Operator Splitting Method for Coupled Problems:Transport and Maxwell Equations

References

[1] M. Ohring, “Materials Science of Thin Films,” 2nd Edition, Academic Press, San Diego, New York, Boston, London, 2002.

[2] J. Geiser and M. Arab, “Simulation of a Chemical Vapor Deposition: Mobile and Immobile Zones and Homogeneous Layers,” Journal of Porous Media, Begell House Inc., Redding, 2009, Vol. 1, No. 2, pp. 123-143.

[3] L. Rudniak, “Numerical Simulation of Chemical Vapour Deposition Process in Electric Field,” Computers & Chemical Engineering, Vol. 22, Supplement 1, 1998, pp. 755-758.

[4] J. Van Roey, J. van der Donk and P. E. Lagasse, “Beam-Propagation Method: Analysis and Assessment,” Journal of the Optical Society of America, Vol. 71, No. 7, 1981, pp. 803-810. doi:10.1364/JOSA.71.000803

[5] M. D. Feit and J. A. Fleck Jr., “Analysis of Rib Waveguides and Couplers by the Propa-gating Beam Method,” Journal of the Optical Society of America A, Vol. 7, No. 1, 1990, pp. 73-79.
doi:10.1364/JOSAA.7.000073

[6] M. D. Feit and J. A. Fleck Jr., “Light Propagation in Graded-Index Optical Fibers,” OSA Applied Optics, Vol. 17, No. 24, 1978, pp. 3990- 3998.
doi:10.1364/AO.17.003990

[7] L. Thylen, E. M. Wright, G. I. Stegeman, C. T. Seaton and J. V. Moloney, “Beam-Propagation Method Analysis of a Nonlinear Directional Coupler,” OSA Optics Letters, Vol. 11, No. 11, 1986, pp. 739-741.
doi:10.1364/OL.11.000739

[8] J. A. Fleck, J. R. Morris Jr. and M. D. Feit, “Time-dependent Propagation of High Energy Laser Beams through the Atmosphere,” Applied Physics, Vol. 10, No. 2, 1976, pp. 129-160. doi:10.1007/BF00896333

[9] M. Lax, J. H. Batteh and G. P. Agrawai, “Channeling of Intense Electromagnetic Beams,” Journal of Applied Physics, Vol. 51, No. 1, 1981, pp. 109-125.
doi:10.1063/1.328442

[10] G. I. Marchuk, “Some Applications of Splitting-up Methods to the Solution of Mathematical Physics Problems,” Aplikace Matematiky, Vol. 1, 1968, pp. 103-132.

[11] G. Strang, “On the Constraction and Comparion of Difference Schemes,” SIAM J. Numerical Analysis, Vol. 5, No. 3, 1968, pp. 506-517. doi:10.1137/0705041

[12] K. Okamoto, “Fundamentals of Optical Waveguides,” Academic Press, New York, 2005.

[13] A Taflove, “Computational Electrodynamics: The Finite Difference Time Domain Method,” Arctech House Inc., 1995.

[14] J. P. Berenger, “A Perfectly Matched Layer for the Absorption of Electromagnetic Waves,” J. Comp. Phys., Vol. 111, 2005, pp. 185-220.

[15] S. D. Gedney, “An Anisotropic Perfectly Matched Layer-Absorbing Medium for the Truncation of Fdtd Lattices,” IEEE Tran. Ant. Prop., Vol. 44, No. 12, 1996, pp. 1630-1639.

[16] W. Sha, X. Wu, M. Chen and Z. Huang, “Application of the High-Order Symplectic Fdtd Scheme to the Curved Three-Dimensional Perfectly Conducting Objects,”

[17] T. Hirono, W. Lui, S. Seki and Y. Yoshikuni, “A Three- Dimensional Fourth-Order Finite-Difference Time-Domain Scheme Using a Symplectic Integrator Propagator,”

[18] J. Geiser, “Numerical Simulation of a Model for Transport and Reaction of Radionuclides, 2001,” Proceedings of the Large Scale Scientific Computations of Engineering and Environmental Problems, Sozopol, 2001.

[19] W. Hackbusch, “Iterative Losung Groser Schwa-chbesetzter Gleichungssysteme,” Teubner-Verlag, Stuttgart, 1993.

[20] I. Farago and J. Geiser, “Iterative Operator-Splitting Methods for Linear Problems,” International Journal of Computational Science and Engineering, Vol. 3, No. 4, 2007, pp. 255-263.

[21] J. Kanney, C. Miller and C. Kelley, “Convergence of Iterative Split-Operator Approaches for Ap-proximating Nonlinear Reactive Transport Problems,” Advances in Water Resources, Vol. 26, 2003, pp. 247-261.
doi:10.1016/S0309-1708(02)00162-8

[22] J. Geiser, “Weighted Iterative Operator-Splitting Methods: Stability-Theory,” Proceedings of the 6th International Conference, NMA 2006, Lecture Notes in Computer Science, Springer, Berlin, Vol. 4310, 2007, pp. 40-47.

[23] W. H. Hundsdorfer and J. G. Verwer, “Numerical Solution of Time-Dependent Advection-Diffusionreaction Equations,” Springer, Berlin, 2003.

[24] J. Geiser, “Iterative Operator-Splitting Methods with Higher Order Time-Integration Methods and Applications for Parabolic Partial Differential Equations,” Journal of Com-putational and Applied Mathematics, Elsevier, Amsterdam, Vol. 217, 2008, pp. 227-242.

[25] E. Zeidler, “Nonlinear Functional Analysis and Its Applications II/B: Nonlinear Montone Opera-tors,” Springer- Verlag, Berlin-Heidelberg-New York, 1990.