Petrov–Galerkin and discontinuous-Galerkin methods for time-domain and frequency-domain electromagnetic simulations

Finite-element discretizations for Maxwell’s first-order curl equations in both the time domain and frequency domain are developed. Petrov–Galerkin and discontinuous-Galerkin formulations are compared using higher-order basis functions. Verification cases are run to examine the accuracy of the algorithms on problems with exact solutions. Comparisons with other, well accepted, methodologies are also considered for problems for which exact solutions do not exist. Effects of several parameters, including spatial and temporal refinement, are also examined and the relative efficiency of each scheme is discussed. By considering test cases previously considered by other researchers, it is also demonstrated that the algorithms do not exhibit spurious solutions. Finally, three-dimensional results are compared with test results for a rectangular waveguide for which experimental data has been obtained with the explicit purpose of code-validation. The ability to predict changes in scattering parameters caused by variations in geometric and material properties are examined and it is demonstrated that the algorithms predict these changes with good accuracy.

► High-order Petrov–Galerkin (PG) finite-element solvers have been developed.
► Verification of order-of-accuracy accomplished using exact solutions.
► Validation using scattering parameters from experimental data.
► Efficiency of implicit time-stepping scheme compared with discontinuous-Galerkin (DG).
► PG scheme has similar accuracy as DG scheme but is significantly more efficient.