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...

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Published in:	Computational geosciences Vol. 25; no. 1; pp. 1 - 16
Main Authors:	Zhu, Xiaoxiong, Liu, Jie, Cui, Yian, Gong, Chunye
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01.02.2021 Springer Nature B.V
Subjects:	Algorithms Boundary conditions Computation Cores Data interpretation Dirichlet problem Distributed memory Earth and Environmental Science Earth Sciences Efficiency Finite element method Geotechnical Engineering & Applied Earth Sciences Hydrogeology Mathematical Modeling and Industrial Mathematics Microprocessors Model accuracy Model testing Modelling Original Paper Parallel processing Soil Science & Conservation Storage Three dimensional models Work platforms Unstructured mesh Magnetotelluric Edge-based finite element Parallel algorithm
ISSN:	1420-0597, 1573-1499
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Abstract	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.
AbstractList	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. 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.
Author	Liu, Jie Zhu, Xiaoxiong Gong, Chunye Cui, Yian
Author_xml	– sequence: 1 givenname: Xiaoxiong surname: Zhu fullname: Zhu, Xiaoxiong organization: Science and Technology on Parallel and Distributed Processing Laboratory, National University of Defense Technology, Laboratory of Software Engineering for Complex Systems, National University of Defense Technology – sequence: 2 givenname: Jie surname: Liu fullname: Liu, Jie email: liujie@nudt.edu.cn organization: Science and Technology on Parallel and Distributed Processing Laboratory, National University of Defense Technology, Laboratory of Software Engineering for Complex Systems, National University of Defense Technology – sequence: 3 givenname: Yian surname: Cui fullname: Cui, Yian organization: School of Geosciences and Info-Physics, Central South University – sequence: 4 givenname: Chunye surname: Gong fullname: Gong, Chunye organization: Science and Technology on Parallel and Distributed Processing Laboratory, National University of Defense Technology, Laboratory of Software Engineering for Complex Systems, National University of Defense Technology
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Snippet	Three-dimensional magnetotelluric modeling algorithm of high accuracy and high efficiency is required for data interpretation and inversion. In this paper,...
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SubjectTerms	Algorithms Boundary conditions Computation Cores Data interpretation Dirichlet problem Distributed memory Earth and Environmental Science Earth Sciences Efficiency Finite element method Geotechnical Engineering & Applied Earth Sciences Hydrogeology Mathematical Modeling and Industrial Mathematics Microprocessors Model accuracy Model testing Modelling Original Paper Parallel processing Soil Science & Conservation Storage Three dimensional models Work platforms
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Title	An efficient parallel algorithm for 3D magnetotelluric modeling with edge-based finite element
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