1887
Volume 73, Issue 1
  • E-ISSN: 1365-2478

Abstract

Abstract

Quantitative interpretation of the data from controlled‐source electromagnetic methods, whether via forward modelling or inversion, requires solving a considerable number of forward problems, and multigrid methods are often employed to accelerate the solving process. In this study, a new extrapolation cascadic multigrid method is employed to solve the large sparse complex linear system arising from the finite element approximation of Maxwell's equations using secondary potentials. The equations using secondary potentials are discretized by the classic nodal finite element method on nonuniform rectilinear grids. The resulting linear systems are solved by the extrapolation cascadic multigrid method with a new prolongation operator and preconditioned Stabilized bi‐conjugate gradient method smoother. High‐order interpolation and global extrapolation formulas are utilized to construct the multigrid prolongation operator. The extrapolation cascadic multigrid method with the new prolongation operator is easier to implement and more flexible in application than the original one. Finally, several synthetic examples including layered models, models with anisotropic anomalous bodies or layers, are used to validate the accuracy and efficiency of the proposed method. Numerical results show that the extrapolation cascadic multigrid method improves the efficiency of 3D controlled‐source electromagnetic forward modelling a lot, compared with traditional iterative solvers and some state‐of‐the‐art methods or software (e.g., preconditioned flexible generalized minimal residual method, emg3d) in the considered models and grid settings. The efficiency benefit is more evident as the number of unknowns increases, and the proposed method is more efficient at low frequencies. The extrapolation cascadic multigrid method can also be used to solve systems of equations arising from related applications, such as induction logging, airborne electromagnetic, etc.

© 2025 European Association of Geoscientists & Engineers. © 2024 European Association of Geoscientists & Engineers.
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3D Controlled‐source electromagnetic modelling in anisotropic media using secondary potentials and a cascadic multigrid solver
Geophysical Prospecting 73, 284 (2024); https://doi.org/10.1111/1365-2478.13624
/content/journals/10.1111/1365-2478.13624
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  • Article Type: Research Article
Keyword(s): anisotropy; controlled‐source electromagnetic modelling; electrical properties; electromagnetics; moldeling; multigrid solver; numerical study

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