A brick-tetrahedron finite-element interface with stable hybrid explicit–implicit time-stepping for Maxwell’s equations

Degerfeldt, David; Rylander, Thomas

doi:10.1016/j.jcp.2006.05.016

Cited by 23 publications

(13 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, a stable hybrid FDTD-FETD method is considered in Ref. [23], while Degerfeldt and Rylander [8] propose a FETD method with stable hybrid explicit-implicit time stepping working on brick-tetrahedral meshes that do not require an intermediate layer of pyramidal elements. The implicit Newmark time stepping scheme is employed for the tetrahedral elements which allows for local mesh refinement while avoiding a reduced time step.…”

Section: Introductionmentioning

confidence: 99%

Locally implicit discontinuous Galerkin method for time domain electromagnetics

Dolean

Fahs

Fézoui

et al. 2010

Journal of Computational Physics

View full text Add to dashboard Cite

In the recent years, there has been an increasing interest in discontinuous Galerkin time domain (DGTD) methods for the solution of the unsteady Maxwell equations modeling electromagnetic wave propagation. One of the main features of DGTD methods is their ability to deal with unstructured meshes which are particularly well suited to the discretization of the geometrical details and heterogeneous media that characterize realistic propagation problems. Such DGTD methods most often rely on explicit time integration schemes and lead to block diagonal mass matrices. However, explicit DGTD methods are also constrained by a stability condition that can be very restrictive on highly refined meshes and when the local approximation relies on high order polynomial interpolation. An implicit time integration scheme is a natural way to obtain a time domain method which is unconditionally stable but at the expense of the inversion of a global linear system at each time step. A more viable approach consists of applying an implicit time integration scheme locally in the refined regions of the mesh while preserving an explicit time scheme in the complementary part, resulting in an hybrid explicit–implicit (or locally implicit) time integration strategy. In this paper, we report on our recent efforts towards the development of such a hybrid explicit–implicit DGTD method for solving the time domain Maxwell equations on unstructured simplicial meshes. Numerical experiments for 3D propagation problems in homogeneous and heterogeneous media illustrate the possibilities of the method for simulations involving locally refined meshes

show abstract

Section: Introductionmentioning

confidence: 99%

Locally implicit discontinuous Galerkin method for time domain electromagnetics

Dolean

Fahs

Fézoui

et al. 2010

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…• The FDTD cubes are connected directly to the unstructured tetrahedrons [7], which simplifies mesh generation as there are commercial software tools available that provide such functionality. This approach imposes a continuous tangential electric field at the hybrid interface in the weak sense.…”

Section: Hybrid Methodsmentioning

confidence: 99%

“…We have developed such hybrids [5,6,7] based on the fact that the FEM formulated on brick shaped elements reduces to the FDTD scheme if trapezoidal integration is employed. This observation provides a unifying platform for the hybridization of the FEM and the FDTD scheme.…”

Section: Introductionmentioning

confidence: 99%

Finite element methods with stable hybrid explicit-implicit time-integration schemes

Rylander

2007

2007 International Conference on Electromagnetics in Advanced Applications

Self Cite

View full text Add to dashboard Cite

Finite element methods with stable hybrid explicit-implicit time-integration schemes are reviewed.In particular, constructions that reduce to the well-known finite-difference time-domain (FDTD) scheme on structured grids of cubes are considered. Unstructured tetrahedrons with implicit time-stepping are used in the vicinity of curved and complex boundaries. The tetrahedrons are connected to the FDTD cells either directly or by means of a layer of pyramids. The hybrid methods show second order convergence (when the field solution is regular) with respect to cell size, preserve the nullspace of the curl-operator, do not suffer from spectral contamination, and provide stable-time stepping up to the Courant condition of the FDTD scheme without artificial damping.

show abstract

“…It is feasible to couple implicitly time-stepped tetrahedrons (or triangles) with the Yee scheme in time-domain methods, cf. Degerfeldt and Rylander [10]. For the purpose of explicit schemes on unstructured meshes, discontinuous Galerkin (DG) methods can be formulated on simplicial meshes [11].…”

Section: Introductionmentioning

confidence: 99%

“…For example, the so-called perfectly matched layer [15] is popular for unbounded problems and there are finite element formulations in both frequency domain [16] and time domain [17]. Our proposed element is also a good candidate for coupling the Yee scheme on rectangles to a boundary-fitted triangular mesh, where the Yee scheme is represented by rectangular lowest-order edge elements with mass-lumping [18] and Nitsche's method is applied at the interface [10].…”

Section: Introductionmentioning

confidence: 99%