An O(N) and parallel approach to integral problems by a kernel-independent fast multipole method: Application to polarization and magnetization of interacting particles

Jiang, Xikai; Li, Jiyuan; Zhao, Xujun; Qin, Jian; Karpeev, Dmitry; Hernandez-Ortiz, Juan; de Pablo, Juan J.; Heinonen, Olle

doi:10.1063/1.4960436

An O(N) and parallel approach to integral problems by a kernel-independent fast multipole method: Application to polarization and magnetization of interacting particles

Journal Article · Wed Aug 10 04:00:00 EDT 2016 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4960436· OSTI ID:1339573

Jiang, Xikai ^[1]; Li, Jiyuan ^[2]; ^[3]; Qin, Jian ^[4]; Karpeev, Dmitry ^[5]; Hernandez-Ortiz, Juan ^[6]; de Pablo, Juan J. ^[7]; ^[8]

Argonne National Lab. (ANL),Lemont, IL (United States)
Univ. of Chicago, Chicago, IL (United States)
Argonne National Lab. (ANL), Lemont, IL (United States)
Stanford Univ., Stanford, CA (United States)
Argonne National Lab. (ANL), Lemont, IL (United States); Univ. of Chicago, Chicago, IL (United States); KCG Holdings, Inc. (United States)
Univ. of Chicago, Chicago, IL (United States); Univ. Nacional de Colombia-Medellin, Medellin (Columbia)
Argonne National Lab. (ANL),Lemont, IL (United States); Univ. of Chicago, Chicago, IL (United States)
Argonne National Lab. (ANL),Lemont, IL (United States); Northwestern-Argonne Institute for Science and Engineering, Evanston, IL (United States)

Large classes of materials systems in physics and engineering are governed by magnetic and electrostatic interactions. Continuum or mesoscale descriptions of such systems can be cast in terms of integral equations, whose direct computational evaluation requires O(N²) operations, where N is the number of unknowns. Such a scaling, which arises from the many-body nature of the relevant Green's function, has precluded wide-spread adoption of integral methods for solution of large-scale scientific and engineering problems. In this work, a parallel computational approach is presented that relies on using scalable open source libraries and utilizes a kernel-independent Fast Multipole Method (FMM) to evaluate the integrals in O(N) operations, with O(N) memory cost, thereby substantially improving the scalability and efficiency of computational integral methods. We demonstrate the accuracy, efficiency, and scalability of our approach in the context of two examples. In the first, we solve a boundary value problem for a ferroelectric/ferromagnetic volume in free space. In the second, we solve an electrostatic problem involving polarizable dielectric bodies in an unbounded dielectric medium. Lastly, the results from these test cases show that our proposed parallel approach, which is built on a kernel-independent FMM, can enable highly efficient and accurate simulations and allow for considerable flexibility in a broad range of applications.

View Accepted Manuscript (DOE)

Research Organization:: Argonne National Lab. (ANL), Argonne, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22) - Materials Sciences and Engineering Division

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1339573

Alternate ID(s):: OSTI ID: 1420630

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 6 Vol. 145; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (50)

Singular integral operators on Riemann surfaces and elliptic differential systems Rodin, Yu. L. The Journal of Geometric Analysis, Vol. 8, Issue 4 https://doi.org/10.1007/bf02921715	journal	July 1998
A fast solution method for three-dimensional many-particle problems of linear elasticity Fu, Yuhong; Klimkowski, Kenneth J.; Rodin, Gregory J. International Journal for Numerical Methods in Engineering, Vol. 42, Issue 7 https://doi.org/10.1002/(SICI)1097-0207(19980815)42:7<1215::AID-NME406>3.0.CO;2-5	journal	August 1998
The fast multipole boundary element method for molecular electrostatics: An optimal approach for large systems Bharadwaj, Ranganathan; Windemuth, Andreas; Sridharan, S. Journal of Computational Chemistry, Vol. 16, Issue 7 https://doi.org/10.1002/jcc.540160707	journal	July 1995
Spectral Approximation of the Free-Space Heat Kernel Greengard, Leslie; Lin, Patrick Applied and Computational Harmonic Analysis, Vol. 9, Issue 1 https://doi.org/10.1006/acha.2000.0310	journal	July 2000
Boundary Integral Methods for Multicomponent Fluids and Multiphase Materials Hou, T. Y.; Lowengrub, J. S.; Shelley, M. J. Journal of Computational Physics, Vol. 169, Issue 2 https://doi.org/10.1006/jcph.2000.6626	journal	May 2001
Geometrical Validity of Curvilinear Finite Elements Johnen, Amaury; Remacle, Jean-François; Geuzaine, Christophe Proceedings of the 20th International Meshing Roundtable https://doi.org/10.1007/978-3-642-24734-7_14	book	January 2011
A regularized boundary integral equation method for elastodynamic crack problems Nishimura, N.; Kobayashi, S. Computational Mechanics, Vol. 4, Issue 4 https://doi.org/10.1007/BF00301390	journal	January 1989
libMesh : a C++ library for parallel adaptive mesh refinement/coarsening simulations Kirk, Benjamin S.; Peterson, John W.; Stogner, Roy H. Engineering with Computers, Vol. 22, Issue 3-4 https://doi.org/10.1007/s00366-006-0049-3	journal	November 2006
Improving the specificity of organophosphorus hydrolase to acephate by mutagenesis at its binding site: a computational study Badakhshan, Reza; Mohammadi, Mozafar; Farnoosh, Gholamreza Journal of Molecular Modeling, Vol. 27, Issue 6 https://doi.org/10.1007/s00894-021-04749-6	journal	May 2021
A 10000 particle molecular dynamics model with long range forces Hockney, R. W.; Goel, S. P.; Eastwood, J. W. Chemical Physics Letters, Vol. 21, Issue 3 https://doi.org/10.1016/0009-2614(73)80315-X	journal	September 1973
Three-dimensional boundary integral simulations of motion and deformation of bubbles with viscous effects Zhang, A. M.; Ni, B. Y. Computers & Fluids, Vol. 92 https://doi.org/10.1016/j.compfluid.2013.12.020	journal	March 2014
Biomolecular electrostatics using a fast multipole BEM on up to 512 gpus and a billion unknowns Yokota, Rio; Bardhan, Jaydeep P.; Knepley, Matthew G. Computer Physics Communications, Vol. 182, Issue 6 https://doi.org/10.1016/j.cpc.2011.02.013	journal	June 2011
The fast multipole boundary element method for potential problems: A tutorial Liu, Y. J.; Nishimura, N. Engineering Analysis with Boundary Elements, Vol. 30, Issue 5 https://doi.org/10.1016/j.enganabound.2005.11.006	journal	May 2006
A theory of interactions between polarizable dielectric spheres Qin, Jian; Li, Jiyuan; Lee, Victor Journal of Colloid and Interface Science, Vol. 469 https://doi.org/10.1016/j.jcis.2016.02.033	journal	May 2016
The black-box fast multipole method Fong, William; Darve, Eric Journal of Computational Physics, Vol. 228, Issue 23 https://doi.org/10.1016/j.jcp.2009.08.031	journal	December 2009
Fast directional multilevel summation for oscillatory kernels based on Chebyshev interpolation Messner, Matthias; Schanz, Martin; Darve, Eric Journal of Computational Physics, Vol. 231, Issue 4 https://doi.org/10.1016/j.jcp.2011.09.027	journal	February 2012
Geometrical validity of curvilinear finite elements Johnen, A.; Remacle, J. -F.; Geuzaine, C. Journal of Computational Physics, Vol. 233 https://doi.org/10.1016/j.jcp.2012.08.051	journal	January 2013
Comparison of efficient techniques for the simulation of dielectric objects in electrolytes Gan, Zecheng; Wu, Huanxin; Barros, Kipton Journal of Computational Physics, Vol. 291 https://doi.org/10.1016/j.jcp.2015.03.019	journal	June 2015
Read and write processes, and head technology for perpendicular recording Gao, Kai Zhong; Heinonen, Olle; Chen, Yonghua Journal of Magnetism and Magnetic Materials, Vol. 321, Issue 6 https://doi.org/10.1016/j.jmmm.2008.05.025	journal	March 2009
Numerical methods for the stray-field calculation: A comparison of recently developed algorithms Abert, Claas; Exl, Lukas; Selke, Gunnar Journal of Magnetism and Magnetic Materials, Vol. 326 https://doi.org/10.1016/j.jmmm.2012.08.041	journal	January 2013
Boundary Integral Equation Methods for Solids and Fluids Bonnet, Marc Meccanica, Vol. 34, Issue 4, p. 301-302 https://doi.org/10.1023/A:1004795120236	journal	January 1999
Direct observation of particle interactions and clustering in charged granular streams Lee, Victor; Waitukaitis, Scott R.; Miskin, Marc Z. Nature Physics, Vol. 11, Issue 9 https://doi.org/10.1038/nphys3396	journal	July 2015
Electrostatic potential inside ionic solutions confined by dielectrics: a variational approach Allen, Rosalind; Hansen, Jean-Pierre; Melchionna, Simone Physical Chemistry Chemical Physics, Vol. 3, Issue 19 https://doi.org/10.1039/b105176h	journal	January 2001
Phase diagram of complex fluids using an efficient integral equation method Charpentier, I.; Jakse, N. The Journal of Chemical Physics, Vol. 123, Issue 20 https://doi.org/10.1063/1.2117010	journal	November 2005
Compression of boundary element matrix in micromagnetic simulations Knittel, A.; Franchin, M.; Bordignon, G. Journal of Applied Physics, Vol. 105, Issue 7 https://doi.org/10.1063/1.3072032	journal	April 2009
An iterative, fast, linear-scaling method for computing induced charges on arbitrary dielectric boundaries Tyagi, Sandeep; Süzen, Mehmet; Sega, Marcello The Journal of Chemical Physics, Vol. 132, Issue 15 https://doi.org/10.1063/1.3376011	journal	April 2010
Demagnetizing factors for rectangular ferromagnetic prisms Aharoni, Amikam Journal of Applied Physics, Vol. 83, Issue 6 https://doi.org/10.1063/1.367113	journal	March 1998
Particle mesh Ewald: An N ⋅log( N ) method for Ewald sums in large systems Darden, Tom; York, Darrin; Pedersen, Lee The Journal of Chemical Physics, Vol. 98, Issue 12 https://doi.org/10.1063/1.464397	journal	June 1993
Efficient and accurate simulation of dynamic dielectric objects Barros, Kipton; Sinkovits, Daniel; Luijten, Erik The Journal of Chemical Physics, Vol. 140, Issue 6 https://doi.org/10.1063/1.4863451	journal	February 2014
Order N algorithm for computation of electrostatic interactions in biomolecular systems Lu, B.; Cheng, X.; Huang, J. Proceedings of the National Academy of Sciences, Vol. 103, Issue 51 https://doi.org/10.1073/pnas.0605166103	journal	December 2006
The finite element method with penalty Babuška, Ivo Mathematics of Computation, Vol. 27, Issue 122 https://doi.org/10.1090/S0025-5718-1973-0351118-5	journal	May 1973
Magnetization reversal in circularly exchange-biased ferromagnetic disks Tanase, M.; Petford-Long, A. K.; Heinonen, O. Physical Review B, Vol. 79, Issue 1 https://doi.org/10.1103/PhysRevB.79.014436	journal	January 2009
Phase separation versus supersolid behavior in frustrated antiferromagnets Albuquerque, A. Fabricio; Laflorencie, Nicolas; Picon, Jean-David Physical Review B, Vol. 83, Issue 17 https://doi.org/10.1103/PhysRevB.83.174421	journal	May 2011
Computing induced charges in inhomogeneous dielectric media: Application in a Monte Carlo simulation of complex ionic systems Boda, Dezsö; Gillespie, Dirk; Nonner, Wolfgang Physical Review E, Vol. 69, Issue 4 https://doi.org/10.1103/PhysRevE.69.046702	journal	April 2004
Comparison of three-dimensional Poisson solution methods for particle-based simulation and inhomogeneous dielectrics Berti, Claudio; Gillespie, Dirk; Bardhan, Jaydeep P. Physical Review E, Vol. 86, Issue 1 https://doi.org/10.1103/PhysRevE.86.011912	journal	July 2012
Comparison of scalable fast methods for long-range interactions Arnold, Axel; Fahrenberger, Florian; Holm, Christian Physical Review E, Vol. 88, Issue 6 https://doi.org/10.1103/PhysRevE.88.063308	journal	December 2013
Direct Observation of Unconventional Topological Spin Structure in Coupled Magnetic Discs Phatak, C.; Petford-Long, A. K.; Heinonen, O. Physical Review Letters, Vol. 108, Issue 6 https://doi.org/10.1103/PhysRevLett.108.067205	journal	February 2012
Dielectric Effects in the Self-Assembly of Binary Colloidal Aggregates Barros, Kipton; Luijten, Erik Physical Review Letters, Vol. 113, Issue 1 https://doi.org/10.1103/PhysRevLett.113.017801	journal	July 2014
Hybrid method for computing demagnetizing fields Fredkin, D. R.; Koehler, T. R. IEEE Transactions on Magnetics, Vol. 26, Issue 2 https://doi.org/10.1109/20.106342	journal	March 1990
Fast boundary methods for magnetostatic interactions in micromagnetics Forster, H.; Schrefl, T.; Fidler, J. Digests of INTERMAG 2003. International Magnetics Conference, Digest of INTERMAG 2003. International Magnetics Conference (Cat. No.03CH37401) https://doi.org/10.1109/INTMAG.2003.1230308	conference	January 2003
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems Saad, Youcef; Schultz, Martin H. SIAM Journal on Scientific and Statistical Computing, Vol. 7, Issue 3 https://doi.org/10.1137/0907058	journal	July 1986
Task-Based FMM for Multicore Architectures Agullo, Emmanuel; Bramas, Bérenger; Coulaud, Olivier SIAM Journal on Scientific Computing, Vol. 36, Issue 1 https://doi.org/10.1137/130915662	journal	January 2014
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs Karypis, George; Kumar, Vipin SIAM Journal on Scientific Computing, Vol. 20, Issue 1 https://doi.org/10.1137/S1064827595287997	journal	January 1998
Boundary Integral Methods for Multicomponent Fluids and Multiphase Materials J. S., Lowengrub,; M. J., Shelley,; T. Y., Hou, The University of North Carolina at Chapel Hill University Libraries https://doi.org/10.17615/9nwv-nv53	text	January 2001
Order N algorithm for computation of electrostatic interactions in biomolecular systems J., Huang,; X., Cheng,; A., McCammon, J. The University of North Carolina at Chapel Hill University Libraries https://doi.org/10.17615/y6as-qp12	text	January 2006
CUBIT Mesh Generation Environment. Volume 1: Users Manual Blacker, Ted D.; Bohnhoff, William J.; Edwards, Tony L. https://doi.org/10.2172/10176386	report	May 1994
The Finite Element Method with Penalty Babuska, Ivo Mathematics of Computation, Vol. 27, Issue 122 https://doi.org/10.2307/2005611	journal	April 1973
Biomolecular electrostatics using a fast multipole BEM on up to 512 GPUs and a billion unknowns Yokota, Rio; Bardhan, Jaydeep P.; Knepley, Matthew G. arXiv https://doi.org/10.48550/arxiv.1007.4591	text	January 2010
Numerical Methods for the Stray-Field Calculation: A Comparison of recently developed Algorithms Abert, Claas; Exl, Lukas; Selke, Gunnar arXiv https://doi.org/10.48550/arxiv.1204.4302	text	January 2012
Dielectric effects in the self-assembly of binary colloidal aggregates Barros, Kipton; Luijten, Erik arXiv https://doi.org/10.48550/arxiv.1406.1854	text	January 2014

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