Journal article
An efficient multigrid solver based on a four-color cell-block Gauss-Seidel smoother for 3D magnetotelluric forward modeling
Geophysics, Vol.87(3), pp.E121-E133
05/01/2022
DOI: 10.1190/geo2021-0275.1
Abstract
Practical application of 3D magnetotelluric inversion requires efficient forward modeling of electromagnetic (EM) fields in the earth. To resolve realistic 3D structures, large computational domains and extremely large linear systems of equations are required. The iterative solvers, which are almost exclusively used to solve these systems, can be inefficient due to the abundant null space of the curl-curl operator. Multigrid (MG) solvers are considered a potentially efficient technique for solving such problems. However, due to the abundant null solution space and existence of the air layer, MG solvers can still converge slowly or even diverge. We have developed an efficient MG solver for finite-difference frequency-domain EM solution. In this algorithm, the excellent smoothing property of an efficient fourcolor cell-block Gauss-Seidel (GS) is exploited to remove the short-range errors effectively, and the interpolation and prolongation operators are used to handle the long-range errors. They work as a whole to speed the convergence of our algorithm remarkably. Because all of the nodes for the four-color cell block GS are grouped into four colors and the edge components attached to different nodes in each color are completely de coupled, this can be used to develop a highly vectorized or parallelized algorithm. Another important property is that our algorithm is locally current divergence free, effectively eliminating spurious solutions in the null space of the curl-curl operator. The accuracy and efficiency of the algorithm are verified by comparing the numerical solutions obtained with our MG solver to those from the biconjugate gradient stabilized solver with different preconditioners based on synthetic models and a model from 3D inversion. Comparisons, in terms of iteration number and computational time, indicate that our algorithm is extremely stable and efficient relative to the other solvers. Our MG algorithm will be suitable for massively parallel computing as well.
Details
- Title: Subtitle
- An efficient multigrid solver based on a four-color cell-block Gauss-Seidel smoother for 3D magnetotelluric forward modeling
- Creators
- Rongwen Guo - Central South UniversityYongfei Wang - Central South UniversityGary D. Egbert - Oregon State UniversityJianxin Liu - Central South UniversityRong Liu - Central South UniversityKejia Pan - Central South UniversityJian Li - Central South UniversityHang Chen - Boise State University
- Resource Type
- Journal article
- Publication Details
- Geophysics, Vol.87(3), pp.E121-E133
- DOI
- 10.1190/geo2021-0275.1
- ISSN
- 0016-8033
- eISSN
- 1942-2156
- Publisher
- SOC EXPLORATION GEOPHYSICISTS - SEG
- Number of pages
- 13
- Grant note
- 42130810; 41674079; 41874086; 42004065; 42074165; 42174171 / National Natural Science Foundation of China; National Natural Science Foundation of China (NSFC) CX20210127 / Project of Innovation-driven Plan from Hunan province GXNSFGA380004 / Guangxi Natural Science Foundation; National Natural Science Foundation of Guangxi Province 2020JJ4692 / Hunan Natural Science Foundation; Natural Science Foundation of Hunan Province
- Language
- English
- Date published
- 05/01/2022
- Academic Unit
- Earth and Environmental Sciences
- Record Identifier
- 9984962534002771
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