O. Hassan¹, K. Morgan, J. Jones, B. Larwood, N. P. Weatherill

CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.5, pp. 383-394, 2004, DOI:10.3970/cmes.2004.005.383

Abstract A numerical procedure for the simulation of 3D problems involving the scattering of electromagnetic waves is presented. As practical problems of interest in this area often involve domains of complex geometrical shape, an unstructured mesh based method is adopted. The solution algorithm employs an explicit finite element procedure for the solution of Maxwell's curl equations in the time domain using unstructured tetrahedral meshes. A PML absorbing layer is added at the artificial far field boundary that is created by the truncation of the physical domain prior to the numerical solution. The complete solution procedure is More >

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 >

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 >

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 >

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 >

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 >

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 >

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 >

K. Woo¹, H. Igawa², C.H. Jenkins³

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.4, pp. 397-408, 2004, DOI:10.3970/cmes.2004.006.397

Abstract This paper presents the development and evaluation of a wrinkling analysis procedure for anisotropic membranes. The procedure is based on a penalty-parameter modified material model and a non-linear root finding to simulate the uni-axial stress state. The procedure was implemented in the ABAQUS finite element code as a user subroutine, and then applied to annular and square membranes. The wrinkle problems were also solved by shell element post-buckling analysis and the results were compared. The effect of anisotropy and unsymmetric loading on the wrinkling behavior was investigated. More >

Michael Yu Wang¹, Xiaoming Wang²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.4, pp. 373-396, 2004, DOI:10.3970/cmes.2004.006.373

Abstract This paper addresses the problem of structural shape and topology optimization. A level set method is adopted as an alternative approach to the popular homogenization based methods. The paper focuses on four areas of discussion: (1) The level-set model of the structure’s shape is characterized as a region and global representation; the shape boundary is embedded in a higher-dimensional scalar function as its “iso-surface.” Changes of the shape and topology are governed by a partial differential equation (PDE). (2) The velocity vector of the Hamilton-Jacobi PDE is shown to be naturally related to the shape… More >