Edge-based Finite Element Analysis Research Articles

Numerical Modelling of TEM Fields by the Edge-Based Finite Element Method Using Tetrahedral Element for Central Rectangular Loops

In this study, we have implemented an edge-based finite element method for the numerical modeling of the transient electromagnetic method. We took the Helmholtz equation of the electric field as the governing equation for the edge-based finite element analysis. The modeling domain was discretized using linear tetrahedral mesh supported by Whitney-type vector basis functions. We inferred the equations by applying the Galerkin method. The system of equation was solved using a corrected version of the Bi Conjugate Gradient Stabilized Method (BiCGStab) algorithm to reduce the computational time. We obtained numerical solution for electric field in the Laplace domain; then the field was transformed into the time domain using the Gaver-Stehfest algorithm. Following this, the impulse response of the magnetic field was obtained through the Faraday law of electromagnetic induction as it is considerably more stable and computationally more efficient than inversion using the Fourier Transform. 3D geoelectric models were used to investigate the convergence of the edge-based finite element method with the analytic solution. The results are in good agreement with the analytical solution value for two resistivity contrasts in the 3D geoelectric brick model. We also compared the results of tetrahedral elements with the brick element in the 3D horizontal sheet and 3D conductive brick model. The results indicated that these two elements show very similar errors, but tetrahedral reflects fewer relative errors. For the low resistivity geoelectric model, numerical checks against the analytical solution, integral-equation method, and finite-difference time-domain solutions showed that the solutions would provide accurate results.

On the Practical Implementation of ICCG Method Solving Real Symmetric Linear Equation Arising in Edge-based Finite Element Analysis

On the Practical Implementation of ICCG Method Solving Real Symmetric Linear Equation Arising in Edge-based Finite Element Analysis

Robustness of Nested Multigrid Method for Edge-Based Finite Element Analysis

The multigrid method is known as the faster linear solver for large scale finite element analysis. In the edge-based finite element analysis, the geometric multigrid (GMG) method requires careful treatment for the stable convergence. In this paper we investigate factors for stable convergence of nested GMG method. The Numerical results show that the unsuitable application of essential boundary condition to the system matrix results in poor convergence of GMG method. We indicate that the appropriate boundary condition for the system or restriction matrix enable the stable convergence.

Comparison of geometric and algebraic multigrid methods in edge-based finite-element analysis

This paper discusses the comparison between the geometric multigrid (GMG) method and the algebraic multigrid (AMG) method in edge-based finite-element (FE) analysis. The GMG method requires the hierarchical meshes. On the other hand, the AMG method requires the only a single mesh information. The system matrices of the coarse grids are generated using algebraic operation in AMG. The numerical results show that both multigrid methods are faster than the conventional solvers in large-scale analysis. Although multigrid methods require the setup procedures, the calculation time of these procedures is comparatively short and increase linearly with the number of unknowns.

Robustness of the multigrid method for edge‐based finite element analysis

AbstractThe dependence of the multigrid finite element method solving three‐dimensional magnetostatic fields on the quality of the finite element mesh is reported. It is shown that the convergence of the multigrid method is strongly influenced by the mesh quality. Moreover, the multigrid method with ICCG smoother is shown to be more robust against mesh distortion than that with Gauss–Seidel and SOR smoothers. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 148(1): 75–81, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.10289

Edge‐based finite‐element analysis of the field patterns in V‐shaped microshield line

AbstractIn this paper, field patterns in V‐shaped microshield transmission line are calculated by using the edge‐based finite element method. The dependence of the field patterns upon the thickness of metallic signal strip and the dielectric constant of dielectric substrate is presented. The figures in this paper have important values in the design of microshield lines in microwave and millimeter‐wave integrated circuits. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 41: 43–47, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20041

Three-dimensional edge-based finite-element analysis for discrete bodies of revolution

An extension to three-dimensional (3-D) edge-based finite-element analysis for modeling electrically large fan-like bodies as discrete bodies of revolution is given. By exploiting the overlapping symmetries between a fan-like body and a modal expansion of the electromagnetic fields, only one lobe of the problem need be solved by the finite-element method without introducing approximations. This computational scaling makes possible the solution of electrically large structures much more efficiently. However, a periodic phase-boundary condition (PBC) must be applied to the faces of the mesh describing a single slice of the body and this condition must be enforced on both the electric and magnetic fields for a robust solution. Details on the implementation of the PBCs are given along with results which validate the overall technique.

Edge-Based Finite Element Analysis of Singly-and Doubly-Periodic Scatterers Using Absorging and Periodic Boundary Conditions

ABSTRACT This paper presents a simple but accurate Finite Element Method (FEM) technique which is based on hexahedral parallelepiped finite elements and Whitney's edge basis functions. The technique is useful for the analysis of scattering from 1-D, 2-D, or from isolated 3-D scatterers. Numerical results are presented for a variety of such scatterers to show the usefulness of the method. The results also point to the need for the use of improved absorbing boundary conditions (ABCs) as well as of higher order basis functions when more accurate results are required. The emphasis in the proposed method is on its simplicity and versatility.