A Space-Time Discontinuous Galerkin Trefftz Method for Time Dependent Maxwell's Equations

DOI10.1137/140999323zbMath1330.65148arXiv1412.2637OpenAlexW1899086482MaRDI QIDQ2947049

Fritz Kretzschmar, Herbert Egger, Sascha M. Schnepp, Thomas Weiland

Publication date: 21 September 2015

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.2637

zbMATH Keywords

stabilityconsistencydiscontinuous Galerkin methodelectromagnetic wave propagationinitial boundary value problemnumerical testTrefftz methods

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Electromagnetic theory (general) (78A25) Maxwell equations (35Q61)

Related Items (19)

An arbitrary-order cell method with block-diagonal mass-matrices for the time-dependent 2D Maxwell equations ⋮ Space-time discontinuous Galerkin discretizations for linear first-order hyperbolic evolution systems ⋮ A Space-Time Trefftz Discontinuous Galerkin Method for the Linear Schrödinger Equation ⋮ A space-time interior penalty discontinuous Galerkin method for the wave equation ⋮ Development of an explicit non-staggered scheme for solving three-dimensional Maxwell's equations ⋮ An asynchronous spacetime discontinuous Galerkin finite element method for time domain electromagnetics ⋮ On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation ⋮ A Trefftz Polynomial Space-Time Discontinuous Galerkin Method for the Second Order Wave Equation ⋮ Global space-time Trefftz DG schemes for the time-dependent linear wave equation ⋮ Embedded Trefftz discontinuous Galerkin methods ⋮ Tent pitching and Trefftz-DG method for the acoustic wave equation ⋮ A space-time Trefftz DG scheme for the time-dependent Maxwell equations in anisotropic media ⋮ A space-time DG method for the Schrödinger equation with variable potential ⋮ A ray-based IPDG method for high-frequency time-domain acoustic wave propagation in inhomogeneous media ⋮ A discontinuous Galerkin method for poroelastic wave propagation: the two-dimensional case ⋮ Transparent boundary conditions for a discontinuous Galerkin Trefftz method ⋮ A space-time Trefftz discontinuous Galerkin method for the acoustic wave equation in first-order formulation ⋮ Space–time Trefftz-DG approximation for elasto-acoustics ⋮ A space–time quasi-Trefftz DG method for the wave equation with piecewise-smooth coefficients

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Non-dissipative space-time \(hp\)-discontinuous Galerkin method for the time-dependent Maxwell equations
• Efficient large scale electromagnetic simulations using dynamically adapted meshes with the discontinuous Galerkin method
• Discretization of the wave equation using continuous elements in time and a hybridizable discontinuous Galerkin method in space
• Transparent boundary conditions for a discontinuous Galerkin Trefftz method
• The complete Trefftz method
• Stabilized interior penalty methods for the time-harmonic Maxwell equations.
• Plane wave approximation of homogeneous Helmholtz solutions
• Dispersive and dissipative properties of discontinuous Galerkin finite element methods for the second-order wave equation
• A spatial high-order hexahedral discontinuous Galerkin method to solve Maxwell's equations in time domain
• Discontinuous Galerkin methods with Trefftz approximations
• A hybrid discontinuous in space and time Galerkin method for wave propagation problems
• Modeling Effects of Electromagnetic Waves on Thin Wires with a High-Order Discontinuous Galerkin Method
• Plane Wave Discontinuous Galerkin Methods for the 2D Helmholtz Equation: Analysis of the p-Version
• Time Domain Integral Equation Methods in Computational Electromagnetism
• A space-time discontinuous Galerkin method for the solution of the wave equation in the time domain
• Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media
• Survey of trefftz-type element formulations
• Natural Boundary Element Methods for the Electric Field Integral Equation on Polyhedra
• Mixed Discontinuous Galerkin Approximation of the Maxwell Operator
• A priorierror analysis of space–time Trefftz discontinuous Galerkin methods for wave problems
• Finite‐volume time‐domain (FVTD) modelling of a broadband double‐ridged horn antenna
• Finite Element Methods for Maxwell's Equations
• The $hp$-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell equations
• Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations
• Computing with hp-ADAPTIVE FINITE ELEMENTS
• RF & Microwave Simulation with the Finite Integration Technique – From Component to System Design
• Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes

This page was built for publication: A Space-Time Discontinuous Galerkin Trefftz Method for Time Dependent Maxwell's Equations