Applications

Applications of Multipole Methods

Here is an incomplete collection of some representative applications.

Heat Equation

  • J. Strain. Fast adaptive methods for the free-space heat equation. SIAM J. Sci. Comput. 15:185-206, 1994
  • L. Greengard and J. Strain. A fast algorithm for the evaluation of heat potentials. Comm. Pure Appl. Math. 43:949-963, 1990
  • L. Greengard and P. Lin. Spectral approximation of the free-space heat kernel. Appl. Comput. Harmon. Anal. 9:83-97, 2000
  • S. K. Veerapaneni and G. Biros. A fast high-order integral equation solver for the heat equation with moving boundaries in 1D. SIAM J. Sci. Comput. 29:2581-2606, 2007

Wave Equation

  • A. Ergin, B. Shanker, and E. Michielssen. Fast evaluation of three-dimensional transient wave fields using diagonal translation operators. J. Comput. Phys. 146:157-180, 1998
  • A. Ergin, B. Shanker, and E. Michielssen. The plane-wave time-domain algorithm for the fast analysis of transient wave phenomena. IEEE Antennas Propag. Mag. 41:39-52, 1999
  • A. Ergin, B. Shanker, and E. Michielssen. Fast transient analysis of acoustic wave scattering from rigid bodies using a two-level plane wave time domain algorithm. J. Acoust. Soc. Am. 106:2405-2416, 1999
  • A. Ergin, B. Shanker, and E. Michielssen. Fast analysis of transient acoustic wave scattering from rigid bodies using a multilevel plane wave time domain algorithm. J. Acoust. Soc. Am. 107:1168-1178, 2000

Stokes Equation

  • L. Greengard, M. C. Kropinski, and A. Mayo. Integral equation methods for Stokes flow and isotropic elasticity in the plane. J. Comput. Phys. 125:403-414, 1996
  • L. Greengard and M. C. Kropinski. An integral equation approach to the incompressible Navier-Stokes equations in two dimensions. SIAM J. Sci. Comput. 20:318-336, 1998
  • G. Biros, L. Ying, and D. Zorin. A fast solver for the Stokes equations with distributed forces in complex geometries. J. Comput. Phys. 193:317-348, 2004
  • L. Greengard and M. C. Kropinski. Integral equation methods for Stokes flow in doubly-periodic domains. J. Engrg. Math. 48:157-170, 2004

Linear Elasticity

Linearized Poisson-Boltzmann Equation

  • A.H. Boschitsch, M.O. Fenley, and H.X. Zhou. Fast Boundary Element Method for the Linear Poisson-Boltzmann Equation. J. Phys. Chem. B, 106:2741-2754, 2002
  • B. Lu, X. Cheng, J. Huang, and J. A. McCammon. Order N algorithm for computation of electrostatic interactions in biomolecular systems. PNAS, 2006
  • S. S. Kuo, M. D. Altman, J. P. Bardhan, B. Tidor, and J. White. Fast methods for simulation of biomolecule electrostatics, ICCAD, 2002.

Dislocation Dynamics

  • D. Zhao, J. Huang, and Y. Xiang. A new version fast multipole method for evaluating the stress field of dislocation ensembles. DOI: 10.1088/0965-0393/18/4/045006

Time Domain Maxwell Equations

Elastic Wave Propagations

  • T. Saitoh, S. Hirose, and T. Fukuil. Application of Fast Multipole Boundary Element Method to Multiple Scattering Analysis of Acoustic and Elastic Waves. AIP Conf. Proc., 894:79, 2007

Lippmann-Schwinger equation

  • Y. Chen. Direct algorithm for the Lippmann-Schwinger integral equation in two dimensions. Modeling and computation in optics and electromagnetics. Adv. Comput. Math. 16:175-190, 2002

Nonreflecting Boundary Conditions

  • B. Alpert, L. Greengard, and T. Hagstrom. Rapid evaluation of nonreflecting boundary kernels for time-domain wave propagation. SIAM J. Numer. Anal. 37:1138-1164, 2000
  • B. Alpert, L. Greengard, and T. Hagstrom. Nonreflecting boundary conditions for the time-dependent wave equation. J. Comput. Phys. 180:270-296, 2002

Applications of DASHMM

This section will showcase some results and applications from end users.