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This work presents a stable implementation of the Multilevel Planewave Time Domain (PWTD) Algorithm. For stabilization, the separable kernel expansion method of [1] is used. This method allows for accurate evaluation of retarded potential integrals, which is essential if one is to obtain a stable time domain integral equation (TDIE) solution. Preliminary results for scattering from a sphere are presented...
We present a method for the stable solution of time-domain integral equations. The method uses a technique developed in [1] to accurately evaluate matrix elements. As opposed to existing stabilization schemes, the method presented uses higher order basis functions in time to improve the accuracy of the solver. The method is validated by showing convergence in temporal basis function order, time step...
Accurate integration of singular and near-singular functions is critical to the accuracy of the method of moments solution to surface integral equations. While this problem has been widely addressed for flat geometries, its extensions to higher order surface descriptions have been limited. This letter provides a systematic prescription for the application of the rules for weakly singular integrals...
Accurate integration of singular and near-singular functions is critical to the accuracy of the method of moments solution to integral equations. While this problem has been widely addressed for flat geometries, their extensions to higher order surface descriptions have been limited. This paper provides a comprehensive prescription for the application of the singularity cancellation schemes to higher...
Since the initial development of Time-Domain Integral Equations (TDIEs), the issue of instability has limited their use by computational practitioners. Significant progress notwithstanding, there is still a need for theoretical understanding of the causes of instability, their remedies (in the continuous case) and solution schemes applicable to electrically large, complex structures. It was in an...
A scheme for the evaluation of retarded potential integrals is presented wherein the convolution of the retarded potential Green's function with the basis functions is approximated using an expansion of separable functions in time and space. The proposed scheme renders the spatial integrands required in this computation smooth over both the source and testing domains, which is typically not true in...
The state of art of transient simulation using integral equation (TDIE) based methods has grown by leaps and bounds over the past few decades, both in terms of late time stability and computational complexity. This paper aims to address two additional functionalities: (i) development of a framework to enlarge the spatial approximation space using the generalized method of moments (GMM), and (ii) development...
In this work, we develop the GMM scheme for the discretization of the TDIE. We will describe a scheme for the extension of the GMM to time domain using products of GMM functions (for spatial basis functions) and interpolatory polynomials (for temporal basis functions). First, we will show that these basis functions provide accurate scattering results over a wide variety of geometries. Further, we...
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