The adaptive cross approximation is applied to boundary element matrices coming from 2D scattering problems by an infinite periodic surface. This compression technique has the advantage to be applied before the assembly of the matrix. As a result, the computational times for both assembly and solution phases are reduced. Numerical results assess the efficacy of the method on scattering problems with several periodic surfaces.
2. DeSanto, J., G. Erdmann, W. Hereman, and M. Misra, "Theoretical and computational aspects of scattering from rough surfaces: One dimensional perfectly reecting surfaces," Waves in Random, and Complex Media, Vol. 8, No. 4, 385-414, 1998.
3. Falconer, K., Fractal Geometry: Mathematical Foundations and Applications, John Wiley & Sons, 2013.
4. Hackbusch, W., "A sparse matrix arithmetic based on H-matrices. Part I: Introduction to H-matrices," Computing, Vol. 62, 89-108, 1999.
5. Hackbusch, W. and Z. P. Nowak, "On the fast matrix multiplication in the boundary element method by panel clustering," Numerische Mathematik, Vol. 54, 463-491, 1989.
6. Lee, J. F., K. Zhao, and M. N. Vouvakis, "The adaptive cross approximation algorithm for accelerated method of moments computations of EMC problem," IEEE Transactions on Electromagnetic Compatibility, Vol. 47, No. 4, 763-773, 2005.
7. Linton, C. M., "Lattice sums for the Helmholtz equation," SIAM Review, Vol. 52, No. 4, 630-674, 2010.
8. Otani, Y. and N. Nishimura, "A periodic FMM for Maxwell's equation in 3D and its application to problems related to photonic crystals," Journal of Computational Physics, Vol. 227, No. 9, 4630-4652, Feb. 2008.
9. Saad, Y. and M. H. Schultz, "GMRES: A generalized minimal residual algorithm for solving non symmetric linear systems," SIAM J. Stat Comput., Vol. 7, No. 3, 856-869, Jul. 1986.
10. Stolper, M. and S. Rjasanow, "A compression method for the Helmholtz equation," Numerical Mathematics and Advanced Applications, 786-795, M. Feistauer, V. T. Dolej, P. Knobloch, and K. Najzar, Eds., Springer Berlin Heidelberg, 2004.
11. Tournier, S., J. Girardin, J.-R. Poirier, and P. Borderies, "Analysis of QR-compression techniques for improving electromagnetic scattering computation by periodic rough surfaces," AMPERE, 13th International Conference on Microwave and RF Heating, Sep. 2011.