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
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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.