High order non-conforming multi-element discontinuous Galerkin method for time-domain electromagnetics

We are interested here in a multielement Discontinuous Galerkin Time Domain method to solve the system of Maxwell equations. The method is formulated on non-conforming and hybrid meshes combining an unstructured triangulation for an accurate discretization of the irregularly shaped objects with a structured (orthogonal) quadrangulation for a gain in CPU time on the rest of the computational domain. We present the discretization schemes and the theoritical aspects in 3D, and we expose the numerical simulations.

[1]  M. Fernandez Pantoja,et al.  A New Hybrid DGTD/FDTD Method in 2-D , 2008, IEEE Microwave and Wireless Components Letters.

[2]  Philippe G. Ciarlet,et al.  The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[3]  M. König,et al.  The Discontinuous Galerkin Time-Domain method for Maxwell’s equations with anisotropic materials , 2010 .

[4]  L. Fezoui,et al.  Convergence and stability of a discontinuous galerkin time-domain method for the 3D heterogeneous maxwell equations on unstructured meshes , 2005 .

[5]  Wei Cai,et al.  An upwinding embedded boundary method for Maxwell's equations in media with material interfaces: 2D case , 2003 .

[6]  S. Lanteri,et al.  Convergence of a Discontinuous Galerkin scheme for the mixed time domain Maxwell's equations in dispersive media. , 2013 .

[7]  Z. Cendes,et al.  Keeping Time with Maxwell's Equations , 2010, IEEE Microwave Magazine.

[8]  Sébastien Pernet,et al.  HP a-priori error estimates for a non-dissipative spectral discontinuous Galerkin method to solve the Maxwell equations in the time domain , 2007, Math. Comput..

[9]  Kurt Busch,et al.  Higher-order time-domain methods for the analysis of nano-photonic systems , 2009 .

[10]  Thomas Weiland,et al.  A hybrid Finite Integration-Finite Volume Scheme , 2010, J. Comput. Phys..

[11]  J. Hesthaven,et al.  Nodal high-order methods on unstructured grids , 2002 .

[12]  Stéphane Lanteri,et al.  A high-order non-conforming discontinuous Galerkin method for time-domain electromagnetics , 2010, J. Comput. Appl. Math..

[13]  Oubay Hassan,et al.  A high order hybrid finite element method applied to the solution of electromagnetic wave scattering problems in the time domain , 2009 .

[14]  R.G. Martin,et al.  Hybridizing DGTD and FDTD , 2007, 2007 International Conference on Electromagnetics in Advanced Applications.

[15]  H. Fahs.  Development of a hp-like discontinuous Galerkin time-domain method on non-conforming simplicial meshes for electromagnetic wave propagation , 2009 .

[16]  Bo Zhao,et al.  Non-conformal and parallel discontinuous Galerkin time domain method for Maxwell's equations: EM analysis of IC packages , 2013, J. Comput. Phys..

[17]  Gary Cohen,et al.  A spatial high-order hexahedral discontinuous Galerkin method to solve Maxwell's equations in time domain , 2006, J. Comput. Phys..

[18]  Kurt Busch,et al.  Discontinuous Galerkin time-domain computations of metallic nanostructures. , 2009, Optics express.

[19]  X. Ferrieres,et al.  Application of a hybrid finite difference/finite volume method to solve an automotive EMC problem , 2004, IEEE Transactions on Electromagnetic Compatibility.

[20]  FahsHassan,et al.  A high-order non-conforming discontinuous Galerkin method for time-domain electromagnetics , 2010 .

[21]  Martin Käser,et al.  Non-conforming hybrid meshes for efficient 2-D wave propagation using the Discontinuous Galerkin Method , 2011 .

[22]  Jin-Fa Lee,et al.  Interior Penalty Discontinuous Galerkin Finite Element Method for the Time-Dependent First Order Maxwell's Equations , 2010, IEEE Transactions on Antennas and Propagation.

[23]  E. Montseny,et al.  Dissipative terms and local time-stepping improvements in a spatial high order Discontinuous Galerkin scheme for the time-domain Maxwell's equations , 2008, J. Comput. Phys..

[24]  김덕영.  [신간안내] Computational Electrodynamics (the finite difference time - domain method) , 2001 .