Nonreflecting boundary conditions for time-dependent scattering
Journal of Computational Physics
Three-dimensional perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
Nonreflecting boundary conditions for Maxwell's equations
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
On the construction and analysis of absorbing layers in CEM
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Numerical solution of the Helmholtz equation in 2D and 3D using a high-order Nystro¨m discretization
Journal of Computational Physics
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Field Computation by Moment Methods
Field Computation by Moment Methods
A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods
SIAM Journal on Numerical Analysis
Journal of Scientific Computing
Nodal high-order methods on unstructured grids
Journal of Computational Physics
Journal of Scientific Computing
Journal of Computational Physics
Journal of Scientific Computing
Interior penalty discontinuous Galerkin method for Maxwell's equations: Energy norm error estimates
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
Time step restrictions for Runge-Kutta discontinuous Galerkin methods on triangular grids
Journal of Computational Physics
High Order Strong Stability Preserving Time Discretizations
Journal of Scientific Computing
Interior Penalty Discontinuous Galerkin Method for Maxwell's Equations in Cold Plasma
Journal of Scientific Computing
Locally implicit discontinuous Galerkin method for time domain electromagnetics
Journal of Computational Physics
Explicit local time-stepping methods for Maxwell's equations
Journal of Computational and Applied Mathematics
Error analysis of a discontinuous Galerkin method for Maxwell equations in dispersive media
Journal of Computational Physics
Interior penalty DG methods for Maxwell's equations in dispersive media
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
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In this paper we introduce a new RKDG method for problems of wave propagation that achieves full high-order convergence in time and space. The novelty of the method resides in the way in which it marches in time. It uses an mth-order m-stage, low storage SSP-RK scheme which is an extension to a class of non-autonomous linear systems of a recently designed method for autonomous linear systems. This extension allows for a high-order accurate treatment of the inhomogeneous, time-dependent terms that enter the semi-discrete problem on account of the physical boundary conditions. Thus, if polynomials of degree k are used in the space discretization, the RKDG method is of overall order m = k + 1, for any k 0. Moreover, we also show that the attainment of high-order space--time accuracy allows for an efficient implementation of post-processing techniques that can double the convergence order. We explore this issue in a one-dimensional setting and show that the superconvergence of fluxes previously observed in full space--time DG formulations is also attained in our new RKDG scheme. This allows for the construction of higher-order solutions via local interpolating polynomials. Indeed, if polynomials of degree k are used in the space discretization together with a time-marching method of order 2k + 1, a post-processed approximation of order 2k + 1 is obtained. Numerical results in one and two space dimensions are presented that confirm the predicted convergence properties.