Number Of Spurious Modes Research Articles

Application of the finite-element method for solving a spectral problem in a waveguide with piecewise constant bi-isotropic filling

A spectral problem in a bi-isotropic waveguide filled nonuniformly in the cross section is considered. A generalized formulation of the problem is considered, making possible, while using Lagrange finite elements, a substantial reduction in the number of spurious modes in the spectral region of interest and shifting them to the higher frequency region. An algorithm for calculating the propagation constants and fields in the given waveguide is implemented. A series of calculations of dispersion curves and fields in a waveguide with different cross-section structures are performed.

Modeling of high contrast partially electroded resonators by means of a polynomial approach

This work presents the modeling of high contrast partially electroded resonators by means of a polynomial approach. This method allows easily solving the equations that govern the structure. The boundary, symmetry, and continuity conditions are automatically incorporated into the equations of motion by the use of delta functions for the variables stress (T) and electric displacement (D) and appropriate analytical expression forms for the independent variables, mechanical displacements (u), and electric potential (ϕ). Structure symmetry was used to reduce the number of unknowns. For the zinc oxide (ZnO) resonator in extreme geometrical cases (thin plate and bar cases), a good agreement was obtained between the results of the proposed polynomial approach and those of an analytical approach for both the modal and harmonic analyses. The proposed polynomial approach was used to calculate the 2D resonator electrical admittance (full and partial metallization) near the 1D thickness fundamental mode, and the results highlight the presence of spurious modes. Influence of the metallization rate on the number of spurious modes in the bandwidth is studied. This model can also easily calculate the electromechanical coupling coefficient and the field profiles. Illustrations for both electromechanical coupling coefficient and particle displacement profiles are given for aluminium nitride (AlN), lead zirconate titanate, and ZnO resonators.

The influence of finite extensibility on the eigenspectrum of dilute polymeric solutions

Linear stability of plane Couette flow of dilute polymeric solutions modeled using the FENE-P constitutive equation has been examined. Specifically, the spurious, discrete and continuous spectra are identified as a function of the ratio of the solvent to the total viscosity β, maximum chain length L, disturbance wavenumber α and the Weissenberg number ( We). It is observed that reducing L shifts the entire spectrum to the left (in the eigenspectrum plane) by a factor directly related to the steady-state value of the Peterlin function f. Additionally, decreasing the value of L causes the splitting of the regular continuous spectrum, initially located at −1/ We, into two branches. Overall, the plane Couette flow of a FENE-P model is found to be unconditionally stable. Specifically, decreasing L increases the decay rate of the most dangerous disturbance while increasing the number of discrete and spurious modes. However, increasing both β and α decreases the number of discrete and spurious modes whereas increasing We has no influence on the number of spurious modes but results in an increase in the number of discrete modes.

A finite volume scheme with shock fitting for the steady Euler equations

Analysis of two alternative finite volume formulations, in respect of accuracy on non-uniform meshes and number of spurious modes, leads to a preference for the more compact cell vertex scheme over the cell centre scheme. The resulting equations are solved iteratively by using a Lax-Wendroff procedure as a smoother for a multigrid algorithm: then application of boundary conditions in a natural way leads rapidly to all individual residuals being driven close to zero—except at shocks. At shocks the residuals should not be zero and a shock-fitting procedure is introduced to avoid this inconsistency. Sharp, accurate solutions on a relatively coarse mesh are obtained for a channel (low problem in which the Zierep singularity is displayed, and for the NACA 0012 aerofoil.

On the Reduction of the Number of Spurious Modes in the Vectorial Finite-Element Solution of Three-Dimensional Cavities and Waveguides

A novel approach to the solution of three-dimensional micro-wave cavity and waveguide problems by finite elements reduces the number of spurious, nonphysical modes. Solutions are obtained in terms of the field vector H. Three-dimensional vector boundary conditions are implemented in a way that allows arbitrarily-shaped curved boundaries to be modeled. The formulation is based on a subparametric finite element with 27 interpolation nodes.

Elimination of spurious modes in finite element analysis

A common cause of spurious (non-physical) modes that arise in either finite difference or finite element derived eigenvalue problems is identified. It is shown that these modes are the result of an excessively flexible system. The flexibility is removed by constraining the problem. An analogy is drawn between electromagnetic wave propagation and acoustic wave propagation in liquids to show that the spurious modes encountered in both cases are due to fundamentally the same cause. Results are presented to show that constraining the problem yields a significant reduction in the number of spurious modes, a big improvement in the quality of the eigenvector of the physical modes and only a marginal increase in the error in the eigenvalue for the low order modes.