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Title: 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 · · Journal of Chemical Physics
DOI: https://doi.org/10.1063/1.4960436 · OSTI ID:1339573
 [1];  [2]; ORCiD logo [3];  [4];  [5];  [6];  [7]; ORCiD logo [8]
  1. Argonne National Lab. (ANL),Lemont, IL (United States)
  2. Univ. of Chicago, Chicago, IL (United States)
  3. Argonne National Lab. (ANL), Lemont, IL (United States)
  4. Stanford Univ., Stanford, CA (United States)
  5. Argonne National Lab. (ANL), Lemont, IL (United States); Univ. of Chicago, Chicago, IL (United States); KCG Holdings, Inc. (United States)
  6. Univ. of Chicago, Chicago, IL (United States); Univ. Nacional de Colombia-Medellin, Medellin (Columbia)
  7. Argonne National Lab. (ANL),Lemont, IL (United States); Univ. of Chicago, Chicago, IL (United States)
  8. Argonne National Lab. (ANL),Lemont, IL (United States); Northwestern-Argonne Institute for Science and Engineering, Evanston, IL (United States)
+ Show Author Affiliations

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.

Research Organization:
Argonne National Laboratory (ANL), Argonne, IL (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences and Engineering Division; USDOE
Grant/Contract Number:
AC02-06CH11357
OSTI ID:
1339573
Alternate ID(s):
OSTI ID: 1420630
Journal Information:
Journal of Chemical Physics, Vol. 145, Issue 6; ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English

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