Axisymmetric edge-based finite element formulation for bodies of revolution: application to dielectric resonators

Wong, M.F.; Prak, Myeong Hwan; Hanna, Victor Fouad

doi:10.1109/mwsym.1995.406050

Cited by 24 publications

(17 citation statements)

References 3 publications

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“…Therefore, there are three kinds of conditions for different harmonics [21], [22]. At the outermost point ρ max , a perfectly electric conductor is imposed, for both bounded and unbounded problems with perfectly matched layers discussed later in section II-E.…”

Section: Boundary Conditionsmentioning

confidence: 99%

Efficient Computation of Electromagnetic Waves in Anisotropic Orthogonal-Plano-Cylindrically Layered Media Using the Improved Numerical Mode Matching (NMM) Method

Dai

Liu

2015

IEEE Trans. Antennas Propagat.

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An orthogonal-plano-cylindrically layered (OPCL) medium consists of materials stratified planarly and layered concentrically in the orthogonal directions. The numerical mode matching (NMM) method has previously been shown to be a fast and robust semi-analytical solver to investigate the propagation of electromagnetic (EM) waves in such a complex but isotropic or transversely isotropic medium. In this paper, several important improvements have been made to extend applications of this efficient solver to the anisotropic OCPL medium. The formulas for anisotropic media with three different diagonal elements in the cylindrical coordinate system are deduced to expand its application. The perfectly matched layer (PML) is incorporated along the radial direction as an absorbing boundary condition (ABC) to make the NMM method more accurate and efficient for unbounded low conductivity media and applicable to lossless media. We manipulate the weak form of Maxwell's equations and impose the correct boundary conditions at the cylindrical axis to solve the singularity problem. Finally, we also offer formulas for computing EM fields excited by a magnetic dipole located at any position with an arbitrary orientation. Numerical results have demonstrated the efficiency and accuracy of this method.Index Terms-Numerical mode matching, electromagnetic field, stratified planarly and layered concentrically medium, anisotropic and inhomogeneous medium, perfectly matched layer, cylindrical coordinate singularity , magnetic dipole.

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Section: Boundary Conditionsmentioning

confidence: 99%

Efficient Computation of Electromagnetic Waves in Anisotropic Orthogonal-Plano-Cylindrically Layered Media Using the Improved Numerical Mode Matching (NMM) Method

Dai

Liu

2015

IEEE Trans. Antennas Propagat.

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“…Because of the symmetry of the geometry, only the generatrix that forms the surfaces of the PEC part and dielectric part are needed for solving the BOR problem in a surface integral equation formulation [1][2][3][4][5][6]. Similarly, only the meridian cross section is needed for solving the BOR problem with the finite element method (FEM) [7][8][9]. Both the memory requirement and CPU time in BOR solvers are reduced compared with full three-dimensional methods.…”

Section: Introductionmentioning

confidence: 99%

Fast Inhomogeneous Plane Wave Algorithm for Analysis of Composite Bodies of Revolution

Rui¹,

Hu²,

Liu³

2010

PIER

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Abstract-A fast inhomogeneous plane wave algorithm is developed for the electromagnetic scattering problem from the composite bodies of revolution (BOR). Poggio-Miller-Chang-Harrington-Wu (PMCHW) approach is used for the homogeneous dielectric objects, while the electric field integral equation (EFIE) is used for the perfect electric conducting objects. The aggregation and disaggregation factors can be expressed analytically by using the Weyl identity. Compared with the traditional method of moments (MoM), both the memory requirement and CPU time, are reduced for large-scale composite BOR problems. Numerical results are given to demonstrate the validity and the efficiency of the proposed method.

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“…Axisymmetric cavities are a particular class of cavity structures having a rotational symmetry both in the geometry and in the material constitutive parameters. Various solution techniques have been explored in the past including analytical methods based on mode matching [1], the finite integration method [2], the finite difference time domain method [3] and the finite element method [4,5]. In most of such numerical techniques, due to obvious computational advantages, the rotational symmetry is exploited in reducing the 3D problem to a 2D problem.…”

Section: Introductionmentioning

confidence: 99%

“…In the case of the finite element method, the resulting 2D problems have the electric field solution split into the meridian component (a vector field) and the azimuthal component (a scalar field). Consequently, for the expansion of the electric field, mixed vector and scalar basis functions are employed as proposed in [4,5]. However, the choice of the basis functions must ensure that any irrotational vector field can be represented using such basis functions.…”

Section: Introductionmentioning

confidence: 99%

Efficient computation of Maxwell eigenmodes in axisymmetric cavities using hierarchical vector finite elements

Venkatarayalu

2009

Int J Numerical Modelling

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SUMMARYComputation of Maxwell eigenmodes in an axisymmetric cavity using hierarchical vector finite elements is presented. The use of curl conforming vector basis functions, which span the null space of the curl operator, leads to the appearance of spurious modes with zero eigenvalues. Such spurious modes lead to electric flux solution with non-zero divergence. Constraining the solution space in the variational statement for the eigenvalue problem by weakly enforcing the flux to be divergence-free leads to the elimination of such modes. Discrete equivalent of such a constraint equation is developed for axisymmetric problems solved using hierarchical vector and scalar basis functions of orders complete to p ¼ 2. The discrete constraint equation, developed individually for Fourier modes m ¼ 0 and mX1, is efficiently integrated with a subspace iteration-based eigenvalue solution technique such as the Lanczos/Arnoldi method. The resulting solution technique is free of spurious modes added with an advantage of seeking a solution of a positive definite matrix during each iteration of the eigenvalue solver. Convergence in solution is demonstrated for orders up to p ¼ 2, while the proposed technique can be extended to basis functions of arbitrary order.

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Axisymmetric edge-based finite element formulation for bodies of revolution: application to dielectric resonators

Cited by 24 publications

References 3 publications

Efficient Computation of Electromagnetic Waves in Anisotropic Orthogonal-Plano-Cylindrically Layered Media Using the Improved Numerical Mode Matching (NMM) Method

Efficient Computation of Electromagnetic Waves in Anisotropic Orthogonal-Plano-Cylindrically Layered Media Using the Improved Numerical Mode Matching (NMM) Method

Fast Inhomogeneous Plane Wave Algorithm for Analysis of Composite Bodies of Revolution

Efficient computation of Maxwell eigenmodes in axisymmetric cavities using hierarchical vector finite elements

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