Accurate Solutions of Extremely Large Integral-Equation Problems in Computational Electromagnetics

Cataloged from PDF version of article.Accurate simulations of real-life electromagnetics problems with integral equations require the solution of dense matrix equations involving millions of unknowns. Solutions of these extremely large problems cannot be achieved easily, even when using the most powerful computers with state-of-the-art technology. However, with the multilevel fast multipole algorithm (MLFMA) and parallel MLFMA, we have been able to obtain full-wave solutions of scattering problems discretized with hundreds of millions of unknowns. Some of the complicated real-life problems (such as scattering from a realistic aircraft) involve geometries that are larger than 1000 wavelengths. Accurate solutions of such problems can be used as benchmarking data for many purposes and even as reference data for high-frequency techniques. Solutions of extremely large canonical benchmark problems involving sphere and National Aeronautics and Space Administration (NASA) Almond geometries are presented, in addition to the solution of complicated objects, such as the Flamme. The parallel implementation is also extended to solve very large dielectric problems, such as dielectric lenses and photonic crystals. © 1963-2012 IEEE

Solutions of large-scale electromagnetics problems involving dielectric objects with the parallel multilevel fast multipole algorithm

Fast and accurate solutions of large-scale electromagnetics problems involving homogeneous dielectric objects are considered. Problems are formulated with the electric and magnetic current combined-field integral equation and discretized with the Rao-Wilton-Glisson functions. Solutions are performed iteratively by using the multi-level fast multipole algorithm (MLFMA). For the solution of large-scale problems discretized with millions of unknowns, MLFMA is parallelized on distributed-memory architectures using a rigorous technique, namely, the hierarchical partitioning strategy. Efficiency and accuracy of the developed implementation are demonstrated on very large problems involving as many as 100 million unknowns

Application of computational physics within Northrop

An overview of Northrop programs in computational physics is presented. These programs depend on access to today's supercomputers, such as the Numerical Aerodynamical Simulator (NAS), and future growth on the continuing evolution of computational engines. Descriptions here are concentrated on the following areas: computational fluid dynamics (CFD), computational electromagnetics (CEM), computer architectures, and expert systems. Current efforts and future directions in these areas are presented. The impact of advances in the CFD area is described, and parallels are drawn to analagous developments in CEM. The relationship between advances in these areas and the development of advances (parallel) architectures and expert systems is also presented

Some Key Developments in Computational Electromagnetics and their Attribution

Key developments in computational electromagnetics are proposed. Historical highlights are summarized concentrating on the two main approaches of differential and integral methods. This is seen as timely as a retrospective analysis is needed to minimize duplication and to help settle questions of attribution

An efficient high-order algorithm for acoustic scattering from penetrable thin structures in three dimensions

This paper presents a high-order accelerated algorithm for the solution of the integral-equation formulation of volumetric scattering problems. The scheme is particularly well suited to the analysis of “thin” structures as they arise in certain applications (e.g., material coatings); in addition, it is also designed to be used in conjunction with existing low-order FFT-based codes to upgrade their order of accuracy through a suitable treatment of material interfaces. The high-order convergence of the new procedure is attained through a combination of changes of parametric variables (to resolve the singularities of the Green function) and “partitions of unity” (to allow for a simple implementation of spectrally accurate quadratures away from singular points). Accelerated evaluations of the interaction between degrees of freedom, on the other hand, are accomplished by incorporating (two-face) equivalent source approximations on Cartesian grids. A detailed account of the main algorithmic components of the scheme are presented, together with a brief review of the corresponding error and performance analyses which are exemplified with a variety of numerical results

Leveraging Continuous Material Averaging for Inverse Electromagnetic Design

Inverse electromagnetic design has emerged as a way of efficiently designing active and passive electromagnetic devices. This maturing strategy involves optimizing the shape or topology of a device in order to improve a figure of merit--a process which is typically performed using some form of steepest descent algorithm. Naturally, this requires that we compute the gradient of a figure of merit which describes device performance, potentially with respect to many design variables. In this paper, we introduce a new strategy based on smoothing abrupt material interfaces which enables us to efficiently compute these gradients with high accuracy irrespective of the resolution of the underlying simulation. This has advantages over previous approaches to shape and topology optimization in nanophotonics which are either prone to gradient errors or place important constraints on the shape of the device. As a demonstration of this new strategy, we optimize a non-adiabatic waveguide taper between a narrow and wide waveguide. This optimization leads to a non-intuitive design with a very low insertion loss of only 0.041 dB at 1550 nm.Comment: 20 pages, 9 figure