Efficient methods for the solution of boundary integral equations on fractal antennas - Archive ouverte HAL
Communication Dans Un Congrès Année : 2024

Efficient methods for the solution of boundary integral equations on fractal antennas

Résumé

This work focuses on construction of efficient numerical methods for wave scattering by fractal antennas, see [3]. It builds on the theoretical basis proposed in the recent work [1], which establishes boundary integral (BIE) formulations for solving sound-soft Helmholtz scattering problems on fractal screens. An important feature of such formulations is the use of the Hausdorff measure on fractals instead of the standard Lebesgue’s measure. This adds an extra dimension to the two classical difficulties encountered with numerical BEM simulations, namely the evaluation of boundary integrals and the fact that the underlying matrices are dense. Our idea is to exploit the Hausdorff measure’s self-similar structure in order to deal with these difficulties.
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Dates et versions

hal-04638324 , version 1 (08-07-2024)

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Patrick Joly, Maryna Kachanovska, Zoïs Moitier. Efficient methods for the solution of boundary integral equations on fractal antennas. WAVES 2024 - 16th International Conference on Mathematical and Numerical Aspects of Wave Propagation, Jun 2024, Berlin, Germany. ⟨10.17617/3.MBE4AA⟩. ⟨hal-04638324⟩
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