A new family of mixed finite elements in IR3
Numerische Mathematik
A modified equation approach to constructing fourth order methods for acoustic wave propagation
SIAM Journal on Scientific and Statistical Computing
A mixed finite element formulation for Maxwell's equations in the time domain
Journal of Computational Physics
SIAM Journal on Scientific Computing
Higher Order Triangular Finite Elements with Mass Lumping for the Wave Equation
SIAM Journal on Numerical Analysis
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Nodal high-order methods on unstructured grids
Journal of Computational Physics
Mixed Discontinuous Galerkin Approximation of the Maxwell Operator
SIAM Journal on Numerical Analysis
High-order RKDG Methods for Computational Electromagnetics
Journal of Scientific Computing
Conservative space-time mesh refinement methods for the FDTD solution of Maxwell's equations
Journal of Computational Physics
Discontinuous Galerkin Approximation of the Maxwell Eigenproblem
SIAM Journal on Numerical Analysis
Interior penalty discontinuous Galerkin method for Maxwell's equations: Energy norm error estimates
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
The Mortar-Discontinuous Galerkin Method for the 2D Maxwell Eigenproblem
Journal of Scientific Computing
Optimal Error Estimates for the Fully Discrete Interior Penalty DG Method for the Wave Equation
Journal of Scientific Computing
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Numerical Integration of Damped Maxwell Equations
SIAM Journal on Scientific Computing
Energy Conserving Explicit Local Time Stepping for Second-Order Wave Equations
SIAM Journal on Scientific Computing
High-order explicit local time-stepping methods for damped wave equations
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
Causal-Path Local Time-Stepping in the discontinuous Galerkin method for Maxwell's equations
Journal of Computational Physics
Journal of Scientific Computing
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Explicit local time-stepping methods are derived for time dependent Maxwell equations in conducting and non-conducting media. By using smaller time steps precisely where smaller elements in the mesh are located, these methods overcome the bottleneck caused by local mesh refinement in explicit time integrators. When combined with a finite element discretisation in space with an essentially diagonal mass matrix, the resulting discrete time-marching schemes are fully explicit and thus inherently parallel. In a non-conducting source-free medium they also conserve a discrete energy, which provides a rigorous criterion for stability. Starting from the standard leap-frog scheme, local time-stepping methods of arbitrarily high accuracy are derived for non-conducting media. Numerical experiments with a discontinuous Galerkin discretisation in space validate the theory and illustrate the usefulness of the proposed time integration schemes.