CMES-Vol. 5, No. 4, 2004

Open Access

EDITORIAL

State-of-the-Art, Trends, and Directions in Computational Electromagnetics
F. Reitich¹, K. K. Tamma²
CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.4, pp. 287-294, 2004, DOI:10.3970/cmes.2004.005.287
Abstract This article has no abstract. More >

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Development of New Algorithms for High Frequency Electromagnetic Scattering
E. Bleszynski¹, M. Bleszynski¹, T. Jaroszewicz¹
CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.4, pp. 295-318, 2004, DOI:10.3970/cmes.2004.005.295
Abstract We describe elements of our current work on the development of new methods for high frequency electromagnetic scattering, based on the wavefront (WF) representation of propagating fields and on the asymptotic but rigorous solution of integral equations for surface currents. In the wavefront evolution technique, surfaces of constant phase are constructed and treated not merely as collections of independent rays, but as well defined geometrical objects endowed with the full connectivity information. Hence, a precise determination of shadow and reflection boundaries, a construction of (multiply) diffracted wavefronts, a dynamic adjustment of the number of rays,… More >

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New high-order integral methods in computational electromagnetism
Oscar P. Bruno¹
CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.4, pp. 319-330, 2004, DOI:10.3970/cmes.2004.005.319
Abstract We present a new set of high-order algorithms and methodologies for the numerical solution of problems of scattering by complex bodies in three-dimensional space. These methods, which are based on integral equations, high-order integration and Fast Fourier Transforms, can be used in the solution of problems of electromagnetic and acoustic scattering by surfaces and penetrable scatterers---even in cases in which the scatterers contain geometric singularities such as corners and edges. The solvers presented here exhibit high-order convergence, they run on low memories and reduced operation counts, and they result in solutions with a high degree More >

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ARTICLE

A Discrete Differential Forms Framework for Computational Electromagnetism
P. Castillo², J. Koning³, R. Rieben⁴, D. White⁵
CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.4, pp. 331-346, 2004, DOI:10.3970/cmes.2004.005.331
Abstract In this article, we present a computational framework for solving problems arising in electromagnetism. The framework is derived from a modern geometrical approach and is based on differential forms (or p-forms). These geometrical entities provide a natural framework for modeling of physical quantities such as electric potentials, electric and magnetic fields, electric and magnetic fluxes, etc. We have implemented an object oriented class library, called FEMSTER. The library is designed for high order finite element approximations. In addition, it can be expanded by including user-defined data types or by deriving new classes. Finally, the versatility More >

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Reflection in a Level Set Framework for Geometric Optics ¹
Li-Tien Cheng²³, Myungjoo Kang⁴, Stanley Osher⁴, Hyeseon Shim⁴, Yen-Hsi Tsai⁵
CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.4, pp. 347-360, 2004, DOI:10.3970/cmes.2004.005.347
Abstract Geometric optics makes its impact both in mathematics and real world applications related to ray tracing, migration, and tomography. Of special importance in these problems are the wavefronts, or points of constant traveltime away from sources, in the medium. Previously in [Osher, Cheng, Kang, Shim, and Tsai(2002)], we initiated a level set approach for the construction of wavefronts in isotropic media that handled the two major algorithmic issues involved with this problem: resolution and multivalued solutions. This approach was quite general and we were able to construct wavefronts in the presence of refraction, reflection, higher More >

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Review of Large Scale Computing in Electromagnetics with Fast Integral Equation Solvers
W.C. Chew¹, J.M. Song¹, T.J. Cui¹, S. Velamparambil¹, M.L. Hastriter¹, B. Hu¹
CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.4, pp. 361-372, 2004, DOI:10.3970/cmes.2004.005.361
Abstract This paper reviews recent advances in large-scale computational electromagnetics using frequency domain integral equations. It gives a brief history of methods to solve Maxwell's equations, followed by a description of various historical ages in solution technique developments. Then it describes computational electromagnetics followed by a brief description of how fast integral equation solvers such as the multilevel fast multipole algorithm (MLFMA) is constructed using the tree network. Some examples of large scale computing using MLFMA are given. Ray physics used to further accelerate the speed of MLFMA. The parallel implementation of MLFMA in a code More >

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Computation of Short Wave Equation Pulses Using Nonlinear Solitary Waves
Meng Fan¹, Lesong Wang², John Steinhoff³
CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.4, pp. 373-382, 2004, DOI:10.3970/cmes.2004.005.373
Abstract A new method is described that has the potential to greatly extend the range of application of current Eulerian time domain electromagnetic or acoustic computational methods for certain problems. More >

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