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

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

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 use of liquid metals based on gallium for soft and stretchable electronics is discussed. This emerging class of electronics is motivated, in part, by the new opportunities that arise from devices that have mechanical properties similar to those encountered in the human experience, such as skin, tissue, textiles, and clothing. These types of electronics (e.g., wearable or implantable electronics, sensors for soft robotics, e-skin) must operate during deformation. Liquid metals are compelling materials for these applications because, in principle, they are infinitely deformable while retaining metallic conductivity. Liquid metals have been used for stretchable wires and interconnects, reconfigurable antennas, soft sensors, self-healing circuits, and conformal electrodes. In contrast to Hg, liquid metals based on gallium have low toxicity and essentially no vapor pressure and are therefore considered safe to handle. Whereas most liquids bead up to minimize surface energy, the presence of a surface oxide on these metals makes it possible to pattern them into useful shapes using a variety of techniques, including fluidic injection and 3D printing. In addition to forming excellent conductors, these metals can be used actively to form memory devices, sensors, and diodes that are completely built from soft materials. The properties of these materials, their applications within soft and stretchable electronics, and future opportunities and challenges are considered.

Stretchable and Soft Electronics using Liquid Metals.

Prior to abour 1990, the modeling of electromagnetic engineering systems was primarily implemented using solution techniques for the sinusoidal steady-state Maxwell's equations. Before about 1960, the principal approaches in this area involved closed-form and infinite-series analytical solutions, with numerical results from these analyses obtained using mechanical calculators. After 1960, the increasing availability of programmable electronic digital computers permitted such frequency-domain approaches to rise markedly in sophistication. Researchers were able to take advantage of the capabilities afforded by powerful new high-level programming languages such as Fortran, rapid random-access storage of large arrags of numbers, and computational speeds that were orders of magnitude faster than possible with mechanical calculators. In this period, the principal computational approaches for Maxwell's equations included the high-frequency asymptotic methods of Keller (1962) as well as Kouyoumjian and Pathak (1974) and the integral equation techniques of Harrington (1968) .

9 – Computational Electromagnetics: The Finite-Difference Time-Domain Method

From the Publisher:
Here's a cutting-edge resource that brings you up-to-date with all the recent advances in computational electromagnetics. You get the most-current information available on the multilevel fast multipole algorithm in both the time and frequency domains, as well as the latest developments in fast algorithms for low frequencies and specialized structures, such as the planar and layered media. These algorithms solve large electromagnetics problems with shorter turn around time, using less computer memory. 

Complex problems that once required a supercomputer to solve, can now be solved on a workstation or personal computer with the innovative methods taught in this resource. The book introduces you to new advances in the perfectly matched layer absorbing boundary conditions, and offers you a thorough understanding of error analysis of numerical methods, fast-forward and inverse solvers for inverse problems, hybridization in computational electromagnetics, and asymptotic waveform evaluation.

Fast and Efficient Algorithms in Computational Electromagnetics

The fast multipole method (FMM) has been implemented to speed up the matrix-vector multiply when an iterative method is used to solve the combined field integral equation (CFIE). FMM reduces the complexity from O(N2) to O(N1.5). With a multilevel fast multipole algorithm (MLFMA), it is further reduced to O(N log N). A 110, 592-unknown problem can be solved within 24 h on a SUN Sparc 10. © 1995 John Wiley & Sons, Inc.

Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering

Various methods for efficiently solving electromagnetic problems are presented. Electromagnetic scattering problems can be roughly classified into surface and volume problems, while fast methods are either differential or integral equation based. The resultant systems of linear equations are either solved directly or iteratively. A review of various differential equation solvers, their complexities, and memory requirements is given. The issues of grid dispersion and hybridization with integral equation solvers are discussed. Several fast integral equation solvers for surface and volume scatterers are presented. These solvers have reduced computational complexities and memory requirements.

Fast solution methods in electromagnetics

We present an accurate method of moments (MoM) solution of the combined field integral equation (CFIE) using the multilevel fast multipole algorithm (MLFMA) for scattering by large, three-dimensional (3-D), arbitrarily shaped, homogeneous objects. We first investigate several different MoM formulations of the CFIE and propose a new formulation, which is both accurate and free of interior resonances. We then employ the MLFMA to significantly reduce the memory requirement and computational complexity of the MoM solution. Numerical results are presented to demonstrate the accuracy and capability of the proposed method. The method can be extended in a straightforward manner to scatterers composed of different homogeneous dielectric and conducting objects.

Jiming Song

Papers

Fast and Efficient Algorithms in Computational Electromagnetics

Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects

Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering

Fast solution methods in electromagnetics

Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies