An O( N) and parallel approach to integral problems by a kernelindependent fast multipole method: Application to polarization and magnetization of interacting particles
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( N ^{2}) operations, where N is the number of unknowns. Such a scaling, which arises from the manybody nature of the relevant Green's function, has precluded widespread adoption of integral methods for solution of largescale scientific and engineering problems. In this work, a parallel computational approach is presented that relies on using scalable open source libraries and utilizes a kernelindependent 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 kernelindependent FMM, can enable highly efficient and accuratemore »
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 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 ColombiaMedellin, 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); NorthwesternArgonne Institute for Science and Engineering, Evanston, IL (United States)
 Publication Date:
 Grant/Contract Number:
 AC0206CH11357
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Chemical Physics
 Additional Journal Information:
 Journal Volume: 145; Journal Issue: 6; Journal ID: ISSN 00219606
 Publisher:
 American Institute of Physics (AIP)
 Research Org:
 Argonne National Lab. (ANL), Argonne, IL (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22). Materials Sciences and Engineering Division; USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
 OSTI Identifier:
 1339573
 Alternate Identifier(s):
 OSTI ID: 1420630
Jiang, Xikai, Li, Jiyuan, Zhao, Xujun, Qin, Jian, Karpeev, Dmitry, HernandezOrtiz, Juan, de Pablo, Juan J., and Heinonen, Olle. An O(N) and parallel approach to integral problems by a kernelindependent fast multipole method: Application to polarization and magnetization of interacting particles. United States: N. p.,
Web. doi:10.1063/1.4960436.
Jiang, Xikai, Li, Jiyuan, Zhao, Xujun, Qin, Jian, Karpeev, Dmitry, HernandezOrtiz, Juan, de Pablo, Juan J., & Heinonen, Olle. An O(N) and parallel approach to integral problems by a kernelindependent fast multipole method: Application to polarization and magnetization of interacting particles. United States. doi:10.1063/1.4960436.
Jiang, Xikai, Li, Jiyuan, Zhao, Xujun, Qin, Jian, Karpeev, Dmitry, HernandezOrtiz, Juan, de Pablo, Juan J., and Heinonen, Olle. 2016.
"An O(N) and parallel approach to integral problems by a kernelindependent fast multipole method: Application to polarization and magnetization of interacting particles". United States.
doi:10.1063/1.4960436. https://www.osti.gov/servlets/purl/1339573.
@article{osti_1339573,
title = {An O(N) and parallel approach to integral problems by a kernelindependent fast multipole method: Application to polarization and magnetization of interacting particles},
author = {Jiang, Xikai and Li, Jiyuan and Zhao, Xujun and Qin, Jian and Karpeev, Dmitry and HernandezOrtiz, Juan and de Pablo, Juan J. and Heinonen, Olle},
abstractNote = {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 manybody nature of the relevant Green's function, has precluded widespread adoption of integral methods for solution of largescale scientific and engineering problems. In this work, a parallel computational approach is presented that relies on using scalable open source libraries and utilizes a kernelindependent 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 kernelindependent FMM, can enable highly efficient and accurate simulations and allow for considerable flexibility in a broad range of applications.},
doi = {10.1063/1.4960436},
journal = {Journal of Chemical Physics},
number = 6,
volume = 145,
place = {United States},
year = {2016},
month = {8}
}