1,617 research outputs found
Solution of the time-harmonic Maxwell equations using discontinuous Galerkin methods
We present numerical results concerning the solution of the time-harmonic
Maxwell's equations discretized by discontinuous Galerkin methods. In
particular, a numerical study of the convergence, which compares different
strategies proposed in the literature for the elliptic Maxwell equations, is
performed in the two-dimensional case.Comment: Preprint submitted for publication for the proceedings of ICCAM06
(11/04/2007
Dispersion and dissipation error in high-order Runge-Kutta discontinuous Galerkin discretisations of the Maxwell equations
Different time-stepping methods for a nodal high-order discontinuous Galerkin discretisation of the Maxwell equations are discussed. A comparison between the most popular choices of Runge-Kutta (RK) methods is made from the point of view of accuracy and computational work. By choosing the strong-stability-preserving Runge-Kutta (SSP-RK) time-integration method of order consistent with the polynomial order of the spatial discretisation, better accuracy can be attained compared with fixed-order schemes. Moreover, this comes without a significant increase in the computational work. A numerical Fourier analysis is performed for this Runge-Kutta discontinuous Galerkin (RKDG) discretisation to gain insight into the dispersion and dissipation properties of the fully discrete scheme. The analysis is carried out on both the one-dimensional and the two-dimensional fully discrete schemes and, in the latter case, on uniform as well as on non-uniform meshes. It also provides practical information on the convergence of the dissipation and dispersion error up to polynomial order 10 for the one-dimensional fully discrete scheme
Breaking spaces and forms for the DPG method and applications including Maxwell equations
Discontinuous Petrov Galerkin (DPG) methods are made easily implementable
using `broken' test spaces, i.e., spaces of functions with no continuity
constraints across mesh element interfaces. Broken spaces derivable from a
standard exact sequence of first order (unbroken) Sobolev spaces are of
particular interest. A characterization of interface spaces that connect the
broken spaces to their unbroken counterparts is provided. Stability of certain
formulations using the broken spaces can be derived from the stability of
analogues that use unbroken spaces. This technique is used to provide a
complete error analysis of DPG methods for Maxwell equations with perfect
electric boundary conditions. The technique also permits considerable
simplifications of previous analyses of DPG methods for other equations.
Reliability and efficiency estimates for an error indicator also follow.
Finally, the equivalence of stability for various formulations of the same
Maxwell problem is proved, including the strong form, the ultraweak form, and a
spectrum of forms in between
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