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

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

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

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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

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

Frequency-independent scattering for the large sphere

The high frequency scattering of a scalar plane wave from an impenetrable sphere with the diameter of one thousand wavelength is treated by the saddle-point technique and the numerical steepest descent method. The far-field solution for the sphere is computed in the observation angle range of 0 to 180 degree. In particular, a novel numerical steepest descent method is proposed to overcome the breakdown of the traditional saddle-point technique in the forward region. Numerical results show that the CPU time for the far-field calculation is frequency-independent with controllable error. This work can be used to benchmark future works in frequency-independent methods. ©2009 IEEE.published_or_final_versionThe 2009 Asia Pacific Microwave Conference (APMC 2009), Singapore, 7-10 December 2009. In Proceedings of the Asia Pacific Microwave Conference, 2009, p. 854-85

Fast computation of the dyadic green's function for layered media via interpolation

The use of a dyadic layered-medium Green's function as the kernel in a method of moments (MoM) modeling problem greatly reduces the complexity of modeling a stratified medium. Compared to the free-space Green's function, there is an additional cost of having to compute a semi-infinite Sommerfeld integral for each call to calculate the dyadic layered-medium Green's function. This letter discusses a method to tabulate and interpolate the Green's function as a method of reducing the impedance matrix filling time. This method can be used in conjunction with existing methods for increasing the computational speed of the Green's functions. © 2010 IEEE.published_or_final_versio

Error minimization of multipole expansion

In this paper, we focus on the truncation error of the multipole expansion for the fast multipole method and the multilevel fast multipole algorithm. When the buffer size is large enough, the error can be controlled and minimized by using the conventional selection rules. On the other hand, if the buffer size is small, the conventional selection rules no longer hold, and the new approach which we have recently proposed is needed. However, this method is still not sufficient to minimize the error for small buffer cases. We clarify this fact and show that the information about the placement of true worst-case interaction is needed. A novel algorithm to minimize the truncation error is proposed. © 2005 Society for Industrial and Applied Mathematics.published_or_final_versio

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

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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