Domain decomposition method for Maxwell's equations: Scattering off periodic structures

Journal of Computational Physics

Volumn 226, Issue 1, 2007, Pages 477-493

  Schädle, Achim ^a   Zschiedrich, Lin ^a,b   Burger, Sven ^a,b   Klose, Roland ^a   Schmidt, Frank ^a,b  

^a ZUSE INSTITUTE BERLIN   (Germany)

^b JCMWAVE GMBH   (Germany)

Author keywords

Conical diffraction; Domain decomposition; Electro magnetic scattering; EUV; Finite elements; Lithography; Maxwell's equations; Perfectly matched layer method

Indexed keywords

BOUNDARY CONDITIONS; DOMAIN DECOMPOSITION METHODS; ELECTROMAGNETIC FIELDS; FINITE ELEMENT METHOD; NUMERICAL METHODS; PERIODIC STRUCTURES; PERSONAL COMPUTERS;

CONICAL DIFFRACTION; DOMAIN DECOMPOSITIONS; DOMAIN-DECOMPOSITION METHODS; ELECTRO-MAGNETIC SCATTERING; ELECTROMAGNETICS; EUV; FINITE ELEMENT; MAGNETIC SCATTERING; PERFECTLY MATCHED LAYER METHODS; TRANSPARENT BOUNDARY CONDITIONS;

MAXWELL EQUATIONS;

EID: 34548496489     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.04.017     Document Type: Article

References (31)

1. Benamou J.-D., and Després B. A domain decomposition method for the Helmholtz equation and related optimal control problems. J. Comput. Phys. 136 1 (1997) 68-82
2. Bérenger J.-P. A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114 2 (1994) 185-200
3. Born M., and Wolf E. Principles of Optics (1999), Cambridge University Press
4. S. Burger, R. Klose, A. Schädle, F. Schmidt, L. Zschiedrich, Adaptive FEM solver for the computation of electromagnetic eigenmodes in 3d photonic crystal structures, in: Proc. Sci. Comp. Electr. Eng. 2004, 2005.
5. Burger S., Köhle R., Zschiedrich L., Gao W., Schmidt F., März R., and Nölscher C. Benchmark of FEM waveguide and FDTD algorithms for rigorous mask simulation. In: Weed J.T., and Martin P.M. (Eds). Photomask Technology vol. 5992 (2005), SPIE, Bellingham, Washington, USA 368-379
6. X.-C. Cai, M.A. Casarin, F.W. jun. Elliott, O.B. Widlund, Overlapping Schwarz algorithms for solving Helmholtz's equation, in: J. Mandel, et al. (Eds.), Domain decomposition methods 10, Contemp. Math., vol. 218, AMS, Providence, RI, 1998, pp. 391-399.
7. Collino F., Ghanemi S., and Joly P. Domain decomposition methods for harmonic wave propagation: a general presentation. Comput. Methods Appl. Mech. Engrg. 184 (2000) 171-211
8. Collino F., and Monk P. The perfectly matched layer in curvilinear coordinates. SIAM J. Sci. Comput. (1998)
9. A. de La Bourdonnaye, Ch. Farhat, A. Macedo, F. Magoulés, F.-X. Roux, A non overlapping domain decomposition method for the exterior Helmholtz problem, Technical Report 3271, INRIA, 1997.
10. Després B. Décomposition de domaine et probléme de Helmholtz. C.R. Acad. Sci., Paris, Sér I 311 6 (1990) 313-316
11. Elschner J., Hinder R., Penzel F., and Schmidt G. Existence, uniqueness and regularity for solutions of the conical diffraction problem. Math. Models Methods Appl. Sci. 10 (2000) 317-341
12. Elschner J., Hinder R., and Schmidt G. Finite element solution of conical diffraction problems. Adv. Comput. Math. 16 (2002) 139-156
13. Gander J.M., Magoulés F., and Nataf F. Optimized Schwarz methods without overlap for the Helmholtz equation. J. Sci. Comput. 24 1 (2002) 38-60
14. S. Ghanemi, A domain decomposition method for Helmholtz scattering problems, in: Ninth International Conference on Domain Decomposition Methods, DDM.org, 1998, pp. 105-112.
15. Hohage T., Schmidt F., and Zschiedrich L. Solving time-harmonic scattering problems based on the pole condition II: convergence of the PML method. SIAM J. Math. Anal. 35 3 (2003) 547-560
16. Lassas M., and Somersalo E. On the existence and convergence of the solution of PML equations. Computing 60 3 (1998) 229-241
17. Lassas M., and Somersalo E. Analysis of the PML equations in general convex geometry. Proc. Roy. Soc. Edinburgh Sect. A 131 5 (2001) 1183-1207
18. Lee S.-Ch., Vouvakis M.N., and Lee J.-F. A non-overlapping domain decomposition method with non-matching grids for modeling large finite antenna arrays. J. Comp. Phys. 203 (2005) 1-21
19. Petit R. Electromagnetic Theory of Gratings (1980), Springer-Verlag
20. L. Plattner, A study in biomimetics: nanometer-scale, high-efficiency, dielectric diffractive structures on the wings of butterflies and in the silicon chip factory, Ph.D. thesis, School of Electronics and Computer Science, University of Southampton, 2003. .
21. Pomplun J., Burger S., Schmidt F., Zschiedrich L., and Scholze F. Rigorous FEM-simulation of EUV-masks: influence of shape and material parameters. In: Martin P.M., and Naber R.J. (Eds). Photomask Technology vol. 6349 (2006), SPIE, Bellingham, Washington, USA 63493D
22. Rodríguez A.A., and Gerardo-Giorda L. New nonoverlapping domain decomposition methods for the harmonic Maxwell system. SIAM J. Sci. Comput. 28 1 (2006) 102-122
23. Schädle A., and Zschiedrich L. Additive Schwarz method for scattering problems using the PML method at interfaces. In: Widlung O.B., and Keyes D.E. (Eds). Domain Decomposition Methods in Science and Engineering XVI. Lecture Notes in Computational Science and Engineering vol. 55 (2007), Springer 205-212
24. Schenk O., and Gärtner K. On fast factorization pivoting methods for sparse symmetric indefinite systems. Electronic Transactions on Numerical Analysis 23 (2006) 158-179
25. Schenk O., and Gärtner K. Solving unsymmetric sparse systems of linear equations with PARDISO. J. Future Generation Comput. Syst. 20 3 (2004) 475-487
26. Schuster K. Anwendung der Vierpoltheorie auf die Probleme der optischen Reflexionsminderung, Reflexionsverstärkung und der Interferenzfilter. Ann. der Physik, VI.F. 4 (1949) 352-356
27. Shaidurov V.V., and Ogorodnikov E.I. Some numerical method of solving Helmholtz wave equation. In: Cohen G., Halpern L., and Joly P. (Eds). Mathematical and Numerical Aspects of Wave Propagation Phenomena (1991), SIAM 73-79
28. A. Toselli, Some results on overlapping Schwarz methods for the Helmholtz equation employing perfectly matched layers, Technical Report 765, Courant Institute, 1998.
29. Zschiedrich L., Burger S., Klose R., Schädle A., and Schmidt F. JCMmode: An adaptive finite element solver for the computation of leaky modes. In: Sidorin Y., and Wächter C.A. (Eds). Integrated Optics: Devices, Materials, and Technologies IX vol. 5728 (2005), SPIE, Bellingham, Washington, USA 192-202
30. L. Zschiedrich, S. Burger, A. Schädle, F. Schmidt, Domain decomposition method for electromagnetic scattering problems, in: Proceedings of the 5th International Conference on Numerical Simulation of Optoelectronic Devices, IEEE, ISBN: 0-7803-9149-7. 2005, pp. 55-56.
31. Zschiedrich L., Burger S., Kettner B., and Schmidt F. Advanced finite element method for nano-resonators. In: Osinski M., et al. (Ed). Physics and Simulation of Optoelectronic Devices XIV vol. 6115 (2006), SPIE, Bellingham, Washington, USA 164-174