Journal article
Multicolor-MG: An efficient parallel multigrid code based on multicolor block-wise Gauss-Seidel smoothers for 3D natural source electromagnetic forward modeling
Geophysics, Vol.90(4), pp.F43-F52
07/01/2025
DOI: 10.1190/GEO2024-0942.1
Abstract
Large-scale 3D natural source electromagnetic (EM) inversion requires efficient forward modeling because the inversion necessitates expensive iterations. The multigrid (MG) solvers are considered a potentially efficient technique for the largescale 3D forward modeling of EM fields due to their linear dependence of computational time on grid size. Memory also scales linearly with grid size, making MG solvers very memory efficient and, thus, computationally efficient when compared with direct solvers that scale with N2 and N4/3 (N is degrees of freedom) in time and memory. We develop an open-source Fortran MG code based on multicolor block-wise smoothers for efficient finite-difference frequency-domain forward-modeling of 3D natural source EM data. The code is modular and can be extended easily for other similar forward-modeling problems involving the curl-curl operator. The implemented algorithm includes the four-color cell-block Gauss-Seidel (GS) MG, the four-color line-wise GS MG, and the two-color plane-wise GS MG variants. These all guarantee the divergence-free condition for the currents in local regions defined by blocks in which all components are updated simultaneously. The benefit of applying the coloring strategy is that the algorithm is readily parallelized for the systems associated with the same color. The parallel implementation in the code is based on OpenMP but more advanced parallel strategies can also be developed by the user. Two numerical examples are included where our multicolor block-wise GS MG algorithms are compared with one commonly used auxiliary-space Maxwell solver, based on the algebraic MG and Hiptmair-Xu decomposition, demonstrating the accuracy and numerical efficiency of our multicolor block-wise MG solvers.
Details
- Title: Subtitle
- Multicolor-MG: An efficient parallel multigrid code based on multicolor block-wise Gauss-Seidel smoothers for 3D natural source electromagnetic forward modeling
- Creators
- Yongfei Wang - Tsinghua UniversityJianxin Liu - Central South UniversityGary Egbert - Oregon State UniversityRongwen Guo - Central South UniversityJian Li - Central South UniversityGangqiang Yang - Central South UniversityShengqi Tian - Central South UniversityHang Chen - Boise State University
- Resource Type
- Journal article
- Publication Details
- Geophysics, Vol.90(4), pp.F43-F52
- DOI
- 10.1190/GEO2024-0942.1
- ISSN
- 0016-8033
- eISSN
- 1942-2156
- Publisher
- SOC EXPLORATION GEOPHYSICISTS - SEG
- Number of pages
- 10
- Grant note
- 2024SM114 / Shuimu Tsinghua Scholar Program of Tsinghua University 2024M761704 / China Postdoctoral Science Foundation High Performance Computing Center of Central South University 42130810; 42174171; 42474112 / National Natural Science Foundation of China; National Natural Science Foundation of China (NSFC)
- Language
- English
- Date published
- 07/01/2025
- Academic Unit
- Earth and Environmental Sciences
- Record Identifier
- 9984962529702771
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