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Orbitalenriched partition of unity finite element method for ab initio density functional calculations
Prof. Natarajan. Sukumar from the University of California, invited by Prof. Yongxing Shen, gave us a talk on Aug. 7th, 2017. Professor Natarajan Sukumar presented the jointwork with Dr. John Pask, Physicist at LLNL, a realspace orbitalenriched partition of unity finite element (PUFE) approach to solve the KohnSham equations (coupled Schrodinger and Poisson equations) of density functional theory. In the PUFE method, he builds the known atomic physics into the solution process to solve the Schrodinger eigenproblem using partitionofunity enrichment techniques in finite element analysis. The method developed herein is completely general, applicable to any crystal symmetry and to both metals and insulators alike. Total energy calculations for full selfconsistent KohnSham calculations were presented for LiH that has light atoms, as well as triclinic CeAl (felectron system), which requires large numbers of atomicorbital enrichments. The new PUFE approach attains the required accuracies with substantially fewer degrees of freedom, typically by an order of magnitude or more, than the plane wave (PW) method. He computes the equation of state of LiH and shows that the computed lattice constant and bulk modulus are in excellent agreement with reference PW results, while requiring an order of magnitude fewer degrees of freedom to attain. Time & Date: 10:00 a.m.11:00 a.m., Aug. 7th, 2017 (Monday) Location: Room 228, conference room, JI Building Title: Orbitalenriched partition of unity finite element method for ab initio density functional calculations
Abstract The current stateoftheart for largescale quantummechanical simulations is the planewave (PW) pseudopotential method, as implemented in codes such as VASP, ABINIT, and many others. However, since the PW method uses a global Fourier basis, with strictly uniform resolution at all points in space, it suffers from substantial inefficiencies in calculations involving atoms with localized states, such as firstrow and transitionmetal atoms, and requires significant nonlocal communications that compromises parallel efficiency. Realspace methods such as finitedifferences and finiteelements have partially addressed both resolution and parallelcommunications problems, but have been plagued by one key disadvantage relative to PW: excessive number of degrees of freedom (basis functions) needed to achieve the required 1 mHa (chemical) accuracy in total energy. In this talk, I will present a realspace orbitalenriched partition of unity finite element (PUFE) approach to solve the KohnSham equations (coupled Schrodinger and Poisson equations) of density functional theory. In the PUFE method, we build the known atomic physics into the solution process to solve the Schrodinger eigenproblem using partitionofunity enrichment techniques in finite element analysis. The method developed herein is completely general, applicable to any crystal symmetry and to both metals and insulators alike. Total energy calculations for full selfconsistent KohnSham calculations will be presented for LiH that has light atoms, as well as triclinic CeAl (felectron system), which requires large numbers of atomicorbital enrichments. The new PUFE approach attains the required accuracies with substantially fewer degrees of freedom, typically by an order of magnitude or more, than the PW method. We compute the equation of state of LiH and show that the computed lattice constant and bulk modulus are in excellent agreement with reference PW results, while requiring an order of magnitude fewer degrees of freedom to attain. This is jointwork with Dr. John Pask, Physicist at LLNL
Bio Sukumar holds a B.Tech. from IIT Bombay in 1989, a M.S. from Oregon Graduate Institute in 1992, and a Ph.D. in Theoretical and Applied Mechanics from Northwestern University in 1998. He held postdoctoral appointments at Northwestern and Princeton University, before joining UC Davis in 2001, where he is currently a Professor in Civil and Environmental Engineering. Sukumar is a Regional Editor of International Journal of Fracture and is a member of the Executive Council of the US Association of Computational Mechanics. He has spent sabbatical visits at Cornell University (2007) and SLAC National Accelerator Laboratory (2011). Sukumar's research focuses on smooth maximumentropy approximation schemes, novel discretizations on polytopal meshes, fracture modeling with extended finite element methods, and new methods development (enriched partitionofunity methods) for largescale quantummechanical materials calculations. 