Journal ArticleDOI
An efficient finite‐difference scheme for electromagnetic logging in 3D anisotropic inhomogeneous media
TLDR
In this article, a finite-difference scheme for the electromagnetic field in 3D anisotropic media for electromagnetic logging was proposed, which has the following features: coercivity (i.e., the complete discrete analogy of all continuous equations in every grid cell, even for nondiagonal conductivity tensors), a special conductivity averaging, and a spectrally optimal grid refinement minimizing the error at the receiver locations and optimizing the approximation of the boundary conditions at infinity.Abstract:
We consider a problem of computing the electromagnetic field in 3D anisotropic media for electromagnetic logging. The proposed finite-difference scheme for Maxwell equations has the following new features based on some recent and not so recent developments in numerical analysis: coercivity (i.e., the complete discrete analogy of all continuous equations in every grid cell, even for nondiagonal conductivity tensors), a special conductivity averaging that does not require the grid to be small compared to layering or fractures, and a spectrally optimal grid refinement minimizing the error at the receiver locations and optimizing the approximation of the boundary conditions at infinity. All of these features significantly reduce the grid size and accelerate the computation of electromagnetic logs in 3D geometries without sacrificing accuracy.read more
Citations
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Journal ArticleDOI
Electrical impedance tomography
TL;DR: In this article, the authors review theoretical and numerical studies of the inverse problem of electrical impedance tomography, which seeks the electrical conductivity and permittivity inside a body, given simultaneous measurements of electrical currents and potentials at the boundary.
Journal ArticleDOI
Three-dimensional electromagnetic modelling and inversion from theory to application
TL;DR: This review paper considers the finite-difference, finite-element and integral equation approaches that are presently applied for the rigorous numerical solution of fully 3-D EM forward problems, and addresses the important aspects of nonlinear Newton-type optimisation techniques and computation of gradients and sensitivities associated with these problems.
Journal ArticleDOI
Time-Domain Finite-Difference and Finite-Element Methods for Maxwell Equations in Complex Media
TL;DR: Extensions of finite-difference time domain (FDTD) and finite-element time-domain (FETD) algorithms are reviewed for solving transient Maxwell equations in complex media in this article.
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A parallel finite-element method for three-dimensional controlled-source electromagnetic forward modelling
Vladimir Puzyrev,Jelena Koldan,Josep de la Puente,Guillaume Houzeaux,Mariano Vázquez,José María Cela +5 more
TL;DR: A nodal finite-element method that can be used to compute in parallel highly accurate solutions for 3-D controlled-source electromagnetic forward-modelling problems in anisotropic media and demonstrates the performance in large problems with tens and even hundreds of millions of degrees of freedom.
Journal ArticleDOI
3-D inversion of airborne electromagnetic data parallelized and accelerated by local mesh and adaptive soundings
TL;DR: Commer et al. as mentioned in this paper proposed a three-dimensional controlled-source electromagnetic inversion (CSEMI) method for 3D inversion, which is based on the 3-DOF inversion.
References
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Journal ArticleDOI
Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media
Abstract: Maxwell's equations are replaced by a set of finite difference equations. It is shown that if one chooses the field points appropriately, the set of finite difference equations is applicable for a boundary condition involving perfectly conducting surfaces. An example is given of the scattering of an electromagnetic pulse by a perfectly conducting cylinder.
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Beyond the Born and Rytov approximations: A nonlinear approach to electromagnetic scattering
TL;DR: The Born and Rytov approximations, widely used for solving scattering problems, are of limited utility for low-frequency electromagnetic scattering in geophysical applications where conductivity can vary over many orders of magnitude as discussed by the authors.
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Anisotropic wave propagation through finite‐difference grids
TL;DR: In this article, the authors proposed an algorithm to solve the elastic-wave equation by replacing the partial differentials with finite differences, which enables wave propagation to be simulated in three dimensions through generally anisotropic and heterogeneous models.
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Spectral approach to solving three-dimensional Maxwell's diffusion equations in the time and frequency domains
TL;DR: A new explicit three-dimensional solver for the diffusion of electromagnetic fields in arbitrarily heterogeneous conductive media is described, based on a global Krylov subspace (Lanczos) approximation of the solution in the time and frequency domains.