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On the Numerical Solution of Diffraction Problem by Random Spheres Using Electric Field Integral Equation
Department of Mathematics, University College Adham, Makkah, Kingdom of Saudi Arabia
Department of Mathematics, University College in Qunfudah, Umm Al-Qura University, Makkah, Kingdom of Saudi Arabia
- 1 Department of Mathematics, University College Adham, Makkah, Kingdom of Saudi Arabia
- 2 Department of Mathematics, University College in Qunfudah, Umm Al-Qura University, Makkah, Kingdom of Saudi Arabia
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Abstract
The aim of this paper is to solve the two-dimensional acoustic scattering problems by random sphere using Electric field integral equation. Some approximations for the two-dimensional case are derived. These various approximations are next numerically validated in the case of high-frequency.
KeywordsMultiple ScatteringIntegral EquationHigh FrequencyAcousticIterative Solver
- Antoine, X., Chniti, C. and Ramdani, K. (2008) On the Numerical Approximation of High-Frequency Acoustic Multiple Scattering Problems by Circular Cylinders. Journal of Computational Physics, 227, 1754-1771. https://doi.org/10.1016/j.jcp.2007.09.030
- Antoine, X., Geuzaine, C. and Ramdani, K. (2010) Computational Methods for Multiple Scattering at High Frequency with Applications to Periodic Structures Calculations. In: Ehrhardt, M., Ed., Wave Propagation in Periodic Media—Analysis, Numerical Techniques and Practical Applications, Vol. 1, Bentham Science Publishers Ltd., UAE, 73-107. https://doi.org/10.2174/978160805150211001010073
- Martin, P.A. (2006) Multiple Scattering. Interaction of Time-Harmonic Waves with N Obstacles, Vol. 107 of Encyclopedia of Mathematics and Its Applications. Cambridge University Press, Cambridge.
- Colton, D.L. and Kress, R. (1983) Integral Equation Methods in Scattering Theory. Pure and Applied Mathematics. John Wiley & Sons Inc., New York.
- Nédélec, J.-C. (2001) Acoustic and Electromagnetic Equations. Integral Representations for Harmonic Problems, Vol. 144 of Applied Mathematical Sciences. Springer-Verlag, New York.
- Acosta, S. (2015) On-Surface Radiation Condition for Multiple Scattering of Waves. Computer Methods in Applied Mechanics and Engineering, 283, 1296-1309. https://doi.org/10.1016/j.cma.2014.08.022
- Acosta, S. and Villamizar, V. (2010) Coupling of Dirichlet-to-Neumann Boundary Condition and Finite Difference Methods in Curvilinear Coordinates for Multiple Scattering. Journal of Computational Physics, 229, 5498-5517. https://doi.org/10.1016/j.jcp.2010.04.011
- Antoine, X., Ramdani, K. and Thierry, B. (2012) Wide Frequency Band Numerical Approaches for Multiple Scattering Problems by Disks. Journal of Algorithms & Computational Technology, 6, 241-259. https://doi.org/10.1260/1748-3018.6.2.241
- Chen, J., Lee, Y., Lin, Y., Chen, I. and Lee, J. (2011) Scattering of Sound from Point Sources by Multiple Circular Cylinders Using Addition Theorem and Superposition Technique. Numerical Methods for Partial Differential Equations, 27, 1365-1383. https://doi.org/10.1002/num.20583
- Ehrhardt, M. (2010) Wave Propagation in Periodic Media Analysis, Numerical Techniques and Practical Applications, E-Book Series Progress in Computational Physics (PiCP), Volume 1. Bentham Science Publishers, UAE.
- Ehrhardt, M., Han, H. and Zheng, C. (2009) Numerical Simulation of Waves in Periodic Structures. Communications in Computational Physics, 5, 849-870.