andrewgibbs / fractal-screen-scattering

A collection of codes for modelling acoustic and electro-magnetic scattering by fractal screens.

fractalpp

• A collection of codes for modelling acoustic and electro-magnetic scattering by fractal screens.
• These codes use bempp, but do not require an understanding of the underlying mathematics/machinery of bempp. Click the binder badge above for an interactive example for impedance scattering by a Koch snowflake, which will run in a browser window.
• Contains a graded meshing strategy for the Koch snowflake, based on the ideas of [1]. These codes do not depend on bempp, and can be found in fractalpp/meshes/koch.py
• For numerical analysis, see [2] (Dirichlet) and [3] (Impedance).

Bibliography

[1]: Bagnerini, P., Buffa, A. and Vacca, E., 2013. Mesh generation and numerical analysis of a Galerkin method for highly conductive prefractal layers. Applied Numerical Mathematics, 65, pp.63-78.

[2]: Chandler-Wilde, S.N., Hewett, D.P., Moiola, A. and Besson, J., 2021. Boundary element methods for acoustic scattering by fractal screens. Numerische Mathematik, 147(4), pp.785-837.

[3]: Bannister, J., Gibbs, A. and Hewett, D.P., 2020. Acoustic scattering by impedance screens/cracks with fractal boundary: well-posedness analysis and boundary element approximation. arXiv preprint arXiv:2009.13236.