A Geometric Multigrid Method for 3D Magnetotelluric Forward Modeling Using Finite-Element Method

The traditional three-dimensional (3D) magnetotelluric (MT) forward modeling using Krylov subspace algorithms has the problem of low modeling efficiency. To improve the computational efficiency of 3D MT forward modeling, we present a novel geometric multigrid algorithm for the finite element method....

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Bibliographic Details
Published in:Remote sensing (Basel, Switzerland) Vol. 15; no. 2; p. 537
Main Authors: Huang, Xianyang, Yin, Changchun, Wang, Luyuan, Liu, Yunhe, Zhang, Bo, Ren, Xiuyan, Su, Yang, Li, Jun, Chen, Hui
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.01.2023
Subjects:
Algebra
Algorithms
Boundary conditions
Computer applications
Dirichlet problem
Divergence
electric field
Electric fields
finite element analysis
Finite element method
Finite volume method
forward modeling
geometric multigrid method
geometry
Iterative methods
Linear equations
Magnetic fields
magnetotelluric
Mathematical models
Salt domes
Simulation
Three dimensional models
vector finite element method
ISSN:2072-4292, 2072-4292
Online Access:Get full text
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Summary:The traditional three-dimensional (3D) magnetotelluric (MT) forward modeling using Krylov subspace algorithms has the problem of low modeling efficiency. To improve the computational efficiency of 3D MT forward modeling, we present a novel geometric multigrid algorithm for the finite element method. We use the vector finite element to discretize Maxwell’s equations in the frequency domain and apply the Dirichlet boundary conditions to obtain large sparse complex linear equations for the solution of EM responses. To improve the convergence of the solution at low frequencies we use the divergence correction to correct the electric field. Then, we develop a V-cycle geometric multigrid algorithm to solve the linear equations system. To demonstrate the efficiency and effectiveness of our geometric multigrid method, we take three synthetic models (COMMEMI 3D-2 model, Dublin test model 1, modified SEG/EAEG salt dome model) and compare our results with the published ones. Numerical results show that the geometric multigrid algorithm proposed in this paper is much better than the commonly used Krylov subspace algorithms (such as SOR-GMRES, ILU-BICGSTAB, SOR-BICGSTAB) in terms of the iteration number, the solution time, and the stability, and thus is more suitable for large-scale 3D MT forward modeling.
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ISSN:2072-4292
2072-4292
DOI:10.3390/rs15020537