ G.P. Nikishkov; S.N. Atluri 📂 Article 📅 1988 🏛 Elsevier Science 🌐 English ⚖ 495 KB

Using a finite element method, in conjunction with an equivalent domain integral approach, the elastic-plastic crack-tip J-integral is computed for semielliptical surface flaws in a plate under a remote tensile load. The computed elastic-plastic values of the J-integral are compared to the elastic o

Integration of singular enrichment funct

Integration of singular enrichment functions in the generalized/extended finite element method for three-dimensional problems

✍ Kyoungsoo Park; Jeronymo P. Pereira; C. Armando Duarte; Glaucio H. Paulino 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 751 KB

Note on the choice of basis set in densi

Note on the choice of basis set in density functional theory calculations for electronic structures of molecules (test on the atoms from the first three rows of the periodic table (2 ⩽ N ⩽ Z ⩽ 18), water, ammonia and pyrrole)

✍ Sándor Kristyán 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 808 KB