An efficient algorithm for simulation of stochastic scattering cross-sections

Mahadevan Ganesh, Stuart Collin Hawkins

Abstract


We present an efficient algorithm for uncertainty quantification of scattering cross-sections of stochastic configurations comprising multiple two dimensional sound-soft particles whose locations and orientations are random. Our algorithm has two components. Firstly, we use a high order generalised polynomial chaos approximation of the stochastic cross-sections in the random variables that requires realisation of the exterior sound propagation model for high order quadrature sampling parameters. For each such realisation, we use an efficient spectrally accurate algorithm for deterministic scattering simulations based on solving a boundary integral equation reformulation of the acoustic model. We present numerical results for a stochastic configuration of particles with rough surfaces. Our numerical result demonstrate the high order accuracy of both components of the algorithm for simulation of moments of the scattering cross-section of the configuration.

References
  • M. Abramowitz and I. Stegun. Handbook of Mathematical Functions. Dover Publications, New York, 1970.
  • A. Baren. From the single-scattering properties of ice crystals to climate prediction: A way forward. Atmospheric Research, 112:45--69, 2012. doi:10.1016/j.atmosres.2012.04.010.
  • D. Colton and R. Kress. Inverse Acoustic and Electromagnetic Scattering Theory. Springer, 1998.
  • M. Ganesh and I. G. Graham. A high-order algorithm for obstacle scattering in three dimensions. J. Comput. Phys., 198:211--242, 2004. doi:10.1016/j.jcp.2004.01.007.
  • M. Ganesh and S. C. Hawkins. A high-order algorithm for multiple electromagnetic scattering in three dimensions. Numer. Algorithms, 50:469--510, 2009. doi:10.1007/s11075-008-9238-z.
  • M. Ganesh and S. C. Hawkins. A stochastic pseudospectral and T-matrix algorithm for acoustic scattering by a class of multiple particle configurations. J. Quant. Spectrosc. Radiat. Transfer, 2013 (in press). doi:10.1016/j.jqsrt.2013.01.011.
  • O. P. Le Maitre and O. M. Kino. Spectral Methods for Uncertainty Quantification. Springer, 2010.
  • H. C. van de Hulst. Light Scattering by Small Particles. Dover, 1957.

Keywords


acoustic scattering, stochastic, uncertainty quantification, generalized polynomial chaos

Full Text:

PDF bib


DOI: http://dx.doi.org/10.21914/anziamj.v54i0.6300



Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.