A Space-Time Mixed Galerkin Marching-on-in-Time Scheme for the Time-Domain Combined Field Integral Equation

Abstract

Abstract-The time domain combined field integral equation (TD-CFIE), which is constructed from a weighted sum of the time domain electric and magnetic field integral equations (TD-EFIE and TD-MFIE) for analyzing transient scattering from closed perfect electrically conducting bodies, is free from spurious resonances. The standard marching-on-in-time technique for discretizing the TD-CFIE uses Galerkin and collocation schemes in space and time, respectively. Unfortunately, the standard scheme is theoretically not well understood: stability and convergence have been proven for only one class of spacetime Galerkin discretizations. Moreover, existing discretization schemes are non-conforming, i.e., the TD-MFIE contribution is tested with divergence conforming functions instead of curl conforming functions. We therefore introduce a novel spacetime mixed Galerkin discretization for the TD-CFIE. A family of temporal basis and testing functions with arbitrary order is introduced. It is explained how the corresponding interactions can be computed efficiently by existing collocation-in-time codes. The spatial mixed discretization is made fully conforming and consistent by leveraging both Rao-Wilton-Glisson and BuffaChristiansen basis functions and by applying the appropriate bi-orthogonalization procedures. The combination of both techniques is essential when high accuracy over a broad frequency band is required.

Parallel PWTD-Accelerated Explicit Solution of the Time-Domain Electric Field Volume Integral Equation

“…The implicit MOT scheme require at every time step solution of the linear system [3], which is traditionally constructed upon expanding the flux density with Schaubert-Wilton-Glisson (SWG) spatial basis functions [8] and piecewise polynomial temporal basis functions [9], followed by Galerkin and point testing in space and time, respectively. In addition, modern implicit MOT-based solution of time domain surface and volume integral equations can be made low-and high-frequency stable by using computationally more expensive space-time discretization techniques, such as bandlimited time discretization [7,10], space-time Galerkin testing [11,12], quasi-Helmholtz decomposition [13,14], and highly accurate evaluation of MOT matrix elements [12,[15][16][17][18][19][20]. In contrast, the explicit MOT scheme, usually leverages pulse spatial basis functions and low order temporal basis functions and point testing both in space and time.…”

A Novel Smoothing Scheme of Temporal Basis Function Independent Method in Mot Based Tdie

“…To complete the whole MOT solver, temporal convolutions between the potentials and the temporal basis functions have to be performed as indicated in Eqs. (7) and (8). However, it must be emphasized that the discontinuities in α(r, t) are very important and determinative for the singular behavior existing in Eqs.…”

“…However, these methods reduce the accuracy, increase the computation complexity and are invalid for large-scale and complex geometric structures. Later, implicit time stepping algorithms and appropriate smooth temporal basis functions are also proposed to overcome the above mentioned drawbacks [5][6][7][8][9][10]. Recent studies show that accuracy computation of the MOT impedance matrix is considered as a cure factor, effecting the late time stability and accuracy of the MOT solver [11][12][13][14][15].…”

A hybrid Boundary Element Unstructured Transmission-line (BEUT) method for accurate 2D electromagnetic simulation

“…The method decreases the dimensionality of the problem by 1 dimension which, when combined with modern matrix-vector product acceleration techniques, leads to a method whose computational efficiency is second to none. For details of the state-of-the-art discretization and implementation of marching-on-in-time space-time Galerkin methods, the reader is referred to, for example, [1]- [5].…”