Journal of Computational Physics
FEMSTER: An object-oriented class library of high-order discrete differential forms
ACM Transactions on Mathematical Software (TOMS)
The Gautschi time stepping scheme for edge finite element discretizations of the Maxwell equations
Journal of Computational Physics
Journal of Computational Physics
Higher-order mimetic methods for unstructured meshes
Journal of Computational Physics
Discrete calculus methods for diffusion
Journal of Computational Physics
Application of the symplectic finite-difference time-domain scheme to electromagnetic simulation
Journal of Computational Physics
An efficient vector finite element method for nonlinear electromagnetic modeling
Journal of Computational Physics
Journal of Computational Physics
Reduced models for solving particle beams and plasma physics problems
MATH'08 Proceedings of the American Conference on Applied Mathematics
Application of operator splitting to the Maxwell equations including a source term
Applied Numerical Mathematics
Explicit local time-stepping methods for Maxwell's equations
Journal of Computational and Applied Mathematics
Composition Methods, Maxwell's Equations, and Source Terms
SIAM Journal on Numerical Analysis
Time-integration methods for finite element discretisations of the second-order Maxwell equation
Computers & Mathematics with Applications
Differential forms for scientists and engineers
Journal of Computational Physics
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In this paper the vector finite element time-domain (VFETD) method is derived, analyzed, and validated. The VFETD method uses edge vector finite elements as a basis for the electric field and face vector finite elements as a basis for the magnetic flux density. The Galerkin method is used to convert Maxwell's equations to a coupled system of ordinary differential equations. The leapfrog method is used to advance the fields in time. The method is shown to be stable and to conserve energy and charge for arbitrary hexahedral grids. A numerical dispersion analysis shows the method to be second order accurate on distorted hexahedral grids. Several computational experiments are performed to determine the accuracy and efficiency of the method.