Referencias

Airaksinen, T.; Heikkola, E.; Pennanen, A.; Toivanen, J.(2007). "An algebraic multigrid based shifted-Laplacian preconditioner for the Helmholtz equation", J. Comput. Phys226(1): 1196-1210. [ Links ]

Alvarado, A.(2014) "Método LDG para la Ecuación Vectorial de Helmholtz", Master's thesis, Universidad de Puerto Rico at Mayagüez. [ Links ]

Alvarado, A.; Castillo, P. (2016) "Computational performance of LDG methods applied to time harmonic Maxwell equation in polyhedral domains", J. Scientific Computing67(2): 453-474. [ Links ]

Bao, G.; Wei, G.W.; Zhao, S. (2004) "Numerical solution of the Helmholtz equation with high wavenumbers", Internat. J. Numer. Methods Engrg59(3): 389-408. [ Links ]

Bayliss, A.; Goldstein, C.; Turkel, E. (1983) "An iterative method for the Helmholtz equation", J. Comput. Phys49(3): 443-457. [ Links ]

Bermúdez, A.; Bullón, J.; Pena, F. (1998) "A finite element method for the thermoelectrical modelling of electrodes", Commun. Numer. Meth. Engrg14(6): 581-593. [ Links ]

Brenner, S.; Li, F.; Sung, L. (2006) "A locally divergence-free nonconforming finite element method for the time-harmonic Maxwell's equations", Math. Comp.76(258): 573-595. [ Links ]

Castillo, P. (2002) "Performance of discontinuous Galerkin methods for elliptic PDE's", SIAM J. Sci. Comput24(2): 524-547. [ Links ]

Castillo, P. (2010) "Stencil reduction algorithms for the Local Discontinuous Galerkin method", Internat. J. Numer. Methods Engrg81: 1475-1491. [ Links ]

Castillo, P.; Cockburn, B.; Perugia, I.; Schötzau, D. (2000) "An a priori error analysis of the Local Discontinuous Galerkin method for elliptic problems", SIAM J. Num. Anal38(5): 1676-1706. [ Links ]

Castillo, P.; Sequeira, F.(2013) "Computational aspects of the Local Discontinuous Galerkin method on unstructured grids in three dimensions", Mathematical and Computer Modelling57(9-10): 2279-2288. [ Links ]

Castillo, P.; Velázquez, E. (2008) "A numerical study of a semi-algebraic multilevel preconditioner for the Local Discontinuous Galerkin method", Internat. J. Numer. Methods Engrg79: 255-268. [ Links ]

Clain, S.; Rappaz, J.; Swierkosz, M.; Touzani, R. (1993) "Numerical modeling of induction heating for two-dimensional geometries", Mathematical Models and Methods in Applied Sciences03(06): 805-822. [ Links ]

Cockburn, B.; Shu, C.W. (1998) "The Local Discontinuous Galerkin method for time-dependent convection-diffusion systems", SIAM J. Num. Anal35: 2440-2463. [ Links ]

Demkowicz, L.; Vardapetyan, L. (1998) "Modeling of electromagnetic absorption/scattering problems using hp-adaptive finite elements", Comput. Methods Appl. Mech. Engrg152(1-2): 103-124. [ Links ]

Van der Vorst, H.A. (1992) "Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems", SIAM J. Sci. Stat. Comput13(2): 631-644. [ Links ]

Dolean, V.; Fol, H.; Lanteri, S.; Perrussel, R. (2008) "Solution of the timeharmonic Maxwell equations using Discontinuous Galerkin methods", J. Comput. Applied. Math218(2): 435-445. [ Links ]

El-Azab, A.; Garnich, M.; Kapoor, A. (2003) "Modeling of the electromagnetic forming of sheet metals: state-of-art an future needs", Journal of Materials Processing Technology 142(3): 744-754. [ Links ]

Erlangga, Y.A.; Oosterlee, C.W.; Vuik, C. (2006) "A novel multigrid based preconditioner for heterogeneous Helmholtz problems", SIAM J. Sci. Comput27(4): 1471-1492. [ Links ]

Erlangga, Y.A.; Vuik, C.; Oosterlee, C.W. (2004) "On the class of preconditioners for solving Helmholtz equation", Appl. Numer. Math50(3-4): 409-425. [ Links ]

Greif, C.; Schötzau, D. (2007) "Preconditioners for the discretized timeharmonic Maxwell equation in mixed form", Numerical Linear Algebra with Applications 14(4): 281-297. [ Links ]

Houston, P.; Perugia, I.; Schneebeli, A.; Schötzau, D. (2005) "Mixed Discontinuous Galerkin approximation of the Maxwell Operator: The indefinite case", Modél. Math. Anal. Numér39(4): 727-753. [ Links ]

Houston, P.; Perugia, I.; Schneebeli, A.; Schötzau, D. (2005) "Interior penalty method for the indefinite time-harmonic Maxwell's equations", Numer. Math.100(3): 485-518. [ Links ]

Li, D.; Greif, C.; Schötzau, D. (2012) "Parallel numerical solution of the time-harmonic Maxwell equations in mixed form", Numerical Linear Algebra with Applications 19(3): 525-539. [ Links ]

Maxwell, J.C.(1865) "A dynamical theory of the electromagnetic field", Phil. Trans. Royal Society Lond155: 459-512. [ Links ]

Maxwell, J.C. (1873) A Treatise on Electricity and Magnetism. Clarendon Press, Oxford. [ Links ]

Perugia, I.; Schötzau, D. (2003) "The hp-local discontinuous Galerkin method for low-frecuency time-harmonic Maxwell's equations", Math. Comp.72(243): 1179-1214. [ Links ]

Perugia, I.; Schötzau, D.; Monk, P. (2002) "Stabilized interior penalty methods for the time-harmonic Maxwell's equations", Comput. Methods Appl. Mech. Engrg191(41-42): 4675-4697. [ Links ]

Reitzinger, S.; Schöberl, J.(2002) "An algebraic multigrid method for finite element discretizations with edge elements", Numer. Linear Algebra with Applications9(3): 223-238. [ Links ]

Saad, Y.(2001) Iterative Methods for Large Sparse Linear Systems, Second edition. Society for Industrial and Applied Mathematics, Philadelphia PA. [ Links ]

Theran, C. (2014) "Factorización incompleta IC(l,τ,m) por bloques para matrices generadas por métodos Local Discontinuous Galerkin". Master's thesis, Universidad de Puerto Rico at Mayagüez. [ Links ]

Tuncer, E.; Lee, B.T.; Islam, M.S.; Neikirk, D.P. (1994) "Quasi-static conductor loss calculations in transmission lines using a new conformal mapping technique", IEEE Transactions on Microwave Theory and Techniques42(9): 1807-1815. [ Links ]

Zienkiewicz, O. (2000) "Achievements and some unsolved problems of the finite element method", Internat. J. Numer. Methods Engrg47(1-3): 9-28. [ Links ]