The discrete-dipole approximation (DDA) for scattering calculations, including the relationship between the DDA and other methods, is reviewed. Computational considerations, i.e., the use of complex-conjugate gradient algorithms and fast-Fourier-transform methods, are discussed. We test the accuracy of the DDA by using the DDA to compute scattering and absorption by isolated, homogeneous spheres as well as by targets consisting of two contiguous spheres. It is shown that, for dielectric materials (|m| ≲ 2), the DDA permits calculations of scattering and absorption that are accurate to within a few percent.

Discrete-Dipole Approximation For Scattering Calculations

http://ab-initio.mit.edu/~oskooi/papers/Oskooi10.pdf

Meep: A flexible free-software package for electromagnetic simulations by the FDTD method

This Key Note presents a summary of the development of the Finite Element Method in the field of Electromagnet ic Engineering, together with a description of several contributions of the authors to the Finite Element Method and its application to the solution of electromagnetic problems. First, a self-adaptive mesh scheme is presented in the context of the quasi-static and full-wave analysis of general anisotropic multiconductor arbitrary shaped waveguiding structures. A comparison between two a posteriori error estimates is done. The first one is based on the complete residual of the differential equations defining the problem. The second one is based on a recovery or smoothing technique of the electromagnetic field. Next, an implementation of the first family of Nedelec's curl-conforming elements done by the authors is outlined. Its features are highlighted and compared with other curl-conforming elements. A presentation of an iterative procedure using a numerically exact radiation condition for the analysis of open (scattering and radiation) problems follows. Other contributions of the authors, like the use of wavelet like basis functions and an implementation of a Time Domain Finite Element Method in the context of two-dimensional scattering problems are only mentioned due to the lack of space.

The finite element method in electromagnetics

The fast multipole method (FMM) and multilevel fast multipole algorithm (MLFMA) are reviewed. The number of modes required, block-diagonal preconditioner, near singularity extraction, and the choice of initial guesses are discussed to apply the MLFMA to calculating electromagnetic scattering by large complex objects. Using these techniques, we can solve the problem of electromagnetic scattering by large complex three-dimensional (3-D) objects such as an aircraft (VFY218) on a small computer.

Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects

A practical and complete, but not rigorous, exposition of the fact multiple method (FMM) is provided. The FMM provides an efficient mechanism for the numerical convolution of the Green's function for the Helmholtz equation with a source distribution and can be used to radically accelerate the iterative solution of boundary-integral equations. In the simple single-stage form presented here, it reduces the computational complexity of the convolution from O(N/sup 2/) to O(N/sup 3/2/), where N is the dimensionality of the problem's discretization. >

The fast multipole method for the wave equation: a pedestrian prescription

The electric field integral equation (EFIE) is used with the moment method to develop a simple and efficient numerical procedure for treating problems of scattering by arbitrarily shaped objects. For numerical purposes, the objects are modeled using planar triangular surfaces patches. Because the EFIE formulation is used, the procedure is applicable to both open and closed surfaces. Crucial to the numerical formulation is the development of a set of special subdomain-type basis functions which are defined on pairs of adjacent triangular patches and yield a current representation free of line or point charges at subdomain boundaries. The method is applied to the scattering problems of a plane wave illuminated flat square plate, bent square plate, circular disk, and sphere. Excellent correspondence between the surface current computed via the present method and that obtained via earlier approaches or exact formulations is demonstrated in each case.

Electromagnetic scattering by surfaces of arbitrary shape

Formulas for the potentials due to uniform and Linearly varying source distributions defined on simply shaped domains are systematically developed and presented. Domains considered are infinite planar strips, infinite cylinders of polygonal cross sections, planar surfaces with polygonal boundaries, and volumetric regions with polyhedral boundaries. The expressions obtained are compact in form and their application in the numerical solution of electromagnetics problems by the method of moments is illustrated.

Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains

Introduction. Wire Structure: TDIE Solution. Infinite Conducting Cylinders: TDIE Solution. Finite Conducting Bodies:TDIE Solution. Dielectric Bodies: TDIE Solution. Finite Difference Time Domain Method. Transmission Line Modeling Method. Finite-Element Time Domain Method. Finite-Volume Time Domain Method. Index.

Time domain electromagnetics

The recent development and extension of the method of moments technique for analyzing electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects is presented based on the combined field integral equations. The surfaces of the homogeneous three-dimensional arbitrary geometrical shapes are modeled using surface triangular patches, similar to the case of arbitrary shaped conducting objects. Further, the development and extensions required to treat efficiently three-dimensional lossy dielectric objects are reported. Numerical results and their comparisons are also presented for two canonical dielectric scatterers-a sphere and a finite circular cylinder.

/pdf/electromagnetic-scattering-by-arbitrary-shaped-three-35m4477z8v.pdf

Sadasiva M. Rao

Papers

Electromagnetic scattering by surfaces of arbitrary shape

Electromagnetic scattering by surfaces of arbitrary shape

Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains

Time domain electromagnetics

Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects