Journal
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
Volume 60, Issue -, Pages -Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TGRS.2021.3126291
Keywords
Sparse matrices; Mathematical models; Three-dimensional displays; Solid modeling; Memory management; Numerical models; Electromagnetics; Krylov subspace method; matrix exponential; numerical modeling; time-domain electromagnetic
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Funding
- National Natural Science Foundation of China [41830101, 41704108]
- Fundamental Research Funds for the Central Universities, Chang'an University (CHD) [300102261201]
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In this article, a restarting polynomial Krylov method is presented for modeling 3-D large-scale TEM responses. The method utilizes the mimetic finite volume method for spatial discretization and does not require solving large-scale linear equations. It achieves high accuracy and uses limited memory.
The transient electromagnetic (TEM) method is widely used in near-surface geophysical prospecting. The high-precision forward and inversion of large-scale complex models is a challenging problem. It is difficult to solve the large-scale problems using the direct solvers due to the large memory requirements. In this article, we present a restarting polynomial Krylov method for modeling 3-D large-scale TEM responses. The mimetic finite volume method is carried out for spatial discretization. The step-off TEM response then can be expressed as a matrix exponential function. The restarting polynomial Krylov method is used to solve the matrix exponential function. For a given restart subspace dimension, the residual is used to obtain the forward response at any time that meets the given accuracy. This method does not need to solve large-scale linear equations. Furthermore, the memory usage is mainly determined by the number of spatial discrete grids and the restart subspace order. The numerical experiments of large-scale model demonstrated that the method is accurate and uses limited memory.
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