BOR-FDTD subgridding based on finite element principles

Abstract

In this paper a recently developed provably passive and stable 3D FDTD subgridding technique, based on finite elements principles, is extended to Body-Of-Revolution (BOR) FDTD. First, a suitable choice of basis functions is presented together with the mechanism to assemble them into an overall mesh consisting of coarse and fine mesh cells. Invoking appropriate masslumping concepts then leads to an explicit leapfrog time stepping algorithm for the amplitudes of the basis functions. Attention is devoted to provide the reader with insight into the updating equations, in particular at a subgridding boundary. Stability, grid reflection and dispersion are also discussed. Finally, some numerical examples for toroidal and cylindrical cavities demonstrate the stability and accuracy of the method.

Implicit Local Refinement for Evanescent Layers Combined With Classical FDTD

“…There are only two special cases to be considered: one involving the black arrow (electric field) at the left interface (x = x 1 ), and one involving the black dot (magnetic induction) at the right interface (x = x 2 ). Both the FDTD method and the fully implicit method can be interpreted as finite-element methods with specific basis-and test-functions [1], [4], a fact which has been used to construct explicit local refinement schemes [4], [10]. Without going into detail, these finite-element interpretations lead to the following discrete equation for the magnetic field at the right interface…”

Time-domain formulation of cold plasma based on mass-lumped finite elements

“…In simple dielectrics, the (ε 0 + ∑ s [A 3 ]) −1 factor reduces to a scalar and it hence suffices that the electric basis function E i is curl-conforming. However, in plasma's this does no longer suffice and the classical "Whitney" or "Lobatto" basis functions proposed in [1] or their BOR counterparts presented in [3] are not suitable for cold plasma. A suitable extension of these BOR basis functions is given below.…”

“…for E θ this implies that 9 elementary basis functions are combined to get obtain an overall basis function in one particular cell. The functions that are thus defined are natural generalisations of the BOR-FDTD basis-functions introduced in [3] and reduce to those functions when n = 1. The cell structure ( fig.…”

“…(BOR) FDTD in simple dielectric media can be derived from finite-element principles by approximating testing integrals such as (6) by trapezoidal integration [1,3]. This socalled mass lumping allows to express the effect of place dependent permittivity and permeability by means of diagonal matrices which are easily invertible (specifically, [ ε ] i, j = E i · E j dV must be inverted).…”

Numerical assessment of the combination of subgridding and the perfectly matched layer grid termination in the finite difference time domain method

“…Chilton combined both concepts to one subgridding algorithm with refinement factors 1 : N and later M : N (). This approach was extended to BOR‐FDTD in .…”