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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)

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

References (49)

A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs journal January 1998
Biomolecular electrostatics using a fast multipole BEM on up to 512 gpus and a billion unknowns journal June 2011
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
An iterative, fast, linear-scaling method for computing induced charges on arbitrary dielectric boundaries journal April 2010
The black-box fast multipole method journal December 2009
Comparison of scalable fast methods for long-range interactions journal December 2013
Compression of boundary element matrix in micromagnetic simulations journal April 2009
Particle mesh Ewald: An N ⋅log( N ) method for Ewald sums in large systems journal June 1993
Hybrid method for computing demagnetizing fields journal March 1990
Comparison of efficient techniques for the simulation of dielectric objects in electrolytes journal June 2015
Boundary Integral Methods for Multicomponent Fluids and Multiphase Materials journal May 2001
A theory of interactions between polarizable dielectric spheres journal May 2016
A regularized boundary integral equation method for elastodynamic crack problems journal January 1989
The fast multipole boundary element method for potential problems: A tutorial journal May 2006
Read and write processes, and head technology for perpendicular recording journal March 2009
Direct observation of particle interactions and clustering in charged granular streams journal July 2015
Task-Based FMM for Multicore Architectures journal January 2014
Geometrical validity of curvilinear finite elements journal January 2013
libMesh : a C++ library for parallel adaptive mesh refinement/coarsening simulations journal November 2006
A fast solution method for three-dimensional many-particle problems of linear elasticity journal August 1998
Computing induced charges in inhomogeneous dielectric media: Application in a Monte Carlo simulation of complex ionic systems journal April 2004
Comparison of three-dimensional Poisson solution methods for particle-based simulation and inhomogeneous dielectrics journal July 2012
Magnetization reversal in circularly exchange-biased ferromagnetic disks journal January 2009
Phase separation versus supersolid behavior in frustrated antiferromagnets journal May 2011
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems journal July 1986
Efficient and accurate simulation of dynamic dielectric objects journal February 2014
Electrostatic potential inside ionic solutions confined by dielectrics: a variational approach journal January 2001
Fast directional multilevel summation for oscillatory kernels based on Chebyshev interpolation journal February 2012
The fast multipole boundary element method for molecular electrostatics: An optimal approach for large systems journal July 1995
Order N algorithm for computation of electrostatic interactions in biomolecular systems journal December 2006
A 10000 particle molecular dynamics model with long range forces journal September 1973
Spectral Approximation of the Free-Space Heat Kernel journal July 2000
Numerical methods for the stray-field calculation: A comparison of recently developed algorithms journal January 2013
Three-dimensional boundary integral simulations of motion and deformation of bubbles with viscous effects journal March 2014
Direct Observation of Unconventional Topological Spin Structure in Coupled Magnetic Discs journal February 2012
Phase diagram of complex fluids using an efficient integral equation method journal November 2005
Boundary Integral Equation Methods for Solids and Fluids journal January 1999
Dielectric Effects in the Self-Assembly of Binary Colloidal Aggregates journal July 2014
The finite element method with penalty journal May 1973
Demagnetizing factors for rectangular ferromagnetic prisms journal March 1998
Geometrical Validity of Curvilinear Finite Elements book January 2011
Improving the specificity of organophosphorus hydrolase to acephate by mutagenesis at its binding site: a computational study journal May 2021
The Finite Element Method with Penalty journal April 1973
Order N algorithm for computation of electrostatic interactions in biomolecular systems text January 2006
Boundary Integral Methods for Multicomponent Fluids and Multiphase Materials text January 2001
Biomolecular electrostatics using a fast multipole BEM on up to 512 GPUs and a billion unknowns text January 2010
Numerical Methods for the Stray-Field Calculation: A Comparison of recently developed Algorithms text January 2012
Dielectric effects in the self-assembly of binary colloidal aggregates text January 2014
Singular integral operators on Riemann surfaces and elliptic differential systems journal July 1998