Three-dimensional finite-element modelling of magnetotelluric data with a divergence correction

Farquharson, Colin G.; Miensopust, M. P.

doi:10.1016/j.jappgeo.2011.09.025

Cited by 122 publications

(52 citation statements)

References 38 publications

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“…Much research in recent years has gone into developing FEM codes for geoelectromagnetic modeling (Börner, 2010;Farquharson and Miensopust, 2011;Schwarzbach et al, 2011;Ren et al, 2013;Um et al, 2013;Grayver and Bürg, 2014). They all make use of the so-called Nédélec finite elements, which permit a well-posed representation of EM fields taking into account discontinuities of the normal components (Jin, 2002).…”

Section: Introductionmentioning

confidence: 99%

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

2015

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We have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, large conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.

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Section: Introductionmentioning

confidence: 99%

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

2015

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“…The formed linear equations in (4) given by the discretization of eq. (3) are solved by a multifrontal direct solver MUMPS 5.0.2 parallelized by OpenMP (Amestoy et al 2001(Amestoy et al , 2012, which could avoid uncertainties in pre-conditioning and convergence for iterative solutions, especially for low frequencies (Farquharson & Miensopust 2011;Oldenburg et al 2013). In this section, we will focus on the implementation of CFS-PML in details.…”

Section: Implementation Of Cfs-pmlmentioning

confidence: 99%

Application of the perfectly matched layer in 3-D marine controlled-source electromagnetic modelling

Han

et al. 2017

Geophysical Journal International

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SUMMARYIn this study, the complex frequency-shifted perfectly matched layer (CFS-PML) in stretching Cartesian coordinates, is successfully applied to three-dimensional (3D) frequency-domain marine controlled-source electromagnetic (CSEM) field modelling.The Dirichlet boundary, which is usually used within the traditional framework of EM modeling algorithms, assumes the electric or magnetic field values are zero at the boundaries. This requires the boundaries be sufficiently far away from the sources in the area of interest. To mitigate the boundary artifacts, a large modelling area may be necessary even though cell sizes are allowed to grow toward the boundaries due to the diffusion of the electromagnetic wave propagation. Compared with the conventional Dirichlet boundary, the PML boundary is preferred as the modelling area of interest could be restricted to the target region and only a few absorbing layers surrounding can effectively depress the artificial boundary effect without losing the numerical accuracy. Furthermore, for joint inversion of seismic and marine CSEM data, if we used the PML for CSEM field simulation instead of the conventional Dirichlet, the modeling area for these two different geophysical data collected from the same survey area could the same, which is convenient for joint inversion grid Downloaded from https://academic.oup.com/gji/article-abstract/doi/10.1093/gji/ggx382/4157794/Application-of-the-perfectly-matched-layer-in-3D by GEOMAR Bibliothek Helmholtz-Zentrum fuer Ozeanforschung user on 22 September 2017 2 G. Li and B. Li matching. We apply the CFS-PML boundary to 3D marine CSEM modelling by using the staggered finite-difference (SFD) discretization. Numerical test indicates that the modeling algorithm using the CFS-PML also shows good accuracy compared to the Dirichlet. Furthermore, the modeling algorithm using the CFS-PML shows advantages in computational time and memory saving than that using the Dirichlet boundary. For the 3D example in this study, the memory saving using the PML is nearly 42 % and the time saving is around 48% compared to using the Dirichlet.

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“…Numerical modeling methods for geoelectromagnetic induction problems can be principally categorized into the following classes: volume integral methods (Hohmann, 1975;Avdeev et al, 2002;Kuvshinov et al, 2002;Zhdanov et al, 2006), surface integral methods (Xu et al, 1997;Liu and Lamontagne, 1998;Ren et al, 2013b), finite-difference methods (Mackie et al, 1994;Haber et al, 2000;Weiss and Newman, 2003), finite-volume methods (Haber et al, 2000;Jahandari and Farquharson, 2013), finite-element methods (FEMs) (Mitsuhata and Uchida, 2004;Key and Weiss, 2006;Rücker et al, 2006;Franke et al, 2007;Li and Key, 2007;Nam et al, 2007;Blome et al, 2009;Ren and Tang, 2010;Farquharson and Miensopust, 2011;Mukherjee and Everett, 2011;Schwarzbach et al, 2011;Ren et al, 2013a;Schankee et al, 2013;Wang et al, 2013), and hybrid methods (Erdoğan et al, 2008;Vachiratienchai et al, 2010;Vachiratienchai and Siripunvaraporn, 2013;Ren et al, 2014). The FEMs are generally recognized as the most suitable approach for 3D complicated electromagnetic induction problems in the earth (Avdeev, 2005;Börner, 2010;Everett, 2012).…”

Section: Introductionmentioning

confidence: 99%

A finite-element-based domain-decomposition approach for plane wave 3D electromagnetic modeling

et al. 2014

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We developed a novel parallel domain-decomposition approach for 3D large-scale electromagnetic induction modeling in the earth. We used the edge-based finite-element method and unstructured meshes. Unstructured meshes were divided into sets of nonoverlapping subdomains. We used the curlcurl electric field equation to carry out the analysis. In each subdomain, the electric field was discretized by first-order vector shape functions along the edges of tetrahedral elements. The tangential components of the magnetic field on the interfaces of the subdomains were defined as a set of Lagrange multipliers. The unknown Lagrange multipliers were solved from an interface problem defined on the interfaces of the subdomains. With the availability of the Lagrange multipliers, the electric field values in each subdomain were solved independently. Three synthetic examples were evaluated to verify our code. Excellent agreement with previously published solutions was obtained. Synthetic examples revealed that our domain decomposition technique is scalable with respect to the number of subdomains and robust with regard to frequency and the heterogeneous distribution of material parameters, i.e., electric conductivity, electric permittivity, and magnetic permeability.

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Three-dimensional finite-element modelling of magnetotelluric data with a divergence correction

Cited by 122 publications

References 38 publications

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

Application of the perfectly matched layer in 3-D marine controlled-source electromagnetic modelling

A finite-element-based domain-decomposition approach for plane wave 3D electromagnetic modeling

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