An efficient parallel algorithm for 3D magnetotelluric modeling with edge-based finite element


Three-dimensional magnetotelluric modeling algorithm of high accuracy and high efficiency is required for data interpretation and inversion. In this paper, edge-based finite element method with unstructured mesh is used to solve 3D magnetotelluric problem. Two boundary conditions—Dirichlet boundary condition and Neumann boundary condition—are set for cross-validation and comparison. We propose an efficient parallel algorithm to speed up computation and improve efficiency. The algorithm is based on distributed matrix storage and has three levels of parallelism. The first two are process level parallelization for frequencies and matrix solving, and the last is thread-level parallelization for loop unrolling. The algorithm is validated by several model studies. Scalability tests have been performed on two distributed-memory HPC platforms, one consists of Intel Xeon E5-2660 microprocessors and the other consists of Phytium FT2000 Plus microprocessors. On Intel platform, computation time of our algorithm solving Dublin Test Model-1 with 3,756,373 edges at 21 frequencies is 365 s on 2520 cores. The speedup and efficiency are 1609 and 60% compared to 100 cores. On Phytium platform, scalability test shows that the speedup from 256 cores to 86,016 cores has been increased to 11,255.

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This research work was supported by the National Key Research and Development Program of China (2018YFB0204301) and the National Natural Science Foundation of China No. 41874145. The authors gratefully acknowledge to Professor Zhengyong Ren, Dr. Fen Zhou, and Dr. Tiaojie Xiao for their valuable discussions.

Computer code availability

The code of the algorithm in this paper can refer to The code can run under Linux platforms.

Author information




Xiaoxiong Zhu performed parallel algorithm implementation, data analysis, scalability tests, and drafted the manuscript; Jie Liu designed the parallel algorithm and revised the manuscript; Yian Cui contributed to magnetotelluric theory; Chunye Gong contributed to scalability tests.

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Correspondence to Jie Liu.

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Zhu, X., Liu, J., Cui, Y. et al. An efficient parallel algorithm for 3D magnetotelluric modeling with edge-based finite element. Comput Geosci 25, 1–16 (2021).

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  • Magnetotelluric
  • Edge-based finite element
  • Unstructured mesh
  • Parallel algorithm