Implementation and optimization of GPU‐based parallel one‐step leapfrog ADI‐FDTD for far‐field scattering problems

Abstract

The one‐step leapfrog alternative‐direction‐implicit finite‐difference time‐domain (ADI‐FDTD), free from the Courant‐Friedrichs‐Lewy (CFL) stability condition and sub‐step computations, is efficient when dealing with fine grid problems. However, solution of the numerous tridiagonal systems still imposes a great computational burden and makes the method hard to execute in parallel. In this paper, we proposed an efficient graphic processing unit (GPU)‐based parallel implementation of the one‐step leapfrog ADI‐FDTD for the far‐field EM scattering simulation of objects, in which we present and analyze the manners of calculation area division and thread allocation and a data layout transformation of z components is proposed to achieve better memory access mode, which is a key factor affecting GPU execution efficiency. The simulation experiment is carried out to verify the accuracy and efficiency of the GPU‐based implementation. The simulation results show that there is a good agreement between the proposed one‐step leapfrog ADI‐FDTD method and Yee's FDTD in solving the far‐field scattering problem and huge benefits in performance were encountered when the method was accelerated using GPU technology.

3D memory-reduced form of the one-step leapfrog ADI-FDTD method based on the electromagnetic divergence relationship

“…Therefore, each field component can be explicitly expressed by the rest two. For example, E y can be calculated with known E x and E z using the modified divergence-like formula as described in (10) and so does the magnetic field (11), where the subscript (i, j, k) indicates the specific grid position. Here briefly explains how the proposed algorithm (R-leapfrog ADI-FDTD) is realized through calculating E y locally and saving it temporarily.…”

“…Assume E x and E z have been obtained by one-step leapfrog ADI-FDTD over the entire 3-dimensional simulation region, and E y on the previous plane j − 1 2 has been calculated by (10). E y on plane j + 1 2 could be available using (10) again and stored in the same variable of vez since E y | :,j− 1 2 ,: will not be used anymore. Then E x , E z , and E y is used to update the magnetic field components by the one-step leapfrog ADI-FDTD.…”

“…Therefore, removing the affection caused by the source on (8) is needed. Then update E y locally using (10) with an additional compensation on the source grids.…”

“…For the initial step, E y | :, 1 2 ,: on plane j = 1 2 could be obtained by the conventional one-step leapfrog ADI-FDTD. Assume E x and E z have been obtained by one-step leapfrog ADI-FDTD over the entire 3-dimensional simulation region, and E y on the previous plane j − 1 2 has been calculated by (10). E y on plane j + 1 2 could be available using (10) again and stored in the same variable of vez since E y | :,j− 1 2 ,: will not be used anymore.…”

“…Further developments and wide applications of the one-step leapfrog ADI-FDTD, such as parallel computing and electromagnetic analysis in dispersive and lossy media, have been reported in recent years. [10][11][12][13][14] Besides the CFL limit, another primary drawback of various FDTD algorithms is computer memory-consuming. The size of each spatial grid should be small enough to guarantee high simulation precision.…”