Extension of the FDTD Huygens Subgridding Algorithm to Two Dimensions

Abstract

This paper extends to two dimensions the finite-difference time-domain Huygens subgridding algorithm previously published in the one dimensional case. The algorithm is described in detail and several numerical experiments are provided to illustrate its possibilities and to demonstrate its effectiveness.Index Terms-Domain decomposition, equivalent sources, finite-difference methods, finite-difference time-domain (FDTD) methods, subgrid.

Local time–space mesh refinement for simulation of elastic wave propagation in multi-scale media

“…On the one hand, these values are defined on a fine grid, but due to the consistency of grids (11) Ω C σ 33 ⊆ Ω F σ 33 and Ω C u 1 ⊆ Ω F u 1 ; thus, the corresponding points belong both to the fine and the coarse grids. On the other hand, their straightforward substitution (use of the injection type of restriction operator [80]) can bring about problems with stability, as is reported in [77,52,53]. Therefore, a special restriction operator with spectral smoothing is applied, as specified in the next section.…”

“…A completely different technique was proposed in [47], studied in [48,49] and developed in [50] and [51], where the conditions at the interface are constructed to conserve the total energy of the solution, thus ensuring stability. Another technique has been recently reported in [52][53][54], where the connection between the grids is realized by means of equivalent currents. However, the mentioned techniques have two general drawbacks.…”

Application of Underwater Low Frequency Electromagnetic Fields Detection With TSS FDTD Method

“…In the works [9][10][11][12], Huygens subgridding (HSG) method is presented to divide the entire problem space into several parts with different time and space increments. For the HSG, two spaces are connected by two Huygens surfaces called inner surface (IS) and outer surface (OS).…”

Finite-difference algorithm with local time-space grid refinement for simulation of waves

“…A completely different technique was proposed in [29], studied in [30,31] and developed in [32,33] where the conditions on the interface are constructed to conserve the total energy of the solution thus ensuring the stability. Another technique was reported recently in [34][35][36], where the connection between the grids is realized by means of equivalent currents. However, the mentioned techniques have two general drawbacks.…”

“…9, markers correspond to numerical experiments. Solid lines and crosses correspond to ppw equal to 20, dashed lines and circles correspond to ppw equal to35 …”