Results 1 
3 of
3
Linearly Scaling 3D Fragment Method for LargeScale Electronic Structure Calculations
, 2008
"... We present a new linearly scaling threedimensional fragment (LS3DF) method for large scale ab initio electronic structure calculations. LS3DF is based on a divideandconquer approach, which incorporates a novel patching scheme that effectively cancels out the artificial boundary effects due to the ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
We present a new linearly scaling threedimensional fragment (LS3DF) method for large scale ab initio electronic structure calculations. LS3DF is based on a divideandconquer approach, which incorporates a novel patching scheme that effectively cancels out the artificial boundary effects due to the subdivision of the system. As a consequence, the LS3DF program yields essentially the same results as direct density functional theory (DFT) calculations. The fragments of the LS3DF algorithm can be calculated separately with different groups of processors. This leads to almost perfect parallelization on tens of thousands of processors. After code optimization, we were able to achieve 35.1 Tflop/s, which is 39 % of the theoretical speed on 17,280 Cray XT4 processor cores. Our 13,824atom ZnTeO alloy calculation runs 400 times faster than a direct DFT calculation, even presuming that the direct DFT calculation can scale well up to 17,280 processor cores. These results demonstrate the applicability of the LS3DF method to material simulations, the advantage of using linearly scaling algorithms over conventional O(N 3) methods, and the potential for petascale computation using the LS3DF method. 1
SANDIA REPORT The potential, limitations, and challenges of divide and conquer quantum electronic structure calculations on energetic materials The potential, limitations, and challenges of divide and conquer quantum electronic structure calculations on e
"... Abstract High explosives are an important class of energetic materials used in many weapons applications. Even with modern computers, the simulation of the dynamic chemical reactions and energy release is exceedingly challenging. While the scale of the detonation process may be macroscopic, the dyn ..."
Abstract
 Add to MetaCart
Abstract High explosives are an important class of energetic materials used in many weapons applications. Even with modern computers, the simulation of the dynamic chemical reactions and energy release is exceedingly challenging. While the scale of the detonation process may be macroscopic, the dynamic bond breaking responsible for the explosive release of energy is fundamentally quantum mechanical. Thus, any method that does not adequately describe bonding is destined to lack predictive capability on some level. Performing quantum mechanics calculations on systems with more than dozens of atoms is a gargantuan task, and severe approximation schemes must be employed in practical calculations. We have developed and tested a divide and conquer (DnC) scheme to obtain total energies, forces, and harmonic frequencies within semiempirical quantum mechanics. The method is intended as an approximate but faster solution to the full problem and is possible due to the sparsity of the density matrix in many applications. The resulting total energy calculation scales linearly as the number of subsystems, and the method provides a pathforward to quantum mechanical simulations of millions of atoms. 3 This page intentionally left blank. 4
A POSTERIORI ERROR ESTIMATOR FOR ADAPTIVE LOCAL BASIS FUNCTIONS TO SOLVE KOHNSHAM DENSITY FUNCTIONAL THEORY
"... Abstract. KohnSham density functional theory is one of the most widely used electronic structure theories. The recently developed adaptive local basis functions form an accurate and systematically improvable basis set for solving KohnSham density functional theory using discontinuous Galerkin met ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. KohnSham density functional theory is one of the most widely used electronic structure theories. The recently developed adaptive local basis functions form an accurate and systematically improvable basis set for solving KohnSham density functional theory using discontinuous Galerkin methods, requiring a small number of basis functions per atom. In this paper we develop residualbased a posteriori error estimates for the adaptive local basis approach, which can be used to guide nonuniform basis refinement for highly inhomogeneous systems such as surfaces and large molecules. The adaptive local basis functions are nonpolynomial basis functions, and standard a posteriori error estimates for hprefinement using polynomial basis functions do not directly apply. We generalize the error estimates for hprefinement to nonpolynomial basis functions. We demonstrate the practical use of the a posteriori error estimator in performing threedimensional KohnSham density functional theory calculations for quasi2D aluminum surfaces and a singlelayer graphene oxide system in water. Key words. KohnSham density functional theory, a posteriori error estimator, adaptive local basis function, discontinuous Galerkin method AMS subject classifications. 65N15,65N25,65N30,65Z05 1. Introduction. We