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

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A vector fast multipole algorithm for low frequency problems

Instead of the traditional factorization of the scalar Green's function by using scalar addition theorem in the lowfrequency fast multipole algorithm (LF-FMA), we adopt the vector addition theorem (VAT) for the factorization of the dyadic Green's function to realize memory savings for large scale problems. We validate this factorization and use it to develop a low-frequency vector fast multipole algorithm (LF-VFMA) for low-frequency problems. © 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. 620-62

Microstrip Capacitance for a Circular Disk Through Matched Asymptotic Expansions

The solution of the potential around two parallel circular disks separated by a dielectric slab is obtained by using the method of matched asymptotic expansions, asymptotic formula for the capacitance has been derived in the limit of small separation 2 delta . The formula obtained includes terms of order delta as well. The mixed boundary value problem is solved by dividing the space around the parallel plates into three regions; the exterior region, the edge region, and the interior region. The solution of the edge region incorporating dielectric effects is obtained by using the Wiener-Hopf technique. The exterior solution of the circular disk problem is obtained by using Hankel transforms. The Hankel transform representation of the exterior solution facilitates the easy derivation of its edge expansion from the Lipschitz-Hankel integrals.published_or_final_versio

Thin-stratified medium fast-multipole algorithm (TSMFMA) for solving 2.5D microstrip structures

Proceedings of the IEEE International Symposium of the Antennas and Propagation Society, 2008, p. 1-4published_or_final_versio

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

Angular response of thin-film organic solar cells with periodic metal back nanostrips

We theoretically study the angular response of thin-film organic solar cells with periodic Au back nanostrips. In particular, the equation of the generalized Lambert's cosine law for arbitrary periodic nanostructure is formulated. We show that the periodic strip structure achieves wide-angle absorption enhancement compared with the planar nonstrip structure for both the s-and p-polarized light, which is mainly attributed to the resonant Wood's anomalies and surface plasmon resonances, respectively. The work is important for designing and optimizing high-efficiency photovoltaic cells. © 2011 Optical Society of America.published_or_final_versio

Truncation error analysis of multipole expansion

The multilevel fast multipole algorithm is based on the multipole expansion, which has numerical error sources such as truncation of the addition theorem, numerical integration, and interpolation/anterpolation. Of these, we focus on the truncation error and discuss its control precisely. The conventional selection rule fails when the buffer size is small compared to the desired numerical accuracy. We propose a new approach and show that the truncation error can be controlled and predicted regardless of the number of buffer sizes.published_or_final_versio

Convergence of low-frequency EFIE-based systems with weighted right-hand-side effect

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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 element implementation of the generalized-lorenz gauged A-phi formulation for low-frequency circuit modeling

The A-Φ formulation with generalized Lorenz gauge is free of catastrophic breakdown at low frequencies. In the formulation, A and Φ are completely separated and Maxwell's equations are reduced into two independent equations pertinent to A and Φ, respectively. This, however, leads to more complicated equations in contrast to the traditional A-Φ formulation, which makes the numerical representation of the physical quantities challenging, especially for A. By virtue of the differential forms theory and Whitney elements, both A and Φ are appropriately represented. The condition of the resultant matrix system is wellcontrolled as frequency becomes low, even approaches to 0. The generalized-Lorenz gauged A-Φ formulation is applied to model low-frequency circuits at μm lengthscale.postprin