Domain decomposition for 3D electromagnetic modeling

Xiong, Zonghou

doi:10.1186/bf03351574

Cited by 6 publications

(11 citation statements)

References 13 publications

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“…The coordinate relationship between master cell and slave cell can be described as Eqn. (7), and the differential relationship between master cell and slave cell can be described as Eqn. (8).…”

Section: Finite Element Methodsmentioning

confidence: 99%

Three-dimensional forward modeling for magnetotelluric sounding by finite element method

Xiao-zhong

Liu

Xie

et al. 2009

J. Cent. South Univ. Technol.

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A finite element algorithm combined with divergence condition was presented for computing three-dimensional(3D) magnetotelluric forward modeling. The finite element equation of three-dimensional magnetotelluric forward modeling was derived from Maxwell's equations using general variation principle. The divergence condition was added forcedly to the electric field boundary value problem, which made the solution correct. The system of equation of the finite element algorithm was a large sparse, banded, symmetric, ill-conditioned, non-Hermitian complex matrix equation, which can be solved using the Bi-CGSTAB method. In order to prove correctness of the three-dimensional magnetotelluric forward algorithm, the computed results and analytic results of one-dimensional geo-electrical model were compared. In addition, the three-dimensional magnetotelluric forward algorithm is given a further evaluation by computing COMMEMI model. The forward modeling results show that the algorithm is very efficient, and it has a lot of advantages, such as the high precision, the canonical process of solving problem, meeting the internal boundary condition automatically and adapting to all kinds of distribution of multi-substances.

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Section: Finite Element Methodsmentioning

confidence: 99%

Three-dimensional forward modeling for magnetotelluric sounding by finite element method

Xiao-zhong

Liu

Xie

et al. 2009

J. Cent. South Univ. Technol.

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“…Xiong (1999) demonstrates an overlapping approach for 3D controlledsource problems using finite-difference methods. Zyserman and Santos (2000) apply a nonoverlapping approach to magnetotelluric (MT) problems using nodal-based shape functions and structured elements (rectangular cuboids).…”

Section: Introductionmentioning

confidence: 99%

“…However, the convergence rate of this iterative procedure is a serious issue. To obtain accurate and trustworthy results, large numbers of iterations are normally required, which seriously impairs performance (Xiong, 1999). For approaches using nonoverlapping subdomains, abutting subdomains only share common internal surfaces (Butrylo et al, 2004).…”

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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“…In many problems, when the model domain becomes very large, particularly in 3‐D problems, solving the system of equations with the direct method is impractical due to the large memory requirement (see Ben‐Hadj‐Ali et al 2008 for 3‐D frequency‐domain full‐waveform tomography; Streich 2009 for 3‐D MT). Instead, the system is solved using iterative solvers such as the Bi‐Conjugate Gradient method (Smith 1996; Xiong 1999), Quasi Minimum Residual (Siripunvaraporn et al 2002), Preconditioned Conjugate Gradient (PCG) (Siripunvaraporn & Egbert 2000), Minimum Residual Method (Mackie et al 1994). In many practical MT cases, the electrical resistivity model can be geologically complicated resulting in a large condition number and hence a very long computational time when used repeatedly inside the inversion (Patro & Egbert 2008).…”

Section: Introductionmentioning

confidence: 99%

“…Bitzarakis et al 1997; Lu & Shen 1997; Larsson 1999; Yin et al 2002; Basermann et al 2005; Lu et al 2008; Wang et al 2008) and also in various multidimensional geophysical problems (e.g. Xiong 1999; Zyserman et al 1999; Xie et al 2000; Zyserman & Santos 2000; Pain et al 2002; Ben‐Hadj‐Ali et al 2008; Sourbier et al 2008; Takei et al 2010).…”

Section: Introductionmentioning

confidence: 99%

An efficient modified hierarchical domain decomposition for two-dimensional magnetotelluric forward modelling

Rung-Arunwan

Siripunvaraporn

2010

Geophysical Journal International

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S U M M A R YWe use 2-D magnetotelluric (MT) problems as a feasibility study to demonstrate that 3-D MT problems can be solved with a direct solver, even on a standard single processor PC. The scheme used is a hierarchical domain decomposition (HDD) method in which a global computational domain is uniformly split into many smaller non-overlapping subdomains. To make it more efficient, two modifications are made to the standard HDD method. Instead of three levels as in the standard HDD method, we classify the unknowns into four classes: the interiors, the horizontal interfaces, the vertical interfaces and the intersections. Four sets of smaller systems of equations are successively solved with a direct method (an LU factorization). The separation significantly reduces the large memory requirements of a direct solver. It also reduces the CPU time to almost half that of the standard HDD method although it is still slower than the conventional finite difference (FD) method. To further enhance the speed of the code, a red-black ordering is applied to solve the horizontal and vertical interface reduced systems. Numerical experiments on a 2-D MT problem of a given size running on a single processor machine shows that CPU time and memory used are almost constant for any resistivity models, frequencies and modes. This is a clear advantage of our algorithm and is of particular importance if the method is applied to 3-D problems. We show that our new method results in reductions in both memory usage and CPU time for large enough domains when compared to the standard FD and HDD schemes. In addition, we also introduce a 'memory minimization map', a graphical tool we can use instead of trial-and-error to pre-select the optimal size of subdomains, which yield the best performance in both CPU time and memory even running on a serial machine.

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Domain decomposition for 3D electromagnetic modeling

Cited by 6 publications

References 13 publications

Three-dimensional forward modeling for magnetotelluric sounding by finite element method

Three-dimensional forward modeling for magnetotelluric sounding by finite element method

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

An efficient modified hierarchical domain decomposition for two-dimensional magnetotelluric forward modelling

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