Abstract:
Multigrid (MG) methods are among the best choice for stable and efficient 3D forward modeling of electromagnetic (EM) fields over large area due to their linear dependenc...Show MoreMetadata
Abstract:
Multigrid (MG) methods are among the best choice for stable and efficient 3D forward modeling of electromagnetic (EM) fields over large area due to their linear dependence of computational time on grid size. However, as the frequency decreases to near zero and/or the grid is increasingly stretched, MG solvers for EM modeling based on the curl-curl equations converge slowly or even diverge. In this letter, we develop an efficient MG algorithm combined with a two-color plane Gauss-Seidel (GS) smoother for finite difference forward modeling of EM fields particularly at low frequencies. In this algorithm, we group different planes of the grid nodes into two colors. In each color, the components attached to different planes are totally decoupled and can be solved simultaneously, which can be distributed to different processors. The Dublin Test Model 1 is used to verify the accuracy of our algorithm and examine the numerical performance of our method against MG algorithms based on a four-color cell-block GS smoother and the Bi-Conjugate Gradient stabilized (BICGstab) smoother (as four-color cell-block GS MG and BICGstab-MG, respectively), and BICGstab and Quasi-Minimal Residual (QMR) both preconditioned with block incomplete lower-upper (blockILU) decomposition (as blockILU-BICGstab and blockILU-QMR, respectively). The numerical test based on OpenMP shows the good parallelization of our algorithm. Grids stretched to different degrees are designed to examine its ability to handle grid-stretching. The numerical performance comparison indicates its remarkable dominance in efficiency and stability.
Published in: IEEE Geoscience and Remote Sensing Letters ( Volume: 20)