An efficient finite element formulation to analyze waveguides withlossy inhomogeneous bi-anisotropic materials

In this paper a finite element formulation in terms of the magnetic field is presented for the analysis of waveguides with bianisotropic media. Such a formulation can deal with lossy inhomogeneous materials characterized by simultaneous permittivity, permeability, and cross-coupling (as in optical activity) arbitrary full tensors. The analysis takes into account arbitrary cross sections, and results in spurious-mode suppression, complex-mode computation, and the possibility of alternatively specifying the frequency or the complex propagation constant as an input parameter. In this way, many novel classes of waveguides with promising applications, such as chirowaveguides and chiroferrite-waveguides, can be analyzed. The formulation leads to a quadratic sparse eigenvalue problem which is transformed into a sparse generalized eigenvalue problem. This eigensystem is solved by the subspace method, the sparsity of the matrices being fully utilized. The proposed method has been validated by analyzing waveguides with biisotropic and bianisotropic materials. The agreement with previously published data is found to be excellent     

Full vectorial finite element formalism for lossy anisotropicwaveguides

An efficient computer-aided solution procedure based on the finite-element method is developed for solving general waveguiding structures containing lossy, anisotropic materials. In this procedure a formulation in terms of the transverse magnetic field component is adopted and the eigenvalue of the final matrix equation corresponds to the propagation constant itself. Thus one avoids the unnecessary iterations which arise when using complex frequencies. To demonstrate the strength of the presented method, numerical results are shown for a rectangular waveguide filled with lossy anisotropic dielectric with off-diagonal elements in a permittivity tensor and compared with those obtained by the telegrapher equation method. The results are in excellent agreement both for phase and for attenuation     

Dispersive delay at gigahertz frequencies using magnetostatic waves

Magnetostatic waves are intrinsically suited for use in microwave dispersive delay lines, because they are readily generated at high frequencies and their velocity is frequency dependent. Here we review progress toward meeting the systems requirement that the delay time be linear in frequency. Magnetostatic waves can approach this condition if a ground plane is nearby or if two or more ferrite layers are present; with forward volume waves one may also use a dispersive reflecting array, as is done with surface acoustic waves. The use of a properly shaped ground plane gives the lowest phase errors so far measured (±16° over 0.6 GHz); multiple ferrite layers show promise of allowing the greatest delay.     

Dependence of propagation loss of magnetostatic forward volume waves on device parameters

It is shown that for magnetostatic forward volume waves (MSFVW) the propagation loss depends on device parameters such as thickness of magnetic film, MSFVW wavelength, a static magnetic field, etc. The result suggests that when the film thickness is about a quarter of the wavelength and the effective internal field is comparable to or larger than the saturation magnetisation of the film, the propagation loss per wavelength is minimised. Experimental results were in good agreement with this theoretical prediction, and were carried out using a LaGa substituted YIG film.<>     

Microwave diplexer using magnetostatic surface and backward volume waves

An experimental diplexer based on magnetostatic wave propagation in a tangentially magnetised thin film of YIG is reported. The diplexer function is obtained by using the fact that magnetostatic surface and backward volume waves propagate in contiguous but nominally nonoverlapping frequency bands.     

Coupling of finite element and moment methods for electromagneticscattering from inhomogeneous objects

A hybrid formulation which combines the method of moments (MM) with the finite element method (FEM) to solve electromagnetic scattering and/or absorption problems involving inhomogeneous media is discussed. The basic technique is to apply the equivalence principle and transform the original problem into interior and exterior problems, which are coupled on the exterior dielectric body surface through the continuities of the tangential electric field and magnetic field. The interior problem involving inhomogeneous medium is solved by the FEM, and the exterior problem is solved by the MM. The coupling of the interior and exterior problems on their common surface results in a matrix equation for the equivalent current sources for the interior and exterior problems. Combining advantages of both methods allows complicated inhomogeneous problems with arbitrary geometry to be treated in a straightforward manner. The validity and accuracy of the formulation are checked by two-dimensional numerical results, which are compared with the exact eigenfunction solution, the unimoment solution, and Richmond's pure moment solution     

An efficient GPU acceleration format for finite element analysis

This paper proposes a new Graphics Processing Unit （GPU）-accelerated storage format to speed up Sparse Matrix Vector Products （SMVPs） for Finite Element Method （FEM） analysis of electromagnetic problems. A new format called Modified Compile Time Optimization （MCTO） format is used to reduce much execution time and design for hastening the iterative solution of FEM equations especially when rows have uneven lengths. The MCTO-applied FEM is about 10 times faster than conventional FEM on a CPU, and faster than other row-major ordering formats on a GPU. Numerical results show that the proposed GPU-accelerated storage format turns out to be an excellent accelerator.     

Electrodynamic theory of multiport structures using magnetostatic waves in ferrite films and its applications

The paper presents an electrodynamic analysis of tunable multiport ferrite-dielectric structures with parallel transmission lines of an arbitrary type, coupled through propagating magnetostatic modes of magnetized multilayered ferrite films. The structures are supposed to be excited at one port by an incident electromagnetic wave, and amplitudes and phases of electromagnetic waves at other ports are obtained by an analytical procedure. The model holds for an arbitrary direction of a magnetizing field and describes the interaction of magnetostatic modes in ferrite films of a finite width. The solution is obtained in a self-consistent approach, i.e., a reaction of magnetostatic waves (MSWs) on transducers, which excite them, is taken into account. Derived closed-form expressions for response functions of multiports provide the base for the modeling of a wide class of MSW devices: multichannel adjustable filters and delay lines, directional couplers, frequency-selective power dividers, tunable oscillators and active filters, and multiport resonators. The theory is also valid for the analysis of multi-element, interdigital, and meander MSW transducers. Applications of a general theory are demonstrated for numerical calculations of frequency responses of surface and forward volume MSW filters, delay lines with new types of strip-line transducers (two-port and T-type), and for the analysis of a phenomenon of mutual coupling of transducers in conventional devices.     

An efficient scalar finite element formulation for nonlinearoptical channel waveguides

A self-consistent numerical approach based on the scalar finite element method is described for the analysis of both TE-like and TM-like nonlinear guided waves in optical channel waveguides. In order to improve the convergence and accuracy of solutions, isoparametric elements and numerical integration formulae derived by Hammer et al. are introduced. Numerical results are presented for nonlinear elliptical core optical fibers, and it is confirmed that in this approach, highly accurate solutions can be obtained with small scale computation. Furthermore, graded-index nonlinear optical channel waveguides are also analyzed, and the influence of refractive-index profiles on propagation characteristics of the nonlinear guided waves is investigated     

A finite element analysis on electromagnetic waves in rectangular dielectric chirowaveguide

A finite element algorithm on eigenvalue problem of the dielectric waveguide with chiral material is presented. The chiral material is defined by the constitution relations which make the electromagnetic coupling between the electric and magnetic fields by means of the chirality admittance. The chiral material has potential applications in the areas of infrared and mm-wave band. For different chirality admittance, the computation is developed for different structure of waveguides which are difficult for analytical calculation. From the eigenvalues and the eigenvectors, the dispersion curves, the modes and the field patterns are obtained. The maximum value of dispersion curves is obvious greater than that without chiral material. The main points of the results of finite element calculation are consistent with those of analytical approach.     

Scattering of volume magnetostatic waves by periodic slot lattices

Scattering of volume magnetostatic waves excited in thin films by the lattices composed of metal ribbons and slots in a metal screen is analyzed. A boundary value problem for the Maxwell equations is formulated and solved in the static approximation. An algorithm for the numerical solution of this boundary value problem is proposed. Scattering of volume magnetostatic waves by 2D periodic lattices of slots that are infinite along one coordinate and finite along the other coordinate is studied for an arbitrary orientation of slots and an arbitrary angle of incidence of the magnetostatic wave. The energy-band structure of lattices is analyzed. The possibility of formation of magnon crystals based on the slot lattices is demonstrated.     

Bragg resonances of magnetostatic surface waves in a ferrite-magnonic-crystal-dielectric-metal structure

Formation of Bragg resonances of surface spin waves (SSWs) propagating in a magnonic-crystaldielectric-metal (MC-D-M) structure is studied. It is shown that, in an MC-D-M structure with a finite dielectric interlayer of thickness t, Bragg resonances of the SSWs with the wavenumbers k < 1/t can be destroyed whereas the resonances of the SSWs with k > 1/t persist and lead to formation of rejection bands in the wave spectrum.     

Simultaneous propagation of magnetostatic and spin-elastic waves in nonellipsoidal ferrimagnets

Spin-wave propagation parallel to the static biasing field is considered in the presence of magnetostatic boundary effects for a saturated nonellipsoidal ferrimagnet. It is shown that two principal branches exist in the delay-field characteristics, over the same biasing range, with delay decreasing monotonically with applied field. The predominantly magnetostatic branch is related to the experiments of Kedzie, the coupling mechanisms of wire antennas to spin waves, and observations on magnetostatic-mode parametric amplifiers.     

Directional coupling of magnetostatic surface waves in layered magnetic thin films

The propagation characteristics of magnetostatic surface waves (m.s.s.w.) in a layered system of y.i.g. film, dielectric, y.i.g. film, are theoretically investigated. It is shown that the directional coupling of m.s.s.w. is possible between y.i.g. films. The directional coupling has frequency filtering characteristics due to dispersion of m.s.s.w.     

Dispersion characteristics of magnetostatic surface waves in a two-layer ferromagnetic film

The dispersion characteristics (dispersion and isofrequency curves and dispersion surfaces) of magnetostatic surface waves propagating in an arbitrary direction in a two-layer ferromagnetic film are investigated. The shapes of these curves and surfaces are studied at different ratios between the saturation magnetizations of the ferromagnetic layers, and the conditions for existence of external waves (always forward) and internal waves (forward and backward or only forward) are determined.     

Optimal design for micro-thermoelectric generators using finite element analysis

To fabricate micro-thermoelectric generators (μTEGs), one must design the optimal structure of the μTEGs and achieve thermoelectric thin films with excellent properties. This study investigated the role of the dimensions of μTEGs, including the length of the thermoelements, thickness of the substrates, and cross-sectional area of the thermoelements. To evaluate the power generated by μTEGs and their efficiency, three-dimensional models of μTEGs were subjected to finite element analysis. Three-dimensional models are more accurate than one-dimensional models, since the directions of the heat flux and electrical current are not parallel in μTEGs. The governing equations were derived from the Seebeck effect and Peltier effect, which show thermoelectric energy conversion. In the simulation, the substrate, n-type material, and p-type material were assumed to be silicon, Bi₂Te₃, and Sb₂Te₃, respectively. We calculated the thermoelectric power generated by the μTEGs and their thermoelectric energy conversion efficiency. These two evaluation indices represent the performance of μTEGs. The thermoelectric simulation produced design guidelines for high-performance μTEGs.     

Validation of finite element models of liver tissue using micro-CT

In this work, we aim at validating some soft tissue deformation models using high-resolution micro-computed tomography (Micro-CT) images. The imaging technique plays a key role in detecting the tissue deformation details in the contact region between the tissue and the surgical tool (probe) for small force loads and provides good capabilities of creating accurate 3-D models of soft tissues. Surgical simulations rely on accurate representation of the mechanical response of soft tissues subjected to surgical manipulations. Several finite-element models have been suggested to characterize soft tissues. However, validating these models for specific tissues still remain a challenge. In this study, ex vivo lamb liver tissue is chosen to validate the linear elastic model (LEM), the linear viscoelastic model (LVEM), and the neo-Hooke hyperelastic model (NHM). We find that the LEM is more applicable to lamb liver than the LVEM for smaller force loads (< 20 g) and that the NHM is closer to reality than the LVEM for the range of force loads from 5 to 40 g.     

FEM/BEM混合法计算各向异性不均匀介质柱电磁散射

应用有限元-边界元(FEM/BEM)混合法计算二维各向异性不均匀介质柱电磁散射,对介质柱内、外区域分别采用有限元和边界元法进行分析,然后应用边界条件建立部分稀疏部分满填充的矩阵方程.应用内观法结合多波前法求解该矩阵方程,分别计算了均匀分布和不均匀分布的各向异性介质柱的雷达散射截面.数值计算表明,有限元-边界元混合法在分析和计算不均匀开放域电磁问题时有一定的优势.     

Prediction of microelectronic substrate warpage using homogenized finite element models

The focus of this study was to numerically predict effective thermo-mechanical properties and substrate warpage of high-density microelectronic substrates used in organic CPU packages. Microelectronic substrates are typically composed of several polymer, fiber-weave, and copper layers and are filled with a variety of complex features, such as electric traces, plated-through-holes, micro-vias, and adhesion holes. When subjected to temperature changes, these substrates may warp, driven by the mismatch in coefficients of thermal expansion (CTE) of the constituent materials. This study focused on predicting substrate warpage in an isothermal condition. The numerical approach consisted of three major tasks: estimating homogenized (effective) thermo-mechanical properties of the features; calculating effective properties of discretized layers using the effective properties of the features; and assembling the layers to create two-dimensional (2D) finite element (FE) plate models and to calculate warpage of the substrates. The effective properties of the features were extracted from three-dimensional (3D) unit cell FE models, and closed-form approximate expressions were developed using the numerical results, curve fitting, and some simple bounds. The numerical approach was applied to predict warpage of production substrates, analyzed, and validated against experimentally measured stiffness and CTEs. In this paper, the homogenization approach, numerical predictions, and experimental validation are discussed.     

Measurement of lung hyperelastic properties using inverse finite element approach

Hyperelastic properties of deflated lung tissue have been characterized via an inverse finite element approach. Such properties are useful in many medical diagnosis and treatment applications where tissue deformation can be modeled to account for during the procedure. Several indentation experiments were conducted on various porcine lungs' tissue specimens resected immediately from different regions and lobes after the animals were sacrificed. Three different strain energy models, namely Ogden, Yeoh, and Polynomial, were used and respective hyperelastic parameters were obtained. The parameters for each model were estimated through an optimization process where the experimental force-displacement profiles of indentation were fitted to those obtained from finite element simulations performed specifically for the samples' geometries. Results obtained in this investigation for all the three models indicate convergence with reasonably low average fitting errors ranging from 2.3% to 6.2%. Independent tests were also performed to assess the effects of samples' heterogeneities on the obtained parameters. The outcome of these tests was encouraging and confirmed small impact of tissue inhomogeneities on the estimated parameters. The reported hyperelastic properties can, accordingly, pave the way for more accurate biomechanical modeling of the lung's soft tissue in the emerging applications of minimally invasive medical intervention for lung cancer diagnosis and treatment.