Analysis of Periodic Structures via a Time-Domain Finite-Element Formulation With a Floquet ABC

Faster 3D finite element time domain – Floquet absorbing boundary condition modelling using recursive convolution and vector fitting

“…Following discretisation of (32) using (34, 35), the following matrix equation is obtained (note that for a periodic boundary pair the boundaries have identical finite element meshes) (36) which is different from [1]. Along the non-periodic boundaries S 1 and S 2 the test and basis functions are expressed as follows…”

“…The RC has lower computer memory requirements than the SC in [1]. In addition, although the single section RC uses more exponential terms than the multi-section RC (MS-RC) approach described in [4] The use of a single section RC over a large time window is made possible using the vector fitting (VF) method [5].…”

“…The evaluation of the integral term in (64) affects the stability of the FETD method [1]. The use of the trapezoidal integration is shown in [4].…”

“…In section II we present a detailed description of our finite element formulation as our time domain boundary integral formulation and the convolution implementation are significantly different from those of [1]. This difference is mainly due to the final form of our frequency domain boundary integral formulation (see eq.…”

“…We also employ the reciprocal weighting function approach proposed in [7,8] which does not lead to the stability problem associated with eq. (16) of [1]. Section III considers the RC implementation.…”