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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| Vydáno v: | Remote sensing (Basel, Switzerland) Ročník 15; číslo 2; s. 537 |
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| Jazyk: | angličtina |
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MDPI AG
01.01.2023
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| ISSN: | 2072-4292, 2072-4292 |
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| Abstract | 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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| AbstractList | 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. |
| Author | Li, Jun Huang, Xianyang Liu, Yunhe Chen, Hui Zhang, Bo Ren, Xiuyan Yin, Changchun Wang, Luyuan Su, Yang |
| Author_xml | – sequence: 1 givenname: Xianyang orcidid: 0000-0001-9436-6190 surname: Huang fullname: Huang, Xianyang – sequence: 2 givenname: Changchun surname: Yin fullname: Yin, Changchun – sequence: 3 givenname: Luyuan surname: Wang fullname: Wang, Luyuan – sequence: 4 givenname: Yunhe orcidid: 0000-0002-3634-9832 surname: Liu fullname: Liu, Yunhe – sequence: 5 givenname: Bo surname: Zhang fullname: Zhang, Bo – sequence: 6 givenname: Xiuyan surname: Ren fullname: Ren, Xiuyan – sequence: 7 givenname: Yang surname: Su fullname: Su, Yang – sequence: 8 givenname: Jun surname: Li fullname: Li, Jun – sequence: 9 givenname: Hui surname: Chen fullname: Chen, Hui |
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| SubjectTerms | 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 |
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