STABLE SOLUTION OF TIME DOMAIN INTEGRAL EQUATION METHODS USING QUADRATIC B-SPLINE TEMPORAL BASIS FUNCTIONS

This paper is concerned with stable solutions of time domain integral equation （TDIE） methods for transient scattering problems with 3D conducting objects. We use the quadratic B-spline function as temporal basis functions, which permits both the induced currents and induced charges to be properly approximated in terms of completeness. Because the B-spline function has the least support width among all polynomial basis functions of the same order, the resulting system matrices seem to be the sparsest. The TDIE formula-tions using induced electric polarizations as unknown function are adopted and justified. Numerical results demonstrate that the proposed approach is accurate and efficient, and no late-time instability is observed.

Applying p-Step Lagrange Interpolation as Temporal Basis Functions to TDFEM for 3-D EM Radiation Problems

Accurate simulations of ultra-wideband （UWB） electromagnetic radiation from an antenna were developed based on a time-domain finite element method （TDFEM） based on p-step Lagrange interpolation for the temporal expansion. The motivation was to utilize the good interpolation features and straightforward computations for UWB antenna simulations. Numerical results were obtained from the cases of the cavity resonance problem, a bowtie and a Sierpinski bowtie antenna. Comparisons with an existing TDFEM approach employed linear temporal basis functions show good agreement to demonstrate the validity of the present schemes. The TDFEM with 2-step Lagrange interpolation as the temporal basis functions achieves better numerical results with only a small increase to run time and memory use in terms of the relative errors of the resonant frequency in the cavity for the transverse electric mode and the radiation patterns of the bowtie antenna.

On hybrid temporal basis functions for stable numerical solution of time domain boundary integral equations

Problems in unsteady aerodynamics and aeroacoustics can sometimes be formulated as integral equations,such as the boundary integral equations.Numerical discretization of integral equations in the time domain often leads to so-called March-On-in-Time(MOT)schemes.In the literature,the temporal basis functions used in MOT schemes have been largely limited to low-order shifted Lagrange basis functions.In order to evaluate the accuracy and effectiveness of the temporal basis functions,a Fourier analysis of the temporal interpolation schemes is carried out.Based on the Fourier analysis,the spectral resolutions of various temporal basis functions are quantified.It is argued that hybrid temporal basis functions be used for interpolation of the numerical solution and its derivatives with respect to time.Stability of the proposed hybrid schemes is studied by a matrix eigenvalue method.Substantial improvement in accuracy and efficiency by using the hybrid temporal basis functions for time domain integral equations is demonstrated by numerical examples.Compared with the traditional temporal basis functions,the use of hybrid basis functions keeps numerical errors low for a larger frequency range given the same time step size.Conversely,for a given range of frequency of interest,a larger time step can be used with the hybrid temporal basis functions,resulting in an increase in computational efficiency and,at the same time,a reduction in memory requirement.