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FastBEAST

This package provides fast methods for boundary element simulations targeting BEAST.jl.

Installation

Installing FastBEAST is done by entering the package manager (enter ] at the julia REPL) and issuing:

pkg> add https://github.com/sbadrian/FastBEAST.jl.git

Overview

The following aspects are implemented (✔) and planned (⌛):

Available fast methods:
  • ✔ H-matrix
  • ✔ Kernel independent FMM based on ExaFMM-t
  • ⌛ H2-matrix
Available low-rank compression techniques:
  • ✔ Adaptive cross approximation
  • ⌛ Pseudo-skeleton approximation
  • ⌛ CUR matrix approximation

References

The implementation is based on

  • [1] Adelman, Ross, Nail A. Gumerov, and Ramani Duraiswami. “FMM/GPU-Accelerated Boundary Element Method for Computational Magnetics and Electrostatics.” IEEE Transactions on Magnetics 53, no. 12 (December 2017): 1–11. https://doi.org/10.1109/TMAG.2017.2725951.
  • [2] Bauer, M., M. Bebendorf, and B. Feist. “Kernel-Independent Adaptive Construction of $\mathcal {H}^2$-Matrix Approximations.” Numerische Mathematik 150, no. 1 (January 2022): 1–32. https://doi.org/10.1007/s00211-021-01255-y.
  • [3] Heldring, Alexander, Eduard Ubeda, and Juan M. Rius. “Improving the Accuracy of the Adaptive Cross Approximation with a Convergence Criterion Based on Random Sampling.” IEEE Transactions on Antennas and Propagation 69, no. 1 (January 2021): 347–55. https://doi.org/10.1109/TAP.2020.3010857.
  • [4] Tetzner, Joshua M., and Simon B. Adrian. “On the Adaptive Cross Approximation for the Magnetic Field Integral Equation.” Preprint. Preprints, January 26, 2024. https://doi.org/10.36227/techrxiv.170630205.56494379/v1.