FDFD swMATH ID: 1172 Software Authors: Champagne, Nathan J.II; Berryman, James G.; Buettner, H.Michael Description: FDFD: A 3D finite-difference frequency-domain code for electromagnetic induction tomography. A new 3D code for electromagnetic induction tomography with intended applications to environmental imaging problems has been developed. The approach consists of calculating the fields within a volume using an implicit finite-difference frequency-domain formulation. The volume is terminated by an anisotropic perfectly matched layer region that simulates an infinite domain by absorbing outgoing waves. Extensive validation of this code has been done using analytical and semianalytical results from other codes, and some of those results are presented in this paper. The new code is written in Fortran 90 and is designed to be easily parallelized. Finally, an adjoint field method of data inversion, developed in parallel for solving the fully nonlinear inverse problem for electrical conductivity imaging (e.g., for mapping underground conducting plumes), uses this code to provide solvers for both forward and adjoint fields. Results obtained from this inversion method for high-contrast media are encouraging and provide a significant improvement over those obtained from linearized inversion methods Homepage: https://e-reports-ext.llnl.gov/pdf/234945.pdf Keywords: 3D code; electromagnetic induction tomography; implicit finite-difference frequency-domain formulation; anisotropic perfectly matched layer region; Fortran 90 Related Software: FPINNs; Gridap; DeepXDE; Adam; TensorFlow; LBFGS-B; MT2DInvMatlab; ARPACK; PETSc; Matlab; fminsearch Cited in: 10 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year FDFD: A 3D finite-difference frequency-domain code for electromagnetic induction tomography. Zbl 0984.78012Champagne, Nathan J. II; Berryman, James G.; Buettner, H. Michael 2001 all top 5 Cited by 31 Authors 2 Ying, Lexing 1 Berryman, James G. 1 Bertete-Aguirre, Hugo 1 Buettner, H. Michael 1 Chabory, Alexandre 1 Champagne, Nathan J. II 1 de Hon, Bastiaan P. 1 Delbary, Fabrice 1 Dorn, Oliver 1 Erhard, Klaus 1 Fan, Shanhui 1 Jiao, Yuyong 1 Johnson, Steven G. 1 Kress, Rainer 1 Liang, Jiawei 1 Lu, Lu 1 Nejad, S. Mohammad 1 Papanicolaou, George C. 1 Pestourie, Raphaël 1 Potthast, Roland W. E. 1 Pourmahayabadi, M. 1 Schulz, Jochen 1 Shin, Wonseok 1 Tan, Fei 1 Tijhuis, Anton G. 1 Tong, Defu 1 Tsuji, Paul 1 Verdugo, Francesc 1 Wang, Zhi Cheng 1 Yan, Chongwei 1 Yao, Wenjie all top 5 Cited in 6 Serials 4 Journal of Computational Physics 1 Inverse Problems 1 SIAM Journal on Scientific Computing 1 Engineering Analysis with Boundary Elements 1 Journal of Modern Optics 1 Frontiers of Mathematics in China all top 5 Cited in 6 Fields 9 Optics, electromagnetic theory (78-XX) 6 Numerical analysis (65-XX) 5 Partial differential equations (35-XX) 2 Computer science (68-XX) 1 Geophysics (86-XX) 1 Biology and other natural sciences (92-XX) Citations by Year