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fmm3dbie

FMM-accelerated boundary integral equation solvers

Currently supports high-order triangulations and quadrilaterizations of smooth surfaces

This repository has an external dependency - FMM3D

The package along with the dependency can be obtained by

git clone --recurse-submodules https://github.com/fastalgorithms/fmm3dbie.git

Make sure you have the shared object for the FMM library installed and located in an appropriate location (/usr/local/lib on MacOSX, and environment variable of LD_LIBRARY_PATH set to location of libfmm3d.so on linux machines)

Please see the online documentation.

fmm3dbie team

  • Travis Askham
  • Leslie Greengard
  • Jeremy Hoskins
  • Libin Lu
  • Mike O'Neil
  • Manas Rachh
  • Felipe Vico
  • Vladimir Rokhlin

James Bremer provided generalized Gaussian quadrature rules (src/quadratures/ggq-self-quadrouts.f, src/quadratures/ggq-selfquad.f, and all files in src/quadratures/ggq-self-quads/).

Zydrunas Gimbutas provided the high order quadrature rules for integrating smooth functions src/tria_routs/triasymq.f, src/tria_routs/koorn-uvs-dat.txt, src/tria_routs/koorn-wts-dat.txt, and, src/quad_routs/squarearbq.f; and also provided src/common/dotcross3d.f

References

If you find fmm3dbie useful in your work, please cite this repository, our paper and the papers associated with quadrature contributions by James Bremer and Zydrunas Gimbutas:

  • Greengard, L., O'Neil, M., Rachh, M., & Vico, F. (2021). Fast multipole methods for the evaluation of layer potentials with locally-corrected quadratures. Journal of Computational Physics: X, 10, 100092.

  • Bremer, J., & Gimbutas, Z. (2013). On the numerical evaluation of the singular integrals of scattering theory. Journal of Computational Physics, 251, 327-343.

  • Xiao, H., & Gimbutas, Z. (2010). A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions. Computers & mathematics with applications, 59(2), 663-676.

Funding

Funded in part by the Office of Naval Research under Awards #N00014-17-1-2059, #N00014-17-1-2451, and #N00014-18-1-2307, and the Simons Foundation/SFARI (560651, AB).