Fast and robust all-electron density functional theory calculations in solids using orthogonalized enriched finite elements

Rufus, Nelson D.; Kanungo, Bikash; Gavini, Vikram

doi:10.1103/physrevb.104.085112

Title: Fast and robust all-electron density functional theory calculations in solids using orthogonalized enriched finite elements

Journal Article · 09 August 2021 · Physical Review. B

DOI: https://doi.org/10.1103/physrevb.104.085112 · OSTI ID:1852369

^[1];

^[2]; Gavini, Vikram ^[2]

Univ. of Michigan, Ann Arbor, MI (United States); OSTI
Univ. of Michigan, Ann Arbor, MI (United States)

Here, we present a computationally efficient approach to perform systematically convergent real-space all-electron Kohn-Sham density functional theory calculations for solids using an enriched finite element (FE) basis. The enriched FE basis is constructed by augmenting the classical FE basis with atom-centered numerical basis functions, comprising of atomic solutions to the Kohn-Sham problem. Notably, to improve the conditioning, we orthogonalize the enrichment functions with respect to the classical FE basis, without sacrificing the locality of the resultant basis. In addition to improved conditioning, this orthogonalization procedure also renders the overlap matrix block diagonal, greatly simplifying its inversion. Subsequently, we use a Chebyshev polynomial based filtering technique to efficiently compute the occupied eigenspace in each self-consistent field iteration. We demonstrate the accuracy and efficiency of the proposed approach on periodic unit cells and supercells. The benchmark studies show a staggering 130× speedup of the orthogonalized enriched FE basis over the classical FE basis. We also present a comparison of the orthogonalized enriched FE basis with the linearized augmented plane-wave + local orbitals basis, both in terms of accuracy and efficiency. Notably, we demonstrate that the orthogonalized enriched FE basis can handle large system sizes of ~10 000 electrons. Finally, we observe good parallel scalability of our implementation with 92% efficiency at 22× speedup for a system with 620 electrons

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Research Organization:: Univ. of California, Oakland, CA (United States); Univ. of Michigan, Ann Arbor, MI (United States)

Sponsoring Organization:: US Army Research Office (ARO); USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC02-05CH11231; SC0017380

OSTI ID:: 1852369

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 8 Vol. 104; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (87)

FP-LAPW and pseudopotential calculations of the structural phase transformations of GaN under high-pressure Abu-Jafar, M.; Al-Sharif, A. I.; Qteish, A. Solid State Communications, Vol. 116, Issue 7 https://doi.org/10.1016/s0038-1098(00)00336-7	journal	October 2000
The Partition of Unity Method BabuŠKa, I.; Melenk, J. M. International Journal for Numerical Methods in Engineering, Vol. 40, Issue 4 https://doi.org/10.1002/(SICI)1097-0207(19970228)40:4%3C727::AID-NME86%3E3.0.CO;2-N	journal	February 1997
Recursive Gauss integration Pieper, Wilhelm M. Communications in Numerical Methods in Engineering, Vol. 15, Issue 2 https://doi.org/10.1002/(SICI)1099-0887(199902)15:2%3C77::AID-CNM223%3E3.0.CO;2-J	journal	February 1999
The Pseudopotential Approximation in Electronic Structure Theory Schwerdtfeger, Peter ChemPhysChem, Vol. 12, Issue 17 https://doi.org/10.1002/cphc.201100387	journal	August 2011
Classical and enriched finite element formulations for Bloch-periodic boundary conditions Sukumar, N.; Pask, J. E. International Journal for Numerical Methods in Engineering, Vol. 77, Issue 8 https://doi.org/10.1002/nme.2457	journal	February 2009
Efficient adaptive integration of functions with sharp gradients and cusps in n-dimensional parallelepipeds: EFFICIENT INTEGRATION OF FUNCTIONS WITH SHARP GRADIENTS AND CUSPS Mousavi, S. E.; Pask, J. E.; Sukumar, N. International Journal for Numerical Methods in Engineering, Vol. 91, Issue 4 https://doi.org/10.1002/nme.4267	journal	June 2012
On the adaptive finite element analysis of the Kohn-Sham equations: methods, algorithms, and implementation: On the adaptive finite element analysis of the Kohn-Sham equations: methods, algorithms, and implementation Davydov, Denis; Young, Toby D.; Steinmann, Paul International Journal for Numerical Methods in Engineering, Vol. 106, Issue 11 https://doi.org/10.1002/nme.5140	journal	November 2015
Quantum-mechanical condensed matter simulations with CRYSTAL Dovesi, Roberto; Erba, Alessandro; Orlando, Roberto Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 8, Issue 4 https://doi.org/10.1002/wcms.1360	journal	March 2018
A Comparative Study on Methods for Convergence Acceleration of Iterative Vector Sequences Eyert, V. Journal of Computational Physics, Vol. 124, Issue 2 https://doi.org/10.1006/jcph.1996.0059	journal	March 1996
Stable enrichment and local preconditioning in the particle-partition of unity method Schweitzer, Marc Alexander Numerische Mathematik, Vol. 118, Issue 1 https://doi.org/10.1007/s00211-010-0323-6	journal	July 2010
Finite-element methods in electronic-structure theory Pask, J. E.; Klein, B. M.; Sterne, P. A. Computer Physics Communications, Vol. 135, Issue 1 https://doi.org/10.1016/S0010-4655(00)00212-5	journal	March 2001
Electronic structure calculations of solids using the WIEN2k package for material sciences Schwarz, K.; Blaha, P.; Madsen, G. K. H. Computer Physics Communications, Vol. 147, Issue 1-2 https://doi.org/10.1016/S0010-4655(02)00206-0	journal	August 2002
FP-LAPW and pseudopotential calculations of the structural phase transformations of GaN under high-pressure Abu-Jafar, M.; Al-Sharif, A. I.; Qteish, A. Solid State Communications, Vol. 116, Issue 7 https://doi.org/10.1016/S0038-1098(00)00336-7	journal	October 2000
An alternative way of linearizing the augmented plane-wave method Sjöstedt, E.; Nordström, L.; Singh, D. J. Solid State Communications, Vol. 114, Issue 1 https://doi.org/10.1016/S0038-1098(99)00577-3	journal	March 2000
The partition of unity finite element method: Basic theory and applications Melenk, J. M.; Babuška, I. Computer Methods in Applied Mechanics and Engineering, Vol. 139, Issue 1-4 https://doi.org/10.1016/S0045-7825(96)01087-0	journal	December 1996
Stable Generalized Finite Element Method (SGFEM) Babuška, I.; Banerjee, U. Computer Methods in Applied Mechanics and Engineering, Vol. 201-204 https://doi.org/10.1016/j.cma.2011.09.012	journal	January 2012
A stable and optimally convergent generalized FEM (SGFEM) for linear elastic fracture mechanics Gupta, V.; Duarte, C. A.; Babuška, I. Computer Methods in Applied Mechanics and Engineering, Vol. 266 https://doi.org/10.1016/j.cma.2013.07.010	journal	November 2013
The Orthonormalized Generalized Finite Element Method–OGFEM: Efficient and stable reduction of approximation errors through multiple orthonormalized enriched basis functions Sillem, A.; Simone, A.; Sluys, L. J. Computer Methods in Applied Mechanics and Engineering, Vol. 287 https://doi.org/10.1016/j.cma.2014.11.043	journal	April 2015
Orbital-enriched flat-top partition of unity method for the Schrödinger eigenproblem Albrecht, Clelia; Klaar, Constanze; Pask, John Ernest Computer Methods in Applied Mechanics and Engineering, Vol. 342 https://doi.org/10.1016/j.cma.2018.07.042	journal	December 2018
First-principles calculations of pressure-induced phase transformation in AlN and GaN Xiao, H. Y.; Jiang, X. D.; Duan, G. Computational Materials Science, Vol. 48, Issue 4 https://doi.org/10.1016/j.commatsci.2010.03.028	journal	June 2010
Ab initio molecular simulations with numeric atom-centered orbitals Blum, Volker; Gehrke, Ralf; Hanke, Felix Computer Physics Communications, Vol. 180, Issue 11 https://doi.org/10.1016/j.cpc.2009.06.022	journal	November 2009
NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations Valiev, M.; Bylaska, E. J.; Govind, N. Computer Physics Communications, Vol. 181, Issue 9, p. 1477-1489 https://doi.org/10.1016/j.cpc.2010.04.018	journal	September 2010
dftatom: A robust and general Schrödinger and Dirac solver for atomic structure calculations Čertík, Ondřej; Pask, John E.; Vackář, Jiří Computer Physics Communications, Vol. 184, Issue 7 https://doi.org/10.1016/j.cpc.2013.02.014	journal	July 2013
DFT-FE – A massively parallel adaptive finite-element code for large-scale density functional theory calculations Motamarri, Phani; Das, Sambit; Rudraraju, Shiva Computer Physics Communications, Vol. 246 https://doi.org/10.1016/j.cpc.2019.07.016	journal	January 2020
Partition of unity finite element method for quantum mechanical materials calculations Pask, J. E.; Sukumar, N. Extreme Mechanics Letters, Vol. 11 https://doi.org/10.1016/j.eml.2016.11.003	journal	February 2017
Self-consistent-field calculations using Chebyshev-filtered subspace iteration Zhou, Yunkai; Saad, Yousef; Tiago, Murilo L. Journal of Computational Physics, Vol. 219, Issue 1 https://doi.org/10.1016/j.jcp.2006.03.017	journal	November 2006
A Kohn–Sham equation solver based on hexahedral finite elements Fang, Jun; Gao, Xingyu; Zhou, Aihui Journal of Computational Physics, Vol. 231, Issue 8 https://doi.org/10.1016/j.jcp.2011.12.043	journal	April 2012
An h-adaptive finite element solver for the calculations of the electronic structures Bao, Gang; Hu, Guanghui; Liu, Di Journal of Computational Physics, Vol. 231, Issue 14 https://doi.org/10.1016/j.jcp.2012.04.002	journal	May 2012
Higher-order adaptive finite-element methods for orbital-free density functional theory Motamarri, Phani; Iyer, Mrinal; Knap, Jaroslaw Journal of Computational Physics, Vol. 231, Issue 20 https://doi.org/10.1016/j.jcp.2012.04.036	journal	August 2012
All-electron Kohn–Sham density functional theory on hierarchic finite element spaces Schauer, Volker; Linder, Christian Journal of Computational Physics, Vol. 250 https://doi.org/10.1016/j.jcp.2013.04.020	journal	October 2013
Higher-order adaptive finite-element methods for Kohn–Sham density functional theory Motamarri, P.; Nowak, M. R.; Leiter, K. Journal of Computational Physics, Vol. 253 https://doi.org/10.1016/j.jcp.2013.06.042	journal	November 2013
Hybrid preconditioning for iterative diagonalization of ill-conditioned generalized eigenvalue problems in electronic structure calculations Cai, Yunfeng; Bai, Zhaojun; Pask, John E. Journal of Computational Physics, Vol. 255 https://doi.org/10.1016/j.jcp.2013.07.020	journal	December 2013
Non-periodic finite-element formulation of Kohn–Sham density functional theory Suryanarayana, Phanish; Gavini, Vikram; Blesgen, Thomas Journal of the Mechanics and Physics of Solids, Vol. 58, Issue 2 https://doi.org/10.1016/j.jmps.2009.10.002	journal	February 2010
Energetic, electronic and structural DFT analysis of point defects in refractory BCC metals Fernández-Pello, D.; Fernández-Díaz, J. M.; Cerdeira, M. A. Materials Today Communications, Vol. 24 https://doi.org/10.1016/j.mtcomm.2020.101323	journal	September 2020
Finite element method for solving Kohn–Sham equations based on self-adaptive tetrahedral mesh Zhang, Dier; Shen, Lihua; Zhou, Aihui Physics Letters A, Vol. 372, Issue 30 https://doi.org/10.1016/j.physleta.2008.05.075	journal	July 2008
Electronic Structure Martin, Richard M. https://doi.org/10.1017/CBO9780511805769	book	January 2004
New Basis Set Exchange: An Open, Up-to-Date Resource for the Molecular Sciences Community Pritchard, Benjamin P.; Altarawy, Doaa; Didier, Brett Journal of Chemical Information and Modeling, Vol. 59, Issue 11 https://doi.org/10.1021/acs.jcim.9b00725	journal	October 2019
GW100: Comparison of Methods and Accuracy of Results Obtained with the WEST Code Govoni, Marco; Galli, Giulia Journal of Chemical Theory and Computation, Vol. 14, Issue 4 https://doi.org/10.1021/acs.jctc.7b00952	journal	February 2018
How Large is the Elephant in the Density Functional Theory Room? Jensen, Frank The Journal of Physical Chemistry A, Vol. 121, Issue 32 https://doi.org/10.1021/acs.jpca.7b04760	journal	August 2017
Density Functional Theory and the Basis Set Truncation Problem with Correlation Consistent Basis Sets: Elephant in the Room or Mouse in the Closet? Feller, David; Dixon, David A. The Journal of Physical Chemistry A, Vol. 122, Issue 9 https://doi.org/10.1021/acs.jpca.8b00392	journal	February 2018
The Elephant in the Room of Density Functional Theory Calculations Jensen, Stig Rune; Saha, Santanu; Flores-Livas, José A. The Journal of Physical Chemistry Letters, Vol. 8, Issue 7 https://doi.org/10.1021/acs.jpclett.7b00255	journal	March 2017
Adaptive Finite Element Method for Solving the Exact Kohn−Sham Equation of Density Functional Theory Bylaska, Eric J.; Holst, Michael; Weare, John H. Journal of Chemical Theory and Computation, Vol. 5, Issue 4 https://doi.org/10.1021/ct800350j	journal	March 2009
Exact exchange-correlation potentials from ground-state electron densities Kanungo, Bikash; Zimmerman, Paul M.; Gavini, Vikram Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-12467-0	journal	October 2019
A black-box self-consistent field convergence algorithm: One step closer Kudin, Konstantin N.; Scuseria, Gustavo E.; Cancès, Eric The Journal of Chemical Physics, Vol. 116, Issue 19 https://doi.org/10.1063/1.1470195	journal	January 2002
All-electron density functional theory and time-dependent density functional theory with high-order finite elements Lehtovaara, Lauri; Havu, Ville; Puska, Martti The Journal of Chemical Physics, Vol. 131, Issue 5 https://doi.org/10.1063/1.3176508	journal	January 2009
A divide and conquer real space finite-element Hartree–Fock method Alizadegan, R.; Hsia, K. J.; Martinez, T. J. The Journal of Chemical Physics, Vol. 132, Issue 3 https://doi.org/10.1063/1.3290949	journal	January 2010
The pseudopotential-density functional method applied to nanostructures Chelikowsky, James R. Journal of Physics D: Applied Physics, Vol. 33, Issue 8 https://doi.org/10.1088/0022-3727/33/8/201	journal	March 2000
Use of energy derivative of the radial solution in an augmented plane wave method: application to copper Koelling, D. D.; Arbman, G. O. Journal of Physics F: Metal Physics, Vol. 5, Issue 11 https://doi.org/10.1088/0305-4608/5/11/016	journal	November 1975
exciting: a full-potential all-electron package implementing density-functional theory and many-body perturbation theory Gulans, Andris; Kontur, Stefan; Meisenbichler, Christian Journal of Physics: Condensed Matter, Vol. 26, Issue 36 https://doi.org/10.1088/0953-8984/26/36/363202	journal	August 2014
Finite element methods in ab initio electronic structure calculations Pask, J. E.; Sterne, P. A. Modelling and Simulation in Materials Science and Engineering, Vol. 13, Issue 3 https://doi.org/10.1088/0965-0393/13/3/R01	journal	April 2005
A class of methods for solving nonlinear simultaneous equations Broyden, C. G. Mathematics of Computation, Vol. 19, Issue 92 https://doi.org/10.1090/S0025-5718-1965-0198670-6	journal	January 1965
Inhomogeneous Electron Gas Hohenberg, P.; Kohn, W. Physical Review, Vol. 136, Issue 3B, p. B864-B871 https://doi.org/10.1103/PhysRev.136.B864	journal	November 1964
Self-Consistent Equations Including Exchange and Correlation Effects Kohn, W.; Sham, L. J. Physical Review, Vol. 140, Issue 4A, p. A1133-A1138 https://doi.org/10.1103/PhysRev.140.A1133	journal	November 1965
*Ab initio* pseudopotential and density-functional all-electron study of ionization and excitation energies of actinide atoms Liu, Wenjian; Küchle, Wolfgang; Dolg, Michael Physical Review A, Vol. 58, Issue 2 https://doi.org/10.1103/PhysRevA.58.1103	journal	August 1998
Real time time-dependent density functional theory using higher order finite-element methods Kanungo, Bikash; Gavini, Vikram Physical Review B, Vol. 100, Issue 11 https://doi.org/10.1103/PhysRevB.100.115148	journal	September 2019
Linear methods in band theory Andersen, O. Krogh Physical Review B, Vol. 12, Issue 8 https://doi.org/10.1103/PhysRevB.12.3060	journal	October 1975
Special points for Brillouin-zone integrations Monkhorst, Hendrik J.; Pack, James D. Physical Review B, Vol. 13, Issue 12, p. 5188-5192 https://doi.org/10.1103/PhysRevB.13.5188	journal	June 1976
Self-interaction correction to density-functional approximations for many-electron systems Perdew, J. P.; Zunger, Alex Physical Review B, Vol. 23, Issue 10, p. 5048-5079 https://doi.org/10.1103/PhysRevB.23.5048	journal	May 1981
Full-potential self-consistent linearized-augmented-plane-wave method for calculating the electronic structure of molecules and surfaces: O 2 molecule Wimmer, E.; Krakauer, H.; Weinert, M. Physical Review B, Vol. 24, Issue 2 https://doi.org/10.1103/PhysRevB.24.864	journal	July 1981
Pseudopotentials that work: From H to Pu Bachelet, G. B.; Hamann, D. R.; Schlüter, M. Physical Review B, Vol. 26, Issue 8 https://doi.org/10.1103/PhysRevB.26.4199	journal	October 1982
Total-energy all-electron density functional method for bulk solids and surfaces Weinert, M.; Wimmer, E.; Freeman, A. J. Physical Review B, Vol. 26, Issue 8 https://doi.org/10.1103/PhysRevB.26.4571	journal	October 1982
Finite-element method for electronic structure White, Steven R.; Wilkins, John W.; Teter, Michael P. Physical Review B, Vol. 39, Issue 9 https://doi.org/10.1103/PhysRevB.39.5819	journal	March 1989
Ground-state properties of lanthanum: Treatment of extended-core states Singh, David Physical Review B, Vol. 43, Issue 8 https://doi.org/10.1103/PhysRevB.43.6388	journal	March 1991
Adaptive finite-element method for electronic-structure calculations Tsuchida, Eiji; Tsukada, Masaru Physical Review B, Vol. 54, Issue 11 https://doi.org/10.1103/PhysRevB.54.7602	journal	September 1996
Real-space local polynomial basis for solid-state electronic-structure calculations: A finite-element approach Pask, J. E.; Klein, B. M.; Fong, C. Y. Physical Review B, Vol. 59, Issue 19 https://doi.org/10.1103/PhysRevB.59.12352	journal	May 1999
Efficient linearization of the augmented plane-wave method Madsen, Georg K. H.; Blaha, Peter; Schwarz, Karlheinz Physical Review B, Vol. 64, Issue 19 https://doi.org/10.1103/PhysRevB.64.195134	journal	October 2001
Gaussian finite-element mixed-basis method for electronic structure calculations Yamakawa, Shunsuke; Hyodo, Shi-aki Physical Review B, Vol. 71, Issue 3 https://doi.org/10.1103/PhysRevB.71.035113	journal	January 2005
Taming multiple valency with density functionals: A case study of defective ceria Fabris, Stefano; de Gironcoli, Stefano; Baroni, Stefano Physical Review B, Vol. 71, Issue 4 https://doi.org/10.1103/PhysRevB.71.041102	journal	January 2005
Comment on “Taming multiple valency with density functionals: A case study of defective ceria” Kresse, Georg; Blaha, Peter; Da Silva, Juarez L. F. Physical Review B, Vol. 72, Issue 23 https://doi.org/10.1103/PhysRevB.72.237101	journal	December 2005
B 1 -to- B 8 structural phase transition in MnO under pressure: Comparison of all-electron and pseudopotential approaches Kolorenč, Jindřich; Mitas, Lubos Physical Review B, Vol. 75, Issue 23 https://doi.org/10.1103/PhysRevB.75.235118	journal	June 2007
Optimized norm-conserving Vanderbilt pseudopotentials Hamann, D. R. Physical Review B, Vol. 88, Issue 8 https://doi.org/10.1103/PhysRevB.88.085117	journal	August 2013
Subquadratic-scaling subspace projection method for large-scale Kohn-Sham density functional theory calculations using spectral finite-element discretization Motamarri, Phani; Gavini, Vikram Physical Review B, Vol. 90, Issue 11 https://doi.org/10.1103/PhysRevB.90.115127	journal	September 2014
Real-space formulation of orbital-free density functional theory using finite-element discretization: The case for Al, Mg, and Al-Mg intermetallics Das, Sambit; Iyer, Mrinal; Gavini, Vikram Physical Review B, Vol. 92, Issue 1 https://doi.org/10.1103/PhysRevB.92.014104	journal	July 2015
Spectrum-splitting approach for Fermi-operator expansion in all-electron Kohn-Sham DFT calculations Motamarri, Phani; Gavini, Vikram; Bhattacharya, Kaushik Physical Review B, Vol. 95, Issue 3 https://doi.org/10.1103/PhysRevB.95.035111	journal	January 2017
Large-scale all-electron density functional theory calculations using an enriched finite-element basis Kanungo, Bikash; Gavini, Vikram Physical Review B, Vol. 95, Issue 3 https://doi.org/10.1103/PhysRevB.95.035112	journal	January 2017
Configurational forces in electronic structure calculations using Kohn-Sham density functional theory Motamarri, Phani; Gavini, Vikram Physical Review B, Vol. 97, Issue 16 https://doi.org/10.1103/PhysRevB.97.165132	journal	April 2018
Computational method for general multicenter electronic structure calculations Batcho, P. F. Physical Review E, Vol. 61, Issue 6 https://doi.org/10.1103/PhysRevE.61.7169	journal	June 2000
Parallel self-consistent-field calculations via Chebyshev-filtered subspace acceleration Zhou, Yunkai; Saad, Yousef; Tiago, Murilo L. Physical Review E, Vol. 74, Issue 6 https://doi.org/10.1103/PhysRevE.74.066704	journal	December 2006
Influence of the Core-Valence Interaction and of the Pseudopotential Approximation on the Electron Self-Energy in Semiconductors Gómez-Abal, Ricardo; Li, Xinzheng; Scheffler, Matthias Physical Review Letters, Vol. 101, Issue 10 https://doi.org/10.1103/PhysRevLett.101.106404	journal	September 2008
Norm-Conserving Pseudopotentials Hamann, D. R.; Schlüter, M.; Chiang, C. Physical Review Letters, Vol. 43, Issue 20 https://doi.org/10.1103/PhysRevLett.43.1494	journal	November 1979
Ground State of the Electron Gas by a Stochastic Method Ceperley, D. M.; Alder, B. J. Physical Review Letters, Vol. 45, Issue 7, p. 566-569 https://doi.org/10.1103/PhysRevLett.45.566	journal	August 1980
All-electron density functional calculations for electron and nuclear spin interactions in molecules and solids Ghosh, Krishnendu; Ma, He; Gavini, Vikram Physical Review Materials, Vol. 3, Issue 4 https://doi.org/10.1103/PhysRevMaterials.3.043801	journal	April 2019
Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients Payne, M. C.; Teter, M. P.; Allan, D. C. Reviews of Modern Physics, Vol. 64, Issue 4 https://doi.org/10.1103/RevModPhys.64.1045	journal	October 1992
Large-Scale Electronic-Structure Calculations Based on the Adaptive Finite-Element Method Tsuchida, Eiji; Tsukada, Masaru Journal of the Physical Society of Japan, Vol. 67, Issue 11 https://doi.org/10.1143/JPSJ.67.3844	journal	November 1998
An adaptive algorithm for the approximate calculation of multiple integrals Berntsen, Jarle; Espelid, Terje O.; Genz, Alan ACM Transactions on Mathematical Software, Vol. 17, Issue 4 https://doi.org/10.1145/210232.210233	journal	December 1991
Iterative Procedures for Nonlinear Integral Equations Anderson, Donald G. Journal of the ACM, Vol. 12, Issue 4 https://doi.org/10.1145/321296.321305	journal	October 1965
Linear scaling solution of the all-electron Coulomb problem in solids Sukumar, N. International Journal for Multiscale Computational Engineering https://doi.org/10.1615/IntJMultCompEng.2011002201	journal	January 2011

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