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

Abstract

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.

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

“…Parallel implementations of AMG methods have been under intensive research and development in the past few decades, and several scalable software libraries are currently available (Henson and Yang, 2002;Gee et al, 2006) with some support for definite Maxwell problems Kolev and Vassilevski, 2009). In geoelectromagnetic applications, multigrid and domain-decomposition preconditioners have been shown to be extremely efficient in handling large-scale problems (Grayver and Bürg, 2014;Ren et al, 2014). These works, however, consider only the lowest order Nédélec elements and do not discuss complications related to nonconforming meshes.…”

“…However, the largest part of the computational time is typically spent in solving the resulting large and sparse system of linear equations. Construction of robust and scalable solvers is challenging and requires elaborated methods (Grayver and Bürg, 2014;Ren et al, 2014). High polynomial degrees create an additional challenge here.…”

Magnetotelluric responses of three‐dimensional conductive and magnetic anisotropic anomalies

“…; Ren et al . ; Li, Farquharson and Hu ). The behaviour of EM fields depends on three physical properties of the subsurface (Mukherjee and Everett ): electrical conductivity σ, magnetic permeability μ and dielectric permittivity ε.…”

“…The simulation of geologic structures to magnetotelluric (MT) response has been widely used in several areas of applied geophysics such as exploration of oil and gas and the investigation of deep Earth electrical structures (Mitsuhata, Matsuo and Minegishi 1999;Unsworth et al 2000;Heinson, Direen and Gill 2006;Farquharson and Craven 2009;Hu et al 2013;Spichak et al 2015;Villain et al 2015). Therefore, it is important to study the responses of electromagnetic (EM) fields (Everett 2012; Ren et al 2013;Cai et al 2014;Ren et al 2014;Li, Farquharson and Hu 2016). The behaviour of EM * E-mail: xiaotiaojie16@mails.ucas.ac.cn fields depends on three physical properties of the subsurface (Mukherjee and Everett 2011): electrical conductivity σ , magnetic permeability μ and dielectric permittivity ε.…”

A multi-domain decomposition-based Fourier finite element method for the simulation of 3D marine CSEM measurements

“…The resulting discretization delivers highly accurate simulations of marine CSEM problems with arbitrary 3D geometries while it considerably reduces the computational complexity of full 3D FE simulations for typical marine CSEM problems. Ren et al [27] present a domain decomposition approach for plane wave 3D EM modeling using Lagrange multipliers on the interfaces of the subdomains.…”