Overview of Large-Scale Computing: The Past, the Present, and the Future

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A new green's function formulation for modeling homogeneous objects in layered medium

A new Green's function formulation is developed systematically for modeling general homogeneous (dielectric or magnetic) objects in a layered medium. The dyadic form of the Green's function is first derived based on the pilot vector potential approach. The matrix representation in the moment method implementation is then derived by applying integration by parts and vector identities. The line integral issue in the matrix representation is investigated, based on the continuity property of the propagation factor and the consistency of the primary term and the secondary term. The extinction theorem is then revisited in the inhomogeneous background and a surface integral equation for general homogeneous objects is set up. Different from the popular mixed potential integral equation formulation, this method avoids the artificial definition of scalar potential. The singularity of the matrix representation of the Green's function can be made as weak as possible. Several numerical results are demonstrated to validate the formulation developed in this paper. Finally, the duality principle of the layered medium Green's function is discussed in the appendix to make the formulation succinct. © 1963-2012 IEEE.published_or_final_versio

A novel implementation of discrete complex image method for layered medium Green's function

A novel implementation of discrete complex image method (DCIM) based on the Sommmerfeld branch cut is proposed to accurately capture the far-field behavior of the layered medium Green's function as a complement to the traditional DCIM. By contour deformation, the Green's function can be naturally decomposed into branch-cut integration (radiation modes) and pole contributions (guided modes). For branch-cut integration, matrix pencil method is applied, and the alternative Sommerfeld identity in terms of k z integration is utilized to get a closed-form solution. The guided modes are accounted for with a pole-searching algorithm. Both one-branch-cut and two-branch-cut cases are studied. Several numerical results are presented to validate this method. © 2011 IEEE.published_or_final_versio

A memory saving vector fast multipole algorithm for solving the augmented EFIE

An augmented EFIE (A-EFIE)[9], [10] has been proposed to separate the contributions of the vector potential and the scalar potential for avoiding the imbalance at low frequencies. The corresponding low frequency fast multipole algorithm (LFFMA) [11] was also developed for solving the A-EFIE. Instead of the factorization of the scalar Green's function by using scalar addition theorem in the LF-FMA, we adopt the vector addition theorem for the factorization of the dyadic Green's function to realize memory savings. We are to develop a vector fast multipole algorithm for solving the A-EFIE. © 2010 IEEE.published_or_final_versionThe URSI International Symposium on Electromagnetic Theory (EMTS 2010), Berlin, Germany, 16-19 August 2010. In Proceedings of the URSI International Symposium on Electromagnetic Theory, 2010, p. 134-13

A new closed-form evaluation of layered medium Green'S function

A new closed-form evaluation of layered medium Green's function is proposed in this paper. The discrete complex image method (DCIM) is extended to sampling along the Sommerfeld branch cut, to capture the far field interaction. Contour deformation technique is applied to decompose the Green's function into radiation modes (branch cut integration) and guided modes (surface-wave poles). The matrix pencil method is implemented to get a closed-form solution, with the help of an alternative Sommerfeld identity. Numerical results are presented to demonstrate the accuracy of this method. © 2011 IEEE.published_or_final_versionThe 2011 IEEE International Symposium on Antennas and Propagation (APSURSI), Spokane, WA., 3-8 July 2011. In IEEE Antennas and Propagation Society. International Symposium, 2011, p. 3211-321

Finite-width feed and load models

We demonstrate a new method of applying the feed model for the method of moments (MoM) formulation for the electric field integral equation (EFIE). The model is based around a previously reported magnetic ribbon current model which is accurate and allows for a finite width of the feed port. However, with proper approximations, one can reduce the formulation such that the magnetic field operator can be removed in order to simplify computations arising from the curl of the dyadic Green's function and its singularities. We show here that the new feed model can also be used to model a lumped element. © 1963-2012 IEEE.published_or_final_versio

Enhanced A-EFIE with Calderon multiplicative preconditioner

Session: Well-Conditioned Integral Equation Formulations: paper 106.9In this work, a Calderón multiplicative preconditioner (CMP) is proposed for the augmented electric field integral equation (A-EFIE) to improve the convergence. To avoid the imbalance between the vector potential and the scalar potential in the traditional EFIE, A-EFIE considers both the charge and the current as unknowns. After implementing the appropriate frequency scaling and the enforcement of charge neutrality, its formulation is also stable in the low-frequency regime and applicable for large-scale and complex problems. Instead of using other preconditioners, Calderón preconditioning converts the first kind integral equations into the second kind, thus improving the spectrum of the original A-EFIE system. The numerical results show that the resultant system with the combined methods is more stable at low frequencies and converges faster in the calculation of far-field scattering fields.published_or_final_versio

Recent development of surface integral equation solvers for multiscale interconnects and circuits

This paper presents a brief review and recent development of surface integral equation solvers for multiscale interconnects and circuits modeling. As the future production processes down to 5 nm and the operating frequency increases, both multi-scale and large-scale natures should be taken into account in the electromagnetic simulations. Fast, efficient, stable, and broadband integral equation based solvers become indispensable when millions or ten s of millions of unknowns might be involved in the simulation of the integrated circuit. Recent progress and our latest researches in the development of broadband fast electromagnetic solvers will be demonstrated.published_or_final_versio

Calderon preconditioner for the electric field integral equation with layered medium Green's function

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Methods for fast evaluation of self-energy matrices in tight-binding modeling of electron transport systems

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