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AdaptiveCrossApproximation

This package provides different flavors of the adaptive cross approximation introduced in BEBENDORF. Beside the standard algorithm this package allows to use several different pivoting strategies [] and convergence criteria[]. Further more this package contains an incomplete adaptive cross approximation allowing an efficient pivoting selection for the construction of $\mathcal{H}^2$-matrices [].

Installation

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

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

References

The implementation is based on

  • [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.