A Time-Segmented SAI-Krylov Subspace Approach for Large-Scale Transient Electromagnetic Forward Modeling
After nearly two decades of development, transient electromagnetic (TEM) 3D forward modeling technology has significantly improved both numerical precision and computational efficiency, primarily through advancements in mesh generation and the optimization of linear equation solvers. However, the do...
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MDPI AG
2025-05-01
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| author | Ya’nan Fan Kailiang Lu Juanjuan Li Tianchi Fu |
| author_facet | Ya’nan Fan Kailiang Lu Juanjuan Li Tianchi Fu |
| author_sort | Ya’nan Fan |
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| description | After nearly two decades of development, transient electromagnetic (TEM) 3D forward modeling technology has significantly improved both numerical precision and computational efficiency, primarily through advancements in mesh generation and the optimization of linear equation solvers. However, the dominant approach still relies on direct solvers, which require substantial memory and complicate the modeling of electromagnetic responses in large-scale models. This paper proposes a new method for solving large-scale TEM responses, building on previous studies. The TEM response is expressed as a matrix exponential function with an analytic initial field for a step-off source, which can be efficiently solved using the Shift-and-Invert Krylov (SAI-Krylov) subspace method. The Arnoldi algorithm is used to construct the orthogonal basis for the Krylov subspace, and the preconditioned conjugate gradient (PCG) method is applied to solve large-scale linear equations. The paper further explores how dividing the off-time and optimizing parameters for each time interval can enhance computational efficiency. The numerical results show that this parameter optimization strategy reduces the iteration count of the PCG method, improving efficiency by a factor of 5 compared to conventional iterative methods. Additionally, the proposed method outperforms direct solvers for large-scale model calculations. Conventional approaches require numerous matrix factorizations and thousands of back-substitutions, whereas the proposed method only solves about 300 linear equations. The accuracy of the approach is validated using 1D and 3D models, and the propagation characteristics of the TEM field are studied in large-scale models. |
| format | Article |
| id | doaj-art-c6f2c244f0f2489386edef5ccf0ff628 |
| institution | Kabale University |
| issn | 2076-3417 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
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| spelling | doaj-art-c6f2c244f0f2489386edef5ccf0ff6282025-08-20T03:47:48ZengMDPI AGApplied Sciences2076-34172025-05-011510535910.3390/app15105359A Time-Segmented SAI-Krylov Subspace Approach for Large-Scale Transient Electromagnetic Forward ModelingYa’nan Fan0Kailiang Lu1Juanjuan Li2Tianchi Fu3State Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, ChinaState Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, ChinaState Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, ChinaState Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, ChinaAfter nearly two decades of development, transient electromagnetic (TEM) 3D forward modeling technology has significantly improved both numerical precision and computational efficiency, primarily through advancements in mesh generation and the optimization of linear equation solvers. However, the dominant approach still relies on direct solvers, which require substantial memory and complicate the modeling of electromagnetic responses in large-scale models. This paper proposes a new method for solving large-scale TEM responses, building on previous studies. The TEM response is expressed as a matrix exponential function with an analytic initial field for a step-off source, which can be efficiently solved using the Shift-and-Invert Krylov (SAI-Krylov) subspace method. The Arnoldi algorithm is used to construct the orthogonal basis for the Krylov subspace, and the preconditioned conjugate gradient (PCG) method is applied to solve large-scale linear equations. The paper further explores how dividing the off-time and optimizing parameters for each time interval can enhance computational efficiency. The numerical results show that this parameter optimization strategy reduces the iteration count of the PCG method, improving efficiency by a factor of 5 compared to conventional iterative methods. Additionally, the proposed method outperforms direct solvers for large-scale model calculations. Conventional approaches require numerous matrix factorizations and thousands of back-substitutions, whereas the proposed method only solves about 300 linear equations. The accuracy of the approach is validated using 1D and 3D models, and the propagation characteristics of the TEM field are studied in large-scale models.https://www.mdpi.com/2076-3417/15/10/5359TEMlarge-scale modelstime-segmented methodSAI-Krylov subspace methodPCG method |
| spellingShingle | Ya’nan Fan Kailiang Lu Juanjuan Li Tianchi Fu A Time-Segmented SAI-Krylov Subspace Approach for Large-Scale Transient Electromagnetic Forward Modeling Applied Sciences TEM large-scale models time-segmented method SAI-Krylov subspace method PCG method |
| title | A Time-Segmented SAI-Krylov Subspace Approach for Large-Scale Transient Electromagnetic Forward Modeling |
| title_full | A Time-Segmented SAI-Krylov Subspace Approach for Large-Scale Transient Electromagnetic Forward Modeling |
| title_fullStr | A Time-Segmented SAI-Krylov Subspace Approach for Large-Scale Transient Electromagnetic Forward Modeling |
| title_full_unstemmed | A Time-Segmented SAI-Krylov Subspace Approach for Large-Scale Transient Electromagnetic Forward Modeling |
| title_short | A Time-Segmented SAI-Krylov Subspace Approach for Large-Scale Transient Electromagnetic Forward Modeling |
| title_sort | time segmented sai krylov subspace approach for large scale transient electromagnetic forward modeling |
| topic | TEM large-scale models time-segmented method SAI-Krylov subspace method PCG method |
| url | https://www.mdpi.com/2076-3417/15/10/5359 |
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