GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Computer Methods in Applied Mechanics and Engineering
Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
Stabilized finite element methods. I: Application to the advective-diffusive model
Computer Methods in Applied Mechanics and Engineering
The origin of spurious solutions in computational electromagnetics
Journal of Computational Physics
A comparative study of characteristic-based algorithms for the Maxwell equations
Journal of Computational Physics
High-order accurate discontinuous finite element solution of the 2D Euler equations
Journal of Computational Physics
A Finite-Volume Method for the Maxwell Equations in the Time Domain
SIAM Journal on Scientific Computing
Nodal high-order methods on unstructured grids
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Journal of Computational Physics
Unstructured Grid-Based Discontinuous Galerkin Method for Broadband Electromagnetic Simulations
Journal of Scientific Computing
Locally divergence-free discontinuous Galerkin methods for the Maxwell equations
Journal of Computational Physics
Journal of Computational Physics
Discontinuous Galerkin Methods Applied to Shock and Blast Problems
Journal of Scientific Computing
Preconditioning methods for discontinuous Galerkin solutions of the Navier-Stokes equations
Journal of Computational Physics
Engineering Electromagnetics
Hi-index | 31.45 |
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.