scholarly journals Finite Element Procedure for Overlapping Meshes Based on Domain Decomposition Approach using Background Rectangular Mesh

2011 ◽  
Vol 67 (2) ◽  
pp. I_117-I_125
Author(s):  
Takahiro YAMADA ◽  
Ryo OCHIAI ◽  
Kazumi MATSUI
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Decomposition Approach ◽  
Rectangular Mesh ◽  
Finite Element Procedure

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

Geophysics ◽  
2014 ◽  
Vol 79 (6) ◽  
pp. E255-E268 ◽  
Author(s):  
Zhengyong Ren ◽  
Thomas Kalscheuer ◽  
Stewart Greenhalgh ◽  
Hansruedi Maurer
Keyword(s):  
Finite Element ◽  
Electric Field ◽  
Domain Decomposition ◽  
Lagrange Multipliers ◽  
Large Scale ◽  
Unstructured Meshes ◽  
Interface Problem ◽  
Electromagnetic Modeling ◽  
Heterogeneous Distribution ◽  
Decomposition Approach

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 curl-curl 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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