Proceedings of the Progress In Electromagnetics Research Symposium, 2010, p. 46Session 1A4: Robust and E±cient Electromagnetic Solutions for Large-scale Problemspostprin

Jiang, L

Ruehli, AE

HKU Scholars Hub

Title On the frequency barrier of surface integral equations from acircuit point of viewAuthor(s) Jiang, L; Ruehli, AECitation The Progress In Electromagnetics Research Symposium (PIERS)2010, Cambridge, USA, 5-8 July 2010.Issued Date 2010URL http://hdl.handle.net/10722/126035Rights Creative Commons: Attribution 3.0 Hong Kong LicenseSession 1A4Robust and Efficient Electromagnetic Solutions forLarge-scale ProblemsOn the Frequency Barrier of Surface Integral Equations from a Circuit Point of ViewLijun Jiang, Albert E. Ruehli, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Fast Integral Equation Solution Techniques for Planar-3D Structures in Multilayered MediaThomas Vaupel, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47A Surface Absorber Approach with the Boundary Element Method to Terminate Nanophotonic DevicesLei Zhang, Steven G. Johnson, Jacob K. White, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48A Hybrid PMM-MOM Method for Analyzing Electrically Large and Finite Frequency Selective SurfaceJianxun Su, Xiaowen Xu, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50The Discontinuous Galerkin Method for Highly Inhomogeneous MediaChristoph Schwarzbach, Eldad Haber, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Multi-region Pseudospectral Time Domain (MR/PSTD) Modeling of Electromagnetic Wave PropagationLanbo Liu, Benjamin Barrowes, Zhao Zhao, Zijian Liu, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52Simplified Integral Equation Modeling of Low-frequency Electromagnetic Scattering from a ResistiveUnderground TargetShaaban Ali Bakr, Trond Mannseth, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53A Three-dimensional Inversion Approach for Cross-well Electromagnetic Field DataJianguo Liu, Guangdong Pan, Aria Abubakar, Tarek M. Habashy, Mikhail Zaslavsky,Vladimir L. Druskin, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54Computation of Casimir Forces in Arbitrary Geometries and Materials via the Finite-difference Time-domain MethodAlejandro W. Rodriguez, Alexander P. McCauley, John D. Joannopoulos, Steven G. Johnson, . . . . . . 55Spectral Element Method for 2-D and 3-D Photonic Crystals with Dispersive and Anisotropic MaterialsMa Luo, Qing Huo Liu, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574546 Progress In Electromagnetics Research Symposium Abstracts, Cambridge, USA, July 5–8, 2010On the Frequency Barrier of Surface Integral Equations from aCircuit Point of ViewLijun Jiang1 and Albert E. Ruehli21Department of EEE, The University of Hong Kong, China2Department of EMC, The Missouri University of Science and TechnologyRolla, Missouri, USAAbstract— The failure to provide an accurate low frequency and even DC solution has beena key issue of research for integral equation based formulations. Loop-star techniques wereconceived to extend the low frequency limit of SIEs such as EFIE methods. It has successfullyimproved the low frequency conditioning, but requires complicated graph oriented algorithm. Inaddition, this approach does not work for DC.At the same time, the Partial Element Equivalent Circuit (PEEC) approach has been used tosolve similar electromagnetic problems for packaging and interconnect applications. It uses theModified Nodal Analysis (MNA) circuit solver formulation, which is employed in most of Spicecircuit solvers. PEEC+MNA not only provide a well conditioned low frequency solution, but alsoa dc solution. The attached figure shows an equivalent circuit for this simplest PEEC model.Both PEEC and EFIE approaches separates the MoM impedance Zij into a separate inductanceand a capacitance part for the electromagnetic solution. In fact, most important low frequencyissues can be observed from this simple circuit. The capacitances will represent open circuits atlow frequencies such that the MoM impedances will go to infinity. EFIE mixes the capacitancecontribution with that of the inductance, which causes the underflow of the inductance effects.The PEEC method uses Kirchoff’s Current Law (KCL) in MNA to enforce the continuity of thecurrent. Both nodal potentials and currents are included as unknowns in PEEC. Hence, PEECdemonstrates much better conditioning than EFIE at the low frequency regime (not DC).For a meaningful DC solution, two conditions are necessary. First, the losses must be includedin the model. This is symbolized by the resistance in series to the inductances. Clearly, at DC,the inductances will become short circuits and the remaining circuit only consists of resistivelosses. Second, the solver formulation must be separate the capacitive and inductive circuitsuch that a solution can be found in spite of the open circuited capacitances. It correspondsthe Helmholtz decomposition between the electric field and the magnetic field. For this reason,PEEC use the MNA approach in solving the equations. Again, the key issue is that both thecurrents and the potentials must be included as unknowns. EFIE completely breaks at DC dueto the decomposition.In the presentation we will include example solutions and matrix condition numbers to support thediscussion. Also, we consider the use of RWG basis functions to show that the popular approachcan be formulated such that some of the properties of the PEEC method can be inherited toimprove EFIE, such as the Augmented EFIE developed by Qian and Chew.

On the frequency barrier of surface integral equations from a circuit point of view

http://hub.hku.hk/bitstream/10722/126035/1/Abstract.pdf

On the frequency barrier of surface integral equations from a circuit point of view

Abstract

Similar works

Full text

Available Versions

HKU Scholars Hub