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Published October 2016 | metadata_only
Journal Article

A sublinear-scaling approach to density-functional-theory analysis of crystal defects


We develop a sublinear-scaling method, referred to as MacroDFT, for the study of crystal defects using ab-initio Density Functional Theory (DFT). The sublinear scaling is achieved using a combination of the Linear Scaling Spectral Gauss Quadrature method (LSSGQ) and a Coarse-Graining approach (CG) based on the quasi-continuum method. LSSGQ reformulates DFT and evaluates the electron density without computing individual orbitals. This direct evaluation is possible by recourse to Gaussian quadrature over the spectrum of the linearized Hamiltonian operator. Furthermore, the nodes and weights of the quadrature can be computed independently for each point in the domain. This property is exploited in CG, where fields of interest are computed at selected nodes and interpolated elsewhere. In this paper, we present the MacroDFT method, its parallel implementation and an assessment of convergence and performance by means of test cases concerned with point defects in magnesium.

Additional Information

© 2016 Elsevier Ltd. Received 17 March 2015. Received in revised form 17 May 2016. Accepted 20 May 2016. Available online 24 May 2016. Research was sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-12-2-0022. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein. K.B. and M.O. also acknowledge the partial financial support of the National Science Foundation through the PIRE grant No. OISE-0967140. This research used resources of the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC02-06CH11357.

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August 20, 2023
August 20, 2023