Energy estimates and numerical verification of the stabilized Domain Decomposition Finite Element/Finite Difference approach for time-dependent Maxwell’s system

Assous F., Degond P., Heintze E., Raviart P.-A., Serge J., On a finite-element method for solving the three-dimensional Maxwell equations, J. Comput. Phys., 1993, 109(2), 222–237 Beilina L., Grote M.J., Adaptive hybrid finite element/difference method for Maxwell’s equations, TWMS J. Pure Appl. Math., 2010, 1(2), 176–197 Beilina L., Johnson C., A posteriori error estimation in computational inverse scattering, Math. Models Methods Appl. Sci., 2005, 15(1), 23–37 Beilina L., Johnsson C., Hybrid FEM/FDM method for an inverse scattering problem, In: Numerical Mathematics and Advanced Applications, Ischia, July, 2001, Springer, Milan, 2003, 545–556 Beilina L., Klibanov M.V., Reconstruction of dielectrics from experimental data via a hybrid globally convergent/adaptive inverse algorithm, Inverse Problems, 2010, 26(12), #125009 Beilina L., Samuelsson K., Åhlander K., Efficiency of a hybrid method for the wave equation, In: Finite Element Methods, Jyväskylä, 2000, GAKUTO Internat. Ser. Math. Sci. Appl., 15, Gakkotosho, Tokyo, 2001, 9–21 Brenner S.C., Scott L.R., The Mathematical Theory of Finite Element Methods, Texts Appl. Math., 15, Springer, New York, 1994 Budak B.M., Samarskii A.A., Tikhonov A.N., A Collection of Problems in Mathematical Physics, Dover Phoenix Ed., Dover, Mineola, 1988 Cangellaris A.C., Wright D.B., Analysis of the numerical error caused by the stair-stepped approximation of a conducting boundary in FDTD simulations of electromagnetic phenomena, IEEE Trans. Antennas and Propagation, 1991, 39(10), 1518–1525 Edelvik F., Ledfelt G., Explicit hybrid time domain solver for the Maxwell equations in 3D, J. Sci. Comput., 2000, 15(1), 61–78 Elmkies A., Joly P., Éléments finis d’arête et condensation de masse pour les équations de Maxwell: le cas 2D, C. R. Acad. Sci. Paris Sér. I Math., 1997, 324(11), 1287–1293 Engquist B., Majda A., Absorbing boundary conditions for the numerical simulation of waves, Math. Comp., 1977, 31(139), 629–651 Hughes T.J.R., The Finite Element Method, Prentice Hall, Englewood Cliffs, 1987 Jiang B., The Least-Squares Finite Element Method, Scientific Computation, Springer, Berlin-Heidelberg, 1998 Jiang B.-N., Wu J. Povinelli L.A., The origin of spurious solutions in computational electromagnetics, J. Comput. Phys., 1996, 125(1), 104–123 Jin J., The Finite Element Method in Electromagnetics, John Wiley&Sons, New York, 1993 Joly P., Variational Methods for Time-Dependent Wave Propagation Problems, In: Topics in Computational Wave Propagation, Lect. Notes Comput. Sci. Eng., 31, Springer, Berlin, 2003, 201–264 Klibanov M.V., Fiddy M.A., Beilina L., Pantong N., Schenk J., Picosecond scale experimental verification of a globally convergent algorithm for a coefficient inverse problem, Inverse Problems, 2010, 26(4), #045003 Ladyzhenskaya O.A., The Boundary Value Problems of Mathematical Physics, Appl. Math. Sci., 49, Springer, New York, 1985 Monk P.B., Finite Element Methods for Maxwell’s Equations, Oxford University Press, New York, 2003 Monk P.B., Parrott A.K., A dispersion analysis of finite element methods for Maxwell’s equations, SIAM J. Sci. Comput., 1994, 15(4), 916–937 Munz C.-D., Omnes P., Schneider R., Sonnendrücker E., Voß U., Divergence correction techniques for Maxwell solvers based on a hyperbolic model, J. Comput. Phys., 2000, 161(2), 484–511 Paulsen K.D., Lynch D.R., Elimination of vector parasites in finite element Maxwell solutions, IEEE Trans. Microwave Theory Tech., 1991, 39(3), 395–404 Perugia I., Schötzau D., The hp-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell equations, Math. Comp., 2002, 72(243), 1179–1214 Rylander T., Bondeson A., Stable FEM-FDTD hybrid method for Maxwell’s equations, Comput. Phys. Comm., 2000, 125(1–3), 75–82 Rylander T., Bondeson A., Stability of explicit-implicit hybrid time-stepping schemes for Maxwell’s equations, J. Comput. Phys., 2002, 179(2), 426–438 Yee K.S., Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media, IEEE Trans. Antennas and Propagation, 1966, 14(3), 302–307 7