Scalar Finite Element Method Research Articles

Fast finite element electrostatic analysis with domain decomposition method

Accurate simulation of electrostatic field in electronic devices is very important to improve their performance. When the traditional finite element method is used to analyze the electrostatic field of large and complex structures, the calculation speed is slow and the computing resources are greatly consumed. Therefore, in this paper, we investigate electrostatic analysis with a non-overlapping domain decomposition method based on the scalar finite element method under a novel transmission condition. In order to improve the efficiency of matrix solving and reduce the memory consumption, the block Jacobi preconditioner is introduced. In addition, the multifrontal block incomplete Cholesky preconditioner is utilized to further improve the computational performance based on the block Jacobi preconditioner. Several numerical examples are simulated and compared with the analytical solutions and the commercial software Maxwell 3D. The results demonstrate the accuracy and efficiency of the proposed domain decomposition method.

Fast and Accurate FEM based Model for the Periodic Layered Structure of Vertical Cavity Surface Emitting Lasers

An adaptive numerical approach has been developed based on a scalar finite element method (FEM) for the analysis of vertical cavity surface emitting lasers (VCSELs). The suggested model is designed to handle the various complicated structures of the Bragg grating mirrors, the main component of the laser optical cavity. The targeted results have been achieved in fast, stable and accurate manner with low computational resources.

The three-dimensional finite element forward modelling of complex excitation source NMR

Abstract Traditional nuclear magnetic resonance (NMR) is mainly applied to horizontal ground and one-dimensional electrical structures. However, calculations of the excitation fields rarely consider the three-dimensional electrical changes of the subsurface medium and undulating terrain, or the deformations caused by emission sources. Therefore, to analyse the influences of terrain fluctuations, emission source deformations and three-dimensional electrical changes on NMR, three-dimensional finite element forward modelling of undulating terrain NMR was conducted in this study. First, based on a scalar finite element method, the direct calculations of the excited magnetic fields of a three-dimensional electrical medium were realised, which improved calculation accuracy by avoiding the finite element calculations of magnetic vector potential and vector on the magnetic field. During the source loading process, the equivalent thin wire source of the pseudo δ function was used to load the source function directly into the equation for the purpose of achieving total field calculations. This was completed to enable the calculations to be applied to any shape of the transmitting loop and undulating terrain. Then, the components of the excitation magnetic fields perpendicular to the geomagnetic fields were calculated using the rotation matrix. Finally, the NMR sensitivity function and 3D responses were calculated. The calculations of the excitation magnetic fields were verified using a uniform half-space model. The overall algorithm was tested by the nuclear magnetic responses of the layered medium. Also, a typical undulating terrain model was adopted and the complex excitation source NMR was simulated using the algorithm proposed in this study. The algorithm provided a three-dimensional forward basis for the NMR inversion in the cases of determining the electrical medium for the subsequent undulating terrain.

Characterization and Mode Identification Analysis of a 3-D Rib Waveguide by Using a Modified Scalar Finite Element Method

Characterization and Mode Identification Analysis of a 3-D Rib Waveguide by Using a Modified Scalar Finite Element Method

Modeling of single mode optical fiber having a complicated refractive index profile by using modified scalar finite element method

A numerical method based on modified scalar finite element method (SC-FEM) is presented and programmed on MATLAB platform for optical fiber modeling purpose. We have estimated the dispersion graph, mode cut off condition, and group delay and waveguide dispersion for highly complicated chirped type refractive index profile fiber. The convergence study of our FEM formulation is carried out with respect to the number of division in core. It has been found that the numerical error becomes less than 2 % when the number of divisions in the core is more then 30. To predict the accurate waveguide dispersion characteristics, we need to compute expression $$\frac{{{\text{d}}^{2} \left( {\text{vb}} \right)}}{{{\text{dv}}^{2} }}$$ numerically by the FEM method. For that the normalized propagation constant b (in terms of $$\beta$$ ) should be an accurate enough up to around 6 decimal points. To achieve this target, we have used 1 million sampling points in our FEM simulations. Further to validate our results we have derived the higher order polynomial expression for each case. Comparison with other methods in calculation of normalized propagation constant is found to be satisfactory. In traditional FEM analysis a spurious solution is generated because the functional does not satisfy the boundary conditions in the original waveguide problem, However in our analysis a new term that compensate the missing boundary condition has been added in the functional to eliminate the spurious solutions. Our study will be useful for the analysis of optical fiber having varying refractive index profile.

Beam propagation and mode coupling study in a coupled waveguide structure by using scalar finite element method

Here we present the propagation of pulse in a coupled waveguide structures. Finite element method has been effectively applied to analyze the closely coupled waveguide structure. The mode coupling phenomena is well described in this paper. It is demonstrated that there are substantial amount of power exchange takes place between various modes. We excite the structure with original mode pattern which can be well approximated by slightly deviated Gaussian shape pulse. Then we apply the mode propagation concept to estimate the mode beating phenomena in coupled structure. The effect of waveguide separation is well demonstrated by using examples. We too derive the Fresnel equation and discuss a solution strategy in terms of the finite element method. We apply the transparent boundary condition to avoid the unwanted reflections from the artificial computation windows.

Dosimetry of electromagnetic field exposure of an active armlet and its electromagnetic interference to the cardiac pacemakers using adult, child and infant models

ABSTRACTWearable devices have been popularly used with people from different age groups. As a consequence, the concerns of their electromagnetic field (EMF) exposure to the human body and their electromagnetic interference (EMI) to the implanted medical devices have attracted many studies. The aim of this study was to evaluate the human exposure to the EMF of an active radiofrequency identification (RFID) armlet as well as its EMI to the cardiac pacemaker (CP). Different human models from various age groups were applied to assess the result variability. The scalar potential finite element method was utilized in the simulation. Local EMF exposure and the exposure to the central nerve system tissues were evaluated using different metrics. EMI to the CP was assessed in terms of the conducted voltage to the CP. The results from all the models revealed that the studied RFID armlet would not produce the EMF exposure exceeding the safety limits. The calculated interference voltage was highly dependent on the distance between the RFID armlet and the CP (i.e. the physical dimension of the individual model). The results proposed to evaluate the appropriateness of the current EMI measurement protocol for this kind of devices used by the infants.

Modelling of deep transcranial magnetic stimulation: different coil configurations.

This paper provides a characterization of the induced electric field distributions in the brain of a realistic human model due to 16 different coil configurations. We used the scalar potential finite element method to calculate the induced electric field distributions differentiating the brain structures, e.g. cortex, white matter, cerebellum, thalamus, hypothalamus, hippocampus, pons and midbrain. We found that, despite the presence of a depth-focality tradeoff, some configurations are able to reach subcortical white matter tracts at effective electric field level.

Proposal of Coupled Ring Resonator Based on One-Dimensional Photonic Crystal Nanocavity

We propose the coupled ring resonator based on one-dimensional photonic crystal (1-D PC) nanocavity. The proposed structure is composed by introducing 1-D PC nanocavity into the CROW based on ring resonator, and we expect that it can achieve small group velocity. We investigate the transmission characteristics of the proposed structure by using 2-D scalar finite element method (FEM) for periodic waveguide analysis. We obtained the group velocity vg = 0.033 c with c being light velocity in vacuum because of combining 1-D PC nanocavity and CROW based on ring resonator. Moreover, we consider reduction of footprint of the proposed structure for photonic integration.

Transient elastic wave propagation and scattering in plates: comparison between pulsed TV-holography measurements and finite element method predictions

Pulsed TV-holography (PTVH) can be used for obtaining two-dimensional maps of instantaneous out-of-plane displacements in plates. In particular, our group has demonstrated that scattering patterns generated by the interaction of elastic waves with defects can be measured with PTVH and employed for the characterization of damage in nondestructive inspection of plate structures. Recently, we have succeeded in obtaining a quantitative description of experimental scattering patterns of quasi-Rayleigh (qR) waves produced by holes in harmonic regime using a finite element method (FEM) combined with a two-dimensional scalar wave equation, avoiding the standard and more complex vector approaches based on the rigorous linear elasticity theory. This scheme has been extended here for characterizing equivalent scattering phenomena in transient regime. Simulated scattering patterns, obtained with the scalar FEM, and the corresponding experimental patterns associated to the interaction of qR waves with holes, measured with our specifically developed PTVH system, have been compared. Results have shown that, except for the evaluation of the backscattering coefficient, a reasonable agreement between theory and experiment is obtained in both amplitude and phase, which confirms the feasibility and potential of the proposed scalar approximation for the characterization of experimental transient scattering patterns measured with our PTVH technique.

The design of low-loss curved waveguides

A procedure for the design of low-loss continuous curvature waveguide bends, for use in integrated photonic circuits, is presented. The design employs the scalar finite element method and a technique for drawing waveguide bends based on their curvature. The finite difference beam propagation method is used to determine the power lost along the length of the waveguide structures. This new method allows the design of waveguide bends with lower loss than can be obtained by conventional methods.

Proposal for a Compact Resonant-Coupling-Type Polarization Splitter Based on Photonic Crystal Waveguide With Absolute Photonic Bandgap

We propose a resonant-coupling-type polarization splitter based on a photonic crystal structure with absolute photonic bandgap. The scalar finite-element method was used to calculate resonant frequencies of the cavity and frequency dependences of the polarization splitter. This device supports single-mode operation for both transverse-electric and transverse-magnetic waves. We show that miniaturization of the proposed polarization splitter can be realized by utilizing resonant coupling.

A New Three-Dimensional (3-D) Scalar Finite Element Method to Compute$T_0$

This paper presents a new computational method of magnetic field in the air created by the known current density distribution in coils or solid conductor. The method consists of decoupling three components of the vector field T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> . The method is faster and requires less memory than the classical approach, used in the magnetostatic and magnetodynamic finite-element formulations

Analysis of photonic crystal fibers: Scalar solution and polarization correction

A numerical approach based on the scalar finite element method is applied to analyse the modal properties of photonic crystal fibers having a solid core and a cladding region with either circular or non-circular microstructured holes. A correction which accounts for the polarization effects due to the large refractive index difference between silica materials and air holes is included in the analysis. Numerical results show that the proposed technique is an efficient and accurate alternative to vector ones.

Bending effect on fiber acousto-optic mode coupling

The acousto-optic effect in a bent fiber is studied experimentally and numerically by using the scalar finite-element method. The resulting transmission spectra show that new mode-coupling peaks appear due to the breaking of the mode spatial symmetry. The strength of new peaks increases as the fiber-bending curvature increases with a redshift or blueshift in wavelength, strongly depending on the orientation of fiber bending with respect to the acoustic-wave vibration direction.

Nested multigrid vector and scalar potential finite element method for fast computation of two-dimensional electromagnetic scattering

Nested multigrid techniques are combined with the ungauged vector and scalar potential formulation of the finite-element method to accelerate the convergence of the numerical solution of two-dimensional electromagnetic scattering problems. The finite-element modeling is performed on nested meshes of the same computational domain. The conjugate gradient method is used to solve the resultant finite-element matrix for the finest mesh, while the nested multigrid vector and scalar potential algorithm acts as the preconditioner of the iterative solver. Numerical experiments are used to demonstrate the superior numerical convergence and efficient memory usage of the proposed algorithm.

Modal analysis of anisotropic diffused-channel waveguide by a scalar finite element method

A procedure to model optical diffused-channel waveguides is presented in this work. The dielectric waveguides present anisotropic refractive indexes which are calculated from the proton concentration. The proton concentration inside the channel is calculated by the anisotropic 2D-linear diffusion equation and converted to the refractive indexes using mathematical relations obtained from experimental data. The arbitrary refractive index profile is modeled by a nodal expansion in the base functions. The TE and TM-like propagation properties (effective index) and the electromagnetic fields for well-annealed proton-exchanged (APE) LiNbO/sub 3/ waveguides are computed by the finite element method.

Two-dimensional singular vector elements for finite-element analysis

The finite-element method (FEM) exhibits a reduced convergence rate when used for the analysis of geometries containing sharp edges where the electromagnetic field is singular. The convergence of the method can be-improved by introducing singular elements that model analytically predicted singular behavior. A number of authors have developed singular elements that are compatible with the scalar FEM. In this paper, we propose a new singular element that is compatible with edge-based vector finite elements and can cope with any order of singularity while preserving the sparsity of the FEM equations. Edge-based singular elements more correctly model singular fields and thus require fewer unknowns, while avoiding the introduction of spurious modes in the numerical solution. Numerical results verify that the convergence of the FEM is significantly improved.

Three-dimensional athermal waveguide at 1.3 μm wavelength for temperature independent lightwave devices

To eliminate the temperature dependence of narrow-band filter, a three-dimensional athermal waveguide of which optical path length is independent of temperature was developed at 1.3 μm wavelength. The temperature coefficient of the refractive index of films made of glass materials was measured at this wavelength, and a strip-loaded athermal waveguide was designed using a scalar finite element method. The temperature coefficient of optical path length was successfully decreased to 9.65X10-9[/K] (0.1% of the conventional waveguide).

Iterative finite element solution for cut-off frequencies of inhomogeneous ferrite waveguides

The frequency dependence of the tensor entries in gyrotropic media results in a non-linear eigenvalue problem for the solution of resonant structures. An iterative scalar finite element method is presented here to calculate the modal resonant frequencies for planar inhomogeneous structures. For these calculations, the gyrotropic medium is modelled using material characteristics taken from the hysteresis curve and a specified applied magnetic bias field. The technique is verified by comparing the calculated cut-off frequencies with the exact solution for a ferrite rod in a circular waveguide. The cut-off plane for a triply ridged waveguide with a ferrite rod is also treated.