Tangential Vector Finite Elements Research Articles

Perancangan dan Analisis Antena Dipole Pada Frekuensi 2,4 GHz Untuk Modul Xbee S2 Pro Menggunakan HFFS 14.0

Xbee s2 pro module works at 2,4 Ghz using IEEE 802.15.4 standard and polarization are linear. There are many types of antennas that can be used, which one is the dipole antenna. The simulation model implemented in this study uses Ansoft HFSS 14.0 software. HFSS stands for high frequency structure simulator is a pioneer in the use of finite element method for electromagnetic wave simulators that implement tangential vector finite elements, adaptive meshing and Adaptive Lanczos-Pade Sweep (ALPS) technology. By using HFSS 14.0 simulation, the axial ratio value of 35.0359 dB that means linier polarization. For the value of s-parameter -21,1851 db and VSWR value approaches 1, that is 1.5195 db. The gain value obtained is 0.7469 dB, the gain value needs to be optimized by using a metamaterial to get a good gain.

Fast Frequency Sweep of FEM Models via the Balanced Truncation Proper Orthogonal Decomposition

A fast frequency sweep method for wideband antennas and infinite arrays based on a singular value decomposition (SVD)-Krylov model reduction method for frequency-domain tangential vector finite elements (TVFEMs) is presented. Reduced models are constructed using balanced congruence transformations constructed from the dominant invariant subspace of the system's Hankel matrix. Traditionally, forming such matrix requires the intensive computation of Gramians; the proposed method only forms their low-rank Cholesky factors via a novel adaptive proper orthogonal decomposition (POD) sampling strategy, leading to significant savings. Unlike some other model reduction methods, balanced truncation POD (BT-POD) is directly applicable to lossy and dispersive electromagnetic models. Numerical studies on large-scale wideband antennas and infinite arrays show that the method is stable, error controllable and, without memory overheads capable of up to two orders-of-magnitude speed-ups.

Hybrid Finite Element Methods for Array and FSS Analysis Using Multiresolution Elements and Fast Integral Techniques

Hierarchical mixed-order tangential vector finite elements (TVFEs) for tetrahedra are attractive for accurate and efficient analysis of a wide class of electromagnetic radiation and scattering problems. They provide versatile geometrical modeling and accurate field representation by allowing combination of lowest and higher order TVFEs. In this paper, the finite element-boundary integral method with hierarchical TVFEs for tetrahedra is used for analysis of infinite, doubly periodic antenna arrays. It is shown that accurate prediction of array scanning properties can be obtained by using higher order TVFEs in the regions where large fields and rapid field variations are expected and lowest order TVFEs elsewhere. This type of multi-resolution modeling is applied to several array configurations to demonstrate the accuracy and capabilities of the technique. Adaptive Integral Method (AIM) for the acceleration of the boundary integral is discussed and results regarding the speed-up are also given. Applications to multilayered frequency selective surfaces are also considered.

Adaptive multiresolution antenna modeling using hierarchical mixed-order tangential vector finite elements

Hierarchical mixed-order tangential vector finite elements (TVFEs) for tetrahedra are attractive for accurate and efficient finite element or hybrid finite element/boundary integral (FE/BI) simulation of complicated electromagnetic problems. They provide versatility in the geometrical modeling of physical structures, guarantee solutions free of spurious modes, and allow a local increase of resolution by combination of mixed-order TVFEs of different orders within a computational domain. Regions with higher order mixed-order TVFEs can be selected a priori or be found adaptively via methods for a posteriori error estimation or indication. This paper demonstrates the merits of various explicit residual methods for a posteriori error indication via adaptive refinement of FE/BI solutions of electromagnetic radiation problems using hierarchical mixed-order TVFEs for tetrahedra.

A multiresolution method for simulating infinite periodic arrays

Hierarchical mixed-order tangential vector finite elements (TVFEs) for tetrahedra are attractive for accurate and efficient analysis of a wide class of electromagnetic radiation and scattering problems. They provide versatile geometrical modeling and accurate field representation by allowing combination of lowest and higher order TVFEs. In this letter, the finite-element boundary-integral (FE-BI) method with hierarchical TVFEs for tetrahedra is used for analysis of infinite, doubly periodic antenna arrays. It is shown that accurate prediction of array scanning properties can be obtained by using higher order TVFEs in the regions where large fields and rapid field variations are expected and lowest order TVFEs elsewhere. This is demonstrated in the case of a microstrip patch array.

Development and application of a novel class of hierarchical tangential vector finite elements for electromagnetics

Tangential vector finite elements (TVFEs) overcome most of the shortcomings of node-based finite elements for electromagnetic simulations. For a triangular element, this paper proposes a class of hierarchical TVPEs that differ from traditional TVFEs. The hierarchical nature of the proposed TVFEs makes them ideally suited for employing an efficient selective field expansion (the lowest order TVFE employed within part of the computational domain and a higher order TVFE employed within the remaining part of the computational domain). This is an attractive feature not shared by nonhierarchical TVFEs for which a more traditional approach (the same TVFE employed throughout the computational domain) must be applied. For determining the scattering by composite cylinders, this paper argues that the performance (in terms of accuracy, memory, and, in most cases, CPU time) of the proposed class of hierarchical TVFEs when applying selective field expansion is superior to that of the lowest order TVFE and a traditional nonhierarchical TVFE. This is the case when an artificial absorber as well as a boundary integral is used for truncating the computational domain. A guideline is given as to how lowest and higher order TVFEs shall be combined for optimal performance of the proposed class of hierarchical TVFEs.

Accurate and efficient simulation of antennas using hierarchical mixed-order tangential vector finite elements for tetrahedra

Hierarchical mixed-order tangential vector finite elements (TVFEs) for tetrahedral elements are attractive for accurate and efficient finite-element method simulation of complicated electromagnetic problems. They provide versatility in the geometric modeling of physical structures, guarantee solutions free of spurious modes, and allow local increase of resolution by selective expansion of the unknown electromagnetic field, i.e., by combination of mixed-order TVFEs of different orders within a computational domain. For a realistic antenna radiation problem, this paper demonstrates that field expansion using lowest and higher order hierarchical mixed-order TVFEs selectively is vastly superior [in terms of accuracy, memory, as well as central processing unit (CPU)-time] to field expansion using a lowest order mixed-order TVFE only.

Condition Numbers for Various Fem Matrices

A detailed study is presented that examines the interrelationships between condition numbers of finite element method (FEM) matrices based on various interpolatory and hierarchical tangential vector finite elements (TVFEs). The validity of the generally accepted postulate that interpolatory higher order TVFEs lead to better conditioned matrices than hierarchical higher order TVFEs is found to be questionable. Based on the study, an approach for improving the condition number of FEM matrices resulting from selective field expansion (different order TVFEs combined within the computational domain for effective discretization of the unknown field) is suggested and tested. The improvement comes at the expense of a more complicated formulation and computer code but does not alter accuracy.

Hierarchical tangential vector finite elements for tetrahedra

Tangential vector finite elements (TVFEs) overcome most of the shortcomings of node-based finite elements for electromagnetic simulations. Hierarchical TVFEs are of considerable practical interest since they allow use of effective selective field expansions where different order TVFEs are combined within a computational domain. For a tetrahedral element, this letter proposes a set of hierarchical mixed-order TVFEs up to and including order 2.5 that differ from previously presented TVFEs. The hierarchical mixed-order TVFEs are constructed as the three-dimensional equivalent of hierarchical mixed-order TVFEs for a triangular element. They can be formulated for higher orders than 2.5, and the generalization to curved tetrahedral elements is straightforward.

Mixed-order tangential vector finite elements for triangular elements

The paper begins by reviewing the principles of edge- and face-based vector basis functions for FEM expansion, using tangential vector finite elements (TVFEs) for triangular elements. A basic description of the hierarchical concept is then given and mixed-order TVFEs are described for triangular elements. After an introduction of the geometry, a presentation of the lowest-order TVFE (of order 0.5) is given. Subsequently, a non-hierarchical and a hierarchical TVFE of order 1.5 are presented.

A fully explicit Whitney element-time domain scheme with higher order vector finite elements for three-dimensional high frequency problems

In this paper we propose a new explicit Whitney Element-Time-Domain method for the solution of Maxwell's equations in three dimensions. This scheme could be considered a generalization of the well known Finite Difference Time Domain (FDTD) method for unstructured meshes. However, an entirely different methodology is introduced, based on the use of higher order tangential and normal vector finite elements. The exploitation of higher order approximations in an elaborate leapfrog scheme permits the use of the primary mesh only, thus avoiding the implementation of dual mesh. The new method is, finally, applied to a typical high frequency electromagnetic field formulation.

Finite-element analysis of arbitrarily shaped cavity resonators using H/sup 1/(curl) elements

We propose a finite element method together with a constraint Lanczos algorithm for analyzing arbitrarily-shaped microwave cavities. The proposed methodology is based on the use of H/sup 1//sub 0/(curl) tangential vector finite elements. Moreover, in order to solve for the generalized eigenmatrix equation efficiently, we have also developed a constrained Lanczos algorithm. Specifically, in the constrained Lanczos algorithm, we orthogonalize each new Krylov vector with respect to the spurious DC modes. Consequently, the iterative process can be used to solve for the physical resonant modes, including physical static fields, without the occurrences of any spurious DC modes.

Multiparametric vector finite elements: a systematic approach to the construction of three-dimensional, higher order, tangential vector shape functions

A systematic methodology for the construction of three dimensional tetrahedral higher order vector finite elements is presented. Appropriate degrees of freedom describing tangential field components on interfaces and shape functions depending on a set of unknown coefficients are introduced. A decoupling procedure is applied to determine the shape functions. This leads to a whole family of parameter dependent vector finite elements. However, concerning the irrotational fields to be modeled by the finite element, additional relations among the coefficients are introduced, which fully determines them. The whole procedure is described via the introduction of a new second order tetrahedral finite element. Third order tangential vector finite elements are also derived and the method could be easily generalized to higher orders. A numerical implementation of the second order element in a waveguide scattering problem is finally presented.

Analysis of biaxially anisotropic waveguides using tangential vector finite elements

AbstractProblems of biaxially anisotropic waveguides with arbitrary cross section are formulated in terms of vector and scalar potentials. By using the tangential vector finite elements, electromagnetic characteristics of propagating modes in the waveguides are obtained without the occurrence of any spurious modes. Numerical results are verified and agreements with other published results are achieved. © 1995 John Wiley & Sons, Inc.

Spurious modes in finite-element methods

This paper describes the problem of spurious modes that appear with finite-element solutions of the vector wave equation. It explains that this problem is caused by inconsistent approximations of the static solutions to the wave equation. Tangential-vector finite elements are described that enforce the tangential continuity of the vector field, but leave the normal component discontinuous. It is shown that tangential elements provide consistent approximations of the static solutions to wave problems, and that spurious modes are not produced by this type of finite element. Applications of the theory presented include problems from microwave and antenna design, and from electromagnetic compatibility.

Tangential vector finite elements for electromagnetic field computation

One approach to eliminating spurious modes in the finite-element solution of the vector wave equation is the use of tangential vector finite elements. With tangential vector finite elements, only the tangential components of the vector field are made continuous across the element boundaries. Edge-elements are the simplest example of tangential vector finite elements. However, edge-elements provide only the lowest-order of accuracy in numerical computations, since in this approach the tangential component of the field is assumed to be constant along each edge of the element. The configurations of the tangential vector finite elements which are of higher-order approximations on two- and three-dimensional tetrahedral elements are presented. The vector-valued basis functions are written explicitly, and the interpolatory meanings of the unknowns are derived. >

Vector finite elements for electromagnetic field computation

A novel structure for the finite-element analysis of vector fields is presented. This structure uses the affine transformation to represent vectors and vector operations over triangular domains. Two-dimensional high-order vector elements are derived that are consistent with Whitney forms. One-form elements preserve the continuity of the tangential components of a vector field across element boundaries, while two-form elements preserve the continuity of the normal components. The one-form elements are supplemented with additional variables to achieve pth order completeness in the range space of the curl operator. The resulting elements are called tangential vector finite elements and provide consistent, reliable, and accurate methods for solving electromagnetic field problems. >

Full-wave analysis of dielectric waveguides using tangential vector finite elements

A novel method is presented for the analysis of dielectric waveguides. This method provides four major new contributions: (1) a transformation of variables is introduced that allows propagation constants to be computed directly; (2) H/sub 1/ (curl) tangential vector finite elements are applied to dielectric waveguides to obtain reliable approximate electromagnetic fields; (3) the Lanczos algorithm is modified to solve the required eigenmatrix equation efficiently; and (4) the reaction principle is used to provide a posteriori error estimates for use in adaptive mesh refinement. The method produces reliable solutions and applies to structures that contain both electric and magnetic inhomogeneities. The answers are refined adaptively to generate waveguide eigenmodes to a specified accuracy. Numerical results of an image guide, a microstrip transmission line, and a pedestal-supported stripline are shown. Computed solutions agree very well with previously published results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Tangential vector finite elements for semiconductor device simulation

The authors present a finite element method for semiconductor device simulation using tangential vector finite element basis functions. Tangential vector basis functions are derived by reference to Whitney forms. In the new formulation, current is approximated by a quadratic polynomial, rather than as a constant within the element as has been done previously; the tangential components of a vector along the mesh edges are expressed in a consistent manner with the other variables, and the weak form of the device equations is integrated exactly. It is shown that this weak form is closely related to the Voronoi cell method and that an artificial diffusion constant may be used to stabilize the solutions. Numerical studies show that the new method is superior to the Scharfetter-Gummel algorithm in cases of obtuse and irregular triangulations. >

Analysis of passive microwave devices by using three‐dimensional tangential vector finite elements

AbstractThere are two major difficulties in applying the finite element method to the analysis of microwave devices in three dimensions. One is to obtain a stable vector finite element which does not generate spurious modes, or non‐physical solutions, in the numerical analysis. The other is to model efficiently the coupling of port regions and the discontinuity region. In this paper, we describe the application of two new finite element techniques, the tangential vector finite element method and the transfinite element method, for modelling three‐dimensional microwave devices. The tangential vector finite element method, unlike the conventional nodal finite element methods, imposes only the tangential continuity of the vector unknown across elements' boundaries. As a result, there would be no spurious modes, and reliable solutions are obtained. The transfinite element method, which combines the modal basis functions and the finite element basis functions through the variational technique, provides an efficient way to model the open boundary nature of the device. To validate the current analysis, a low VSWR waveguide connector and two microstrip low‐pass filters are analysed. Numerical results agree very well with the measurements or those obtained by other methods.