Computer Methods in Applied Mechanics and Engineering
A dispersion analysis of finite element methods for Maxwell's equations
SIAM Journal on Scientific Computing
On the solution of time-harmonic scattering problems for Maxwell's equations
SIAM Journal on Mathematical Analysis
Efficient management of parallelism in object-oriented numerical software libraries
Modern software tools for scientific computing
Discrete compactness and the approximation of Maxwell's equations in R3
Mathematics of Computation
Computational aspects of the ultra-weak variational formulation
Journal of Computational Physics
SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems
ACM Transactions on Mathematical Software (TOMS)
A perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.45 |
A Galerkin least squares finite element method for the solution of the time-harmonic Maxwell's equations using Nedelec elements is proposed. This method appends a least-squares term, evaluated within element interiors, to the standard Galerkin method. For the case of lowest order hexahedral element, the numerical parameter multiplying this term is determined so as to optimize the dispersion properties of the resulting formulation. In particular, explicit expressions for this parameter are derived that lead to methods with no dispersion error for propagation along a specified direction and reduced dispersion error over all directions. It is noted that this method is easy to implement and does not add to the computational costs of the standard Galerkin method. The performance of this method is tested on problems of practical interest.