A mass-lumped mixed finite element method for Maxwell's equations

Abstract

A novel mass-lumping strategy for a mixed finite element approximation of Maxwell's equations is proposed. On structured orthogonal grids the resulting method coincides with the spatial discretization of the Yee scheme. The proposed method, however, generalizes naturally to unstructured grids and anisotropic materials and thus yields a variational extension of the Yee scheme for these situations.

A convolution quadrature method for Maxwell's equations in dispersive media

“…Note that equation (11) was obtained from (8) after dividing by ε 0 (ε i,s − ε ′ i,∞ ). For appropriate space discretization schemes, the mass matrices M * are symmetric, positive-definite, and diagonal or block-diagonal [3,7], such that ( 9)- (11) amounts to an explicit time-stepping scheme. Moreover, the method satisfies the following discrete equivalent of the underlying energy-dissipation identity.…”

A second order finite element method with mass lumping for Maxwell's equations on tetrahedra

“…In order to obtain the full geometric flexibility of finite element approximations, we here consider mass-lumping for Maxwell's equations on tetrahedral meshes, for which only few results are available. Lowest order Nédélec elements of type one and two has been proposed in [9] and first order convergence has been established. Related methods have been proposed in [3] in the context of the finite integration technique, but no convergence analysis is given there.…”