A spectral Lanczos decomposition method for solving 3-D low-frequency electromagnetic diffusion by the finite-element method

Zunoubi, Mohammad R.; Jin, Jian‐Ming; Donepudi, K.C.; Chew, Weng Cho

doi:10.1109/8.761063

Cited by 21 publications

(6 citation statements)

References 5 publications

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“…Since the edge basis functions satisfy a constant tangential component along the associated edge and no tangential components along the other edges, the expansion in guarantees the continuity of the tangential electric field, conserving the continuity of a current, which allows the discontinuity of normal electric fields, at an inter–element boundary. The edge finite‐element method satisfying the boundary condition can therefore effectively suppress the spurious solutions (Lynch and Paulsen 1991; Mur 1994b; Mur and Lager 2002), while conventional node‐based finite‐element methods not satisfying the condition achieve the same objective by introducing a penalty factor in the finite‐element formulation (Zunoubi et al . 1999).…”

Section: Edge Finite‐element Methodsmentioning

confidence: 99%

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3D magnetotelluric modelling including surface topography

Nam

Kim

Song

et al. 2007

Geophysical Prospecting

116

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A B S T R A C TAn edge finite-element method has been applied to compute magnetotelluric (MT) responses to three-dimensional (3D) earth topography. The finite-element algorithm uses a single edge shape function at each edge of hexahedral elements, guaranteeing the continuity of the tangential electric field while conserving the continuity of magnetic flux at boundaries. We solve the resulting system of equations using the biconjugate gradient method with a Jacobian preconditioner. The solution gives electric fields parallel to the slope of a surface relief that is often encountered in MT surveys. The algorithm is successfully verified by comparison with other numerical solutions for a 3D-2 model for comparison of modelling methods for EM induction and a ridge model. We use a 3D trapezoidal-hill model to investigate 3D topographic effects, which are caused mainly by galvanic effects, not only in the Zxy mode but also in the Zyx mode. If a 3D topography were approximated by a two-dimensional topography therefore errors occurring in the transverse electric mode would be more serious than those in the transverse magnetic mode.

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Section: Edge Finite‐element Methodsmentioning

confidence: 99%

“…Mackie, Smith and Madden 1994; Sasaki 1999; Newman and Alumbaugh 2002) and the finite‐element method (e.g. Sugeng, Raiche and Xiong 1999; Zunoubi et al . 1999; Badea et al .…”

Section: Introductionmentioning

confidence: 99%

3D magnetotelluric modelling including surface topography

Nam

Kim

Song

et al. 2007

Geophysical Prospecting

116

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“…This apparent attraction is counterbalanced by a nontrivial and usually time-consuming construction of the finite elements themselves. The FE approach has been implemented by many developers (Reddy et al, 1977;Pridmore et al, 1981;Paulsen et al, 1988;Boyce et al, 1992;Livelybrooks, 1993;Lager and Mur, 1998;Sugeng et al, 1999;Zunoubi et al, 1999;Ratz, 1999;Ellis, 1999;Haber, 1999;Zyserman and Santos, 2000;Badea et al, 2001;Mitsuhata and Uchida, 2004, among others).…”

Section: Finite-element Approachmentioning

confidence: 99%

Three-Dimensional Electromagnetic Modelling and Inversion from Theory to Application

Avdeev

2005

Surv Geophys

241

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The whole subject of three-dimensional (3-D) electromagnetic (EM) modelling and inversion has experienced a tremendous progress in the last decade. Accordingly there is an increased need for reviewing the recent, and not so recent, achievements in the field. In the first part of this review paper I consider 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. I mention the merits and drawbacks of these approaches, and focus on the most essential aspects of numerical implementations, such as preconditioning and solving the resulting systems of linear equations. I refer to some of the most advanced, state-of-the-art, solvers that are today available for such important geophysical applications as induction logging, airborne and controlled-source EM, magnetotellurics, and global induction studies. Then, in the second part of the paper, I review some of the methods that are commonly used to solve 3-D EM inverse problems and analyse current implementations of the methods available. In particular, I also address the important aspects of nonlinear Newton-type optimisation techniques and computation of gradients and sensitivities associated with these problems.

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“…3‐D modelling in geo‐electromagnetics has been carried out for several decades (see, e.g. the review papers by Avdeev 2005; Börner 2010), starting predominantly with the integral equation method (Raiche 1974; Hohmann 1975; Weidelt 1975; Wannamaker et al 1984; Newman et al 1986; Wannamaker 1991; Xiong & Tripp 1997; Avdeev et al 1997), followed by the finite difference method (Mackie et al 1993; Newman & Alumbaugh 1995; Smith 1996; Streich 2009), and recently by the finite element method (Mogi 1996; Zunoubi et al 1999; Zyserman & Santos 2000; Badea et al 2001; Mitsuhata & Uchida 2004; Nam et al 2007) and the finite volume method (Haber et al 2000; Haber & Ascher 2001; Weiss & Constable 2006; Haber & Heldmann 2007). Amongst the different numerical methods the finite element method provides the greatest flexibility regarding model geometry, the option for a higher order spatial approximation and a rigorous framework for the treatment of virtually arbitrary constitutive parameter distributions.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional adaptive higher order finite element simulation for geo-electromagnetics-a marine CSEM example

Schwarzbach

Börner

Spitzer

2011

Geophysical Journal International

175

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S U M M A R YWe present a new 3-D vector finite element code and demonstrate its strength by modelling a realistic marine CSEM scenario. Unstructured tetrahedral meshes easily allow for the inclusion of arbitrary seafloor bathymetry so that natural environments are mapped into the model in a close-to-reality way. A primary/secondary field approach, an adaptive mesh refinement strategy as well as a higher order polynomial finite element approximation improve the solution accuracy. A convergence study strongly indicates that the use of higher order finite elements is beneficial even if the solution is not globally smooth. The marine CSEM scenario also shows that seafloor topography gives an important response which needs to be reproduced by numerical modelling to avoid the misinterpretation of measurements.

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A spectral Lanczos decomposition method for solving 3-D low-frequency electromagnetic diffusion by the finite-element method

Cited by 21 publications

References 5 publications

3D magnetotelluric modelling including surface topography

3D magnetotelluric modelling including surface topography

Three-Dimensional Electromagnetic Modelling and Inversion from Theory to Application

Three-dimensional adaptive higher order finite element simulation for geo-electromagnetics-a marine CSEM example

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