An asynchronous spacetime discontinuous Galerkin finite element method for time domain electromagnetics

Abedi, Reza; Mudaliar, Saba

doi:10.1016/j.jcp.2017.09.001

Cited by 11 publications

(3 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An alternative to time-stepping methods is a space-time approach. Most approaches apply discontinuous Galerkin methods to Maxwell's equations, see [1,10,11,24,36] and the references therein. Note that these methods are non-conforming in general.…”

Section: Introductionmentioning

confidence: 99%

Numerical study of conforming space‐time methods for Maxwell's equations

Hauser,

Zank

2023

Numerical Methods Partial

View full text Add to dashboard Cite

Time‐dependent Maxwell's equations govern electromagnetics. Under certain conditions, we can rewrite these equations into a partial differential equation of second order, which in this case is the vectorial wave equation. For the vectorial wave equation, we examine numerical schemes and their challenges. For this purpose, we consider a space‐time variational setting, that is, time is just another spatial dimension. More specifically, we apply integration by parts in time as well as in space, leading to a space‐time variational formulation with different trial and test spaces. Conforming discretizations of tensor‐product type result in a Galerkin–Petrov finite element method that requires a CFL condition for stability which we study. To overcome the CFL condition, we use a Hilbert‐type transformation that leads to a variational formulation with equal trial and test spaces. Conforming space‐time discretizations result in a new Galerkin–Bubnov finite element method that is unconditionally stable. In numerical examples, we demonstrate the effectiveness of this Galerkin–Bubnov finite element method. Furthermore, we investigate different projections of the right‐hand side and their influence on the convergence rates. This paper is the first step toward a more stable computation and a better understanding of vectorial wave equations in a conforming space‐time approach.

show abstract

Section: Introductionmentioning

confidence: 99%

Numerical study of conforming space‐time methods for Maxwell's equations

Hauser,

Zank

2023

Numerical Methods Partial

View full text Add to dashboard Cite

show abstract

“…The methods allow a comparatively easy handling of elements of various types and shapes, irregular non-conforming meshes and even locally varying polynomial degree. For the linear situation the papers [31]- [34] can be mentioned as examples, for dispersive media we refer to [35], [36]. For the system of Maxwell's equations with material nonlinearities, there are still very few rigorous analysis, error estimates, and simulation results using time domain finite element methods ((TDFEM/TDdG) available [26], [37]- [46].…”

Section: Introductionmentioning

confidence: 99%

Energy-Stable Time-Domain Finite Element Methods for the 3D Nonlinear Maxwell's Equations

Anees

Angermann

2020

IEEE Photonics J.

View full text Add to dashboard Cite

In this paper, time-domain finite element methods for the full system of Maxwell's equations with cubic nonlinearities in 3D are presented, including a selection of computational experiments. The new capabilities of these methods are to efficiently model linear and nonlinear effects of the electrical polarization. The novel strategy has been developed to bring under control the discrete nonlinearity model in space and time. It results in energy stable discretizations both at the semi-discrete and the fully discrete levels, with spatial discretization using edge and face elements (Nédeléc-Raviart-Thomas formulation). In particular, the proposed time discretization schemes are unconditionally stable with respect to a specially defined nonlinear electromagnetic energy, which is an upper bound of the electromagnetic energy commonly used. The approaches presented prove to be robust and allow the modeling of 3D optical problems that can be directly derived from the full system of Maxwell's nonlinear equations, and allow the treatment of complex nonlinearities and geometries of various physical systems coupled with electromagnetic fields.

show abstract

“…Many papers have been written about time domain discontinuous Galerkin (TDDG) methods in computational electromagnetics [38]- [49]. Other time domain methods to solve either the Maxwell's equations or the vector wave equation can be found in [50]- [62].…”

Section: Introductionmentioning

confidence: 99%

Time Domain Finite Element Method for Maxwell’s Equations

Anees

Angermann

2019

IEEE Access

View full text Add to dashboard Cite

In this paper, we discuss a time domain finite element method for the approximate solution of Maxwell's equations. A weak formulation is derived for the electric and magnetic fields with appropriate initial and boundary conditions, and the problem is discretized both in space and time. In space, Nédeléc curl-conforming and Raviart-Thomas div-conforming finite elements are used to discretize the electric and magnetic fields, respectively. The backward Euler and symplectic schemes are applied to discretize the problem in time. For this system, we prove an error estimate. In addition, computational experiments are presented to validate the method, the electric and magnetic fields are visualized. The method also allows treating complex geometries of various physical systems coupled to electromagnetic fields in 3D.INDEX TERMS Backward Euler method, error estimates, Maxwell's equations, time domain finite element methods, simulation, symplectic method, visualization.

show abstract

An asynchronous spacetime discontinuous Galerkin finite element method for time domain electromagnetics

Cited by 11 publications

References 49 publications

Numerical study of conforming space‐time methods for Maxwell's equations

Numerical study of conforming space‐time methods for Maxwell's equations

Energy-Stable Time-Domain Finite Element Methods for the 3D Nonlinear Maxwell's Equations

Time Domain Finite Element Method for Maxwell’s Equations

Contact Info

Product

Resources

About