Stabilization of time domain solutions of EFIE based on partial element equivalent circuit models

Transient Time-Dependent Electric Field of Dielectric Bodies Using the Volterra Integral Equation in Three Dimensions

“…As aforementioned, almost all marching-on-in-time numerical solutions for the time domain integral equations based schemes suffer from late time instabilities [13][14][15][16][17][18][19][20]. This is also reported for some of the differential based methods, such as the FDTD [45].…”

“…Recently the efficiency of TDIE techniques has increased dramatically with the advent of acceleration schemes such as the plane wave time domain algorithm [11] and the fast Fourier transform accelerated schemes [12]. Furthermore, the marching-on-in-time methods for solving TDIE, that have been shown prone to late time instabilities, have also been successfully treated for various scenarios through the use of spatial and/or temporal filtering techniques [13][14][15][16], and the implementation of accurate spatial interpolation rules with implicit time-stepping schemes [17][18][19][20]. In addition, a backward finite difference approximation, resulting in an implicit technique, to minimise these late-time oscillations has also been proposed [21,22].…”

Fast Evaluation of Three-Dimensional Transient Wave Fields Using Diagonal Translation Operators

“…Unfortunately, TDIE techniques have long been conceived as intrinsically unstable and computationally expensive when compared to their differentialequation counterparts. However, recently, progress toward stable TDIE-based schemes has been reported [11][12][13][14][15]. In contrast, literature on techniques for reducing the computational complexity of these TDIE techniques is virtually nonexistent.…”

Fast transient analysis of acoustic wave scattering from rigid bodies using a two-level plane wave time domain algorithm

“…4,8,22,23 Recently, it has been experimentally demonstrated that stability can be achieved by employing implicit schemes that use higherorder quadrature rules and/or larger time step sizes. [5][6][7] In the present study, the integrals over triangular domains are numerically evaluated as outlined in Ref. 20, and the time step size is chosen-independent of the mesh size-as ⌬ t ϭ2/(␤ max ).…”

“…Recent research, however, has shown that the MOT schemes can be stabilized by using implicit time stepping along with more accurate numerical integration and differentiation rules. [5][6][7] On the other hand, literature on techniques for reducing its high computational complexity is scarce.…”