Scattering by stochastic boundaries: hybrid low- and high-order quantification algorithms

Ganesh, Mahadevan ; Hawkins, Stuart Collin

ANZIAM Journal, Tome 56 (2016), / Harvested from Australian Mathematical Society

Résumé

We present an efficient framework for simulating the average wave scattering properties of two dimensional randomly shaped particles with statistical properties similar to model aerosols particles that are important in atmospheric science applications. Our framework is based on an efficient high order discretisation of the spatial dimensions and parallel implementations for the large number of stochastic dimensions. We demonstrate our framework by simulating the mean (and higher order moments) of the far field of the model particles. We use tens of thousands of Monte Carlo, quasi-Monte Carlo and sparse grid generalised polynomial chaos realisations of the random particle model. References A. J. Baran. From the single-scattering properties of ice crystals to climate prediction: A way forward. Atmos. Res., 112:45–69, 2012. doi:10.1016/j.atmosres.2012.04.010 C. Chauviere, J. Hesthaven, and L. Wilcox. Efficient computation of RCS from scatterers of uncertain shapes. IEEE T. Antenn. Propag., 55:1437–1448, 2007. doi:10.1109/TAP.2007.895629 D. Colton and R. Kress. Inverse Acoustic and Electromagnetic Scattering Theory. Springer, 2013. doi:10.1007/978-1-4614-4942-3 J. Dick. Walsh spaces containing smooth functions and quasi-Monte Carlo rules of arbitrary high order. SIAM J. Numer. Anal., 46:1519–1553, 2008. doi:10.1137/060666639 J. Dick, F. Y. Kuo, and I. H. Sloan. High-dimensional integration: The quasi-Monte Carlo way. Acta Numer., 22:133–288, 2013. doi:10.1017/S0962492913000044 M. Ganesh and S. C. Hawkins. An efficient algorithm for simulating scattering by a large number of two dimensional particles. CTAC2010, ANZIAM J., 52:C139–C155, 2011. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/3954 T. Gerstner and M. Griebel. Numerical integration using sparse grids. Numer. Algorithms, 18:209–232, 1998. doi:10.1023/A:1019129717644 P. V. Hobbs and M. P. McCormick. Aerosols and Climate. A. Deepak, 1988. http://catalogue.nla.gov.au/Record/514698 L. Lamberg, K. Muinonen, J. Ylonen, and K. Lumme. Spectral estimation of Gaussian random circles and spheres. J. Comput. Appl. Math., 136:109–121, 2001. doi:10.1016/S0377-0427(00)00578-1 T. Nousiainen and G. M. McFarquhar. Light scattering by quasi-spherical ice crystals. J. Atmos. Sci., 61:2229–2248, 2004. doi:10.1175/1520-0469(2004)061<2229:LSBQIC>2.0.CO;2 O. Ozgun and M. Kuzuoglu. A coordinate transformation approach for efficient repeated solution of Helmholtz equation pertaining to obstacle scattering by shape deformations. Comput. Phys. Comm., 185:1616–1627, 2014. doi:10.1016/j.cpc.2014.03.002 C. Schwab and C. J. Gittelson. Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs. Acta Numer., 20:291–467, 2011. doi:10.1017/S0962492911000055 O. P. Le Ma\T1\i tre and O. M. Kino. Spectral Methods for Uncertainty Quantification. Springer, 2010. doi:10.1007/978-90-481-3520-2 P. Tsuji, D. Xiu, and L. Ying. Fast method for high-frequency acoustic scattering from random scatterers. Int. J. Uncertain. Quantif., 1:99–117, 2011. doi:10.1615/IntJUncertaintyQuantification.v1.i2 H. C. van de Hulst. Light Scattering by Small Particles. Dover, 1957. http://store.doverpublications.com/0486642283.html B. Veihelmann, T. Nousiainen, M. Kahnert, and W. J. van der Zande. Light scattering by small feldspar particles simulated using the Gaussian random sphere geometry. J. Quant. Spectrosc. Rad. Trans., 100:393–405, 2006. doi:10.1016/j.jqsrt.2005.11.053 D. Xiu and J. Shen. An efficient spectral method for acoustic scattering from rough surfaces. Commun, Comput. Phys., 2:54–72, 2007. http://www.global-sci.com/freedownload/v2_54.pdf

Détail

Publié le : 2016-01-01
DOI : https://doi.org/10.21914/anziamj.v56i0.9313