Abstract
We provide a novel ready-to-precondition boundary integral formulation to solve Helmholtz scattering problems by heterogenous penetrable objects in two dimensions exhibiting high-contrast ratios. By weakly imposing transmission conditions and integral representations per subdomain, we are able to devise a robust Galerkin-Petrov formulation employing weighted Chebyshev polynomials. Matrix entries are computed by fast Fourier transforms and regularization techniques. Computational results provided are consistent for large contrast scatterers and frequency sweep as well as efficient Calderón-type preconditioning.
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Notes
- 1.
If the subdomain has a length L i and waves propagating therein have a wavelength \(\lambda _{i}\), we consider situations reaching \(L_{i}/\lambda _{i}\mathop{\cong}1000\) with \(\max _{ij}\kappa _{i}/\kappa _{j} \leq 100\). The case of very high frequencies will not be considered as it can only be practically resolved by asymptotic methods.
- 2.
In [8] we used M to account for the maximum polynomial order and N c to denote the number of terms considered in the degenerate kernel approximation.
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Acknowledgements
This project was partially funded by the Chilean National Science and Technology Commission CONICYT via projects Fondecyt Iniciación 11121166 and ACT 1118.
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Jerez-Hanckes, C., Pinto, J., Tournier, S. (2016). Local Multiple Traces Formulation for High-Frequency Scattering Problems by Spectral Elements. In: Bartel, A., Clemens, M., Günther, M., ter Maten, E. (eds) Scientific Computing in Electrical Engineering. Mathematics in Industry(), vol 23. Springer, Cham. https://doi.org/10.1007/978-3-319-30399-4_8
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