Skip to main content Accessibility help
Hostname: page-component-78bd46657c-2pqp7 Total loading time: 0.27 Render date: 2021-05-08T20:49:33.849Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

ADI-FDTD Method for Two-Dimensional Transient Electromagnetic Problems

Published online by Cambridge University Press:  15 January 2016

Wanshan Li
School of Mathematics, Shandong University, Jinan 250199, P.R. China
Yile Zhang
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada
Yau Shu Wong
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada
Dong Liang
Department of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3, Canada
Get access


An efficient and accurate numerical scheme is proposed for solving the transverse electric (TE) mode electromagnetic (EM) propagation problem in two-dimensional earth. The scheme is based on the alternating direction finite-difference time-domain (ADI-FDTD) method. Unlike the conventional upward continuation approach for the earth-air interface, an integral formulation for the interface boundary is developed and it is effectively incorporated to the ADI solver. Stability and convergence analysis together with an error estimate are presented. Numerical simulations are carried out to validate the proposed method, and the advantage of the present method over the popular Du-Fort-Frankel scheme is clearly demonstrated. Examples of the electromagnetic field propagation in the ground with anomaly further verify the effectiveness of the proposed scheme.

Research Article
Copyright © Global-Science Press 2016 

Access options

Get access to the full version of this content by using one of the access options below.


[1]Adhidjaja, J. I., Hohmann, G. W. and Oristaglio, M. L., Two-dimensional transient electromagnetic responses, Geophysics, 50 (1985), 28492861.CrossRefGoogle Scholar
[2]Chen, W., Li, X. and Liang, D., Symmetric energy-conserved splitting FDTD scheme for the Maxwell's equations, Comm. Comput. Phys., 6 (2009), 804825.CrossRefGoogle Scholar
[3]Chung, Y., Son, J.-S., Lee, T. J., Kim, H. J. and Shin, C., Three-dimensional modelling of controlled-source electromagnetic surveys using an edge finite-element method with a direct solver, Geophys. Prospect., 62 (2014), 14681483.CrossRefGoogle Scholar
[4]Commer, M. and Newman, G., A parallel finite-difference approach for 3D transient electromagnetic modeling with galvanic sources, Geophysics, 69 (2004), 11921202.CrossRefGoogle Scholar
[5]Constable, S. and Weiss, C. J., Mapping thin resistors and hydrocarbons with marine EM methods: Insights from 1D modeling, Geophysics, 71 (2006), G43G51.CrossRefGoogle Scholar
[6]da Silva, N. V., Morgan, J. V., MacGregor, L. and Warner, M., A finite element multifrontal method for 3D CSEM modeling in the frequency domain, Geophysics, 77 (2012), E101E115.CrossRefGoogle Scholar
[7]Everett, M. and Edwards, R., Transient marine electromagnetics: the 2.5-D forward problem, Geophys. J. Int., 113 (1993), 545561.CrossRefGoogle Scholar
[8]Freund, R. W. and Nachtigal, N. M., An implementation of the QMR method based on coupled two-term recurrences, SIAM J. Sci. Comput., 15 (1994), 313337.CrossRefGoogle Scholar
[9]Gao, L. and Liang, D., New energy-conserved identities and super-convergence of the symmetric EC-S-FDTD scheme for Maxwell's equations in 2D, Comm. Comput. Phys., 11 (2012), 16731696.CrossRefGoogle Scholar
[10]Goldman, Y., Hubans, C., Nicoletis, S. and Spitz, S., A finite-element solution for the transient electromagnetic response of an arbitrary two-dimensional resistivity distribution, Geophysics, 51 (1986), 14501461.CrossRefGoogle Scholar
[11]Grayver, A., Streich, R. and Ritter, O., Three-dimensional parallel distributed inversion of CSEM data using a direct forward solver, Geophys. J. Int., 193 (2013), 14321446.CrossRefGoogle Scholar
[12]Grayver, A. V. and Bürg, M., Robust and scalable 3-D geo-electromagnetic modelling approach using the finite element method, Geophys.J. Int., 198 (2014), 110125.CrossRefGoogle Scholar
[13]Gronwall, T. H., Note on the derivatives with respect to a parameter of the solutions of a system of differential equations, Ann. Math., 20 (1919), 292296.CrossRefGoogle Scholar
[14]Haber, E. and Ascher, U. M., Fast finite volume simulation of 3D electromagnetic problems with highly discontinuous coefficients, SIAM J. Sci. Comput., 22 (2001), 19431961.CrossRefGoogle Scholar
[15]Haber, E. and Schwarzbach, C., Parallel inversion of large-scale airborne time-domain electromagnetic data with multiple octree meshes, Inverse Prob., 30 (2014), 055011.CrossRefGoogle Scholar
[16]Huang, J. and Wood, A., Analysis and numerical solution of transient electromagnetic scattering from overfilled cavities, Comm. Comput. Phys., 1 (2006), 10431055.Google Scholar
[17]Huang, J., Wood, A. W. and Havrilla, M.J., A hybrid finite element-Laplace transform method for the analysis of transient electromagnetic scattering by an over-filled cavity in the ground plane, Comm. Comput. Phys., 5 (2009), 126141.Google Scholar
[18]Jiang, X., Zhang, L. and Zheng, W., Adaptive hp-finite element computations for time-harmonic Maxwells equations, Comm. Comput. Phys., 13 (2013), 559582.CrossRefGoogle Scholar
[19]Jim, Douglas Jr., On the numerical integration by implicit methods, J. Soc. Ind. Appl. Math., 3 (1955), 4265.Google Scholar
[20]Key, K. and Ovall, J., A parallel goal-oriented adaptive finite element method for 2.5-D electromagnetic modelling, Geophys. J. Int., 186 (2011), 137154.CrossRefGoogle Scholar
[21]Koldan, J., Puzyrev, V., de la Puente, J., Houzeaux, G. and Cela, J. M., Algebraic multigrid pre-conditioning within parallel finite-element solvers for 3-D electromagnetic modelling problems in geophysics, Geophys. J. Int., 197 (2014), 14421458.CrossRefGoogle Scholar
[22]Kuo, J. T. and Cho, D.-h., Transient time-domain electromagnetics, Geophysics, 45 (1980), 271291.CrossRefGoogle Scholar
[23]Lee, K. H., Electromagnetic scattering by two-dimensional inhomogeneity due to an oscillating magnetic dipole, California Univ., Berkeley (USA), 1978.Google Scholar
[24]Leppin, M., Electromagnetic modeling of 3-D sources over 2-D inhomogeneities in the time domain, Geophysics, 57 (1992), 9941003.CrossRefGoogle Scholar
[25]Maaø, R. A., Fast finite-difference time-domain modeling for marine-subsurface electromagnetic problems, Geophysics, 72 (2007), A19A23.CrossRefGoogle Scholar
[26]Mukherjee, S. and Everett, M. E., 3D controlled-source electromagnetic edge-based finite element modeling of conductive and permeable heterogeneities, Geophysics, 76 (2011), F215F226.CrossRefGoogle Scholar
[27]Namiki, T., A new FDTD algorithm based on alternating-direction implicit method, IEEE Trans. Microwave Theory Tech., 47 (1999), 20032007.CrossRefGoogle Scholar
[28]Oristaglio, M. L. and Hohmann, G. W., Diffusion of electromagnetic fields into a two-dimensional earth: A finite-difference approach, Geophysics, 49 (1984), 870894.CrossRefGoogle Scholar
[29]Peaceman, D. W. and Rachford, H. H. Jr., The numerical solution of parabolic and elliptic differential equations, J. Soc. Ind. Appl. Math., 3 (1955), 2841.CrossRefGoogle Scholar
[30]Puzyrev, V., Koldan, J., de la Puente, J., Houzeaux, G., Vázquez, M. and Cela, J. M., A parallel finite-element method for three-dimensional controlled-source electromagnetic forward modelling, Geophys. J. Int., 193 (2013), 678693.CrossRefGoogle Scholar
[31]Ren, Z., Kalscheuer, T., Greenhalgh, S. and Maurer, H., A goal-oriented adaptive finite-element approach for plane wave 3-D electromagnetic modelling, Geophys. J. Int., 194 (2013), 700718.CrossRefGoogle Scholar
[32]Schwarzbach, C. and Haber, E., Finite element based inversion for time-harmonic electromagnetic problems, Geophys. J. Int., 193 (2013), 615634.CrossRefGoogle Scholar
[33]Sheu, W. H. T., Liang, L. Y. and Li, J.-H., Development of an explicit symplectic scheme that optimizes the dispersion-relation equation for the Maxwell's equations, Comm. Comput. Phys., 13 (2013), 11071133.CrossRefGoogle Scholar
[34]Sommer, M., Hölz, S., Moorkamp, M., Swidinsky, A., Heincke, B., Scholl, C. and Jegen, M., GPU parallelization of a three dimensional marine CSEM code, Comput. Geosci., 58 (2013), 9199.CrossRefGoogle Scholar
[35]Streich, R., 3D finite-difference frequency-domain modeling of controlled-source electromagnetic data: Direct solution and optimization for high accuracy, Geophysics, 74 (2009), F95F105.CrossRefGoogle Scholar
[36]Streich, R., Becken, M. and Ritter, O., 2.5D controlled-source EM modeling with general 3D source geometries, Geophysics, 76 (2011), F387F393.CrossRefGoogle Scholar
[37]Sun, Y. and Tao, F., Symplectic and multisymplectic numerical methods for Maxwell's equations, J. Comput. Phys., 230 (2011), 20762094.CrossRefGoogle Scholar
[38]Taflove, A., Application of the finite-difference time-domain method to sinusoidal steady-state electromagnetic-penetration problems, IEEE Trans. Electromagn. Compat., 22 (1980), 191202.CrossRefGoogle Scholar
[39]Thomas, L., Elliptic problems in linear difference equations over a network, Technique report, Watson Scientific Computing Laboratory, Columbia University, New York, 1949.Google Scholar
[40]Um, E. S., Commer, M. and Newman, G. A., Efficient pre-conditioned iterative solution strategies for the electromagnetic diffusion in the earth: finite-element frequency-domain approach, Geophys. J. Int, 193 (2013), 14601473.CrossRefGoogle Scholar
[41]Um, E. S., Harris, J. M. and Alumbaugh, D. L., 3D time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach, Geophysics, 75 (2010), F115F126.CrossRefGoogle Scholar
[42]Wang, T. and Hohmann, G. W., A finite-difference, time-domain solution for three-dimensional electromagnetic modeling, Geophysics, 58 (1993), 797809.CrossRefGoogle Scholar
[43]Xie, Z., Wang, B. and Zhang, Z., Space-time discontinuous Galerkin method for Maxwell's equations, Comm. Comput. Phys., 14 (2013), 916939.CrossRefGoogle Scholar
[44]Yee, K. al., Numerical solution of initial boundary value problems involving Maxwells equations in isotropic media, IEEE Trans. Antennas Propag, 14 (1966), 302307.Google Scholar
[45]Zaslavsky, M., Druskin, V., Davydycheva, S., Knizhnerman, L., Abubakar, A. and Habashy, T., Hybrid finite-difference integral equation solver for 3D frequency domain anisotropic electromagnetic problems, Geophysics, 76 (2011), F123F137.CrossRefGoogle Scholar

Send article to Kindle

To send this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

ADI-FDTD Method for Two-Dimensional Transient Electromagnetic Problems
Available formats

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

ADI-FDTD Method for Two-Dimensional Transient Electromagnetic Problems
Available formats

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

ADI-FDTD Method for Two-Dimensional Transient Electromagnetic Problems
Available formats

Reply to: Submit a response

Your details

Conflicting interests

Do you have any conflicting interests? *