Magnetic Current Combined-field Integral Equation Research Articles

H-Matrix-Based Direct Solver of JMCFIE for the Analysis of Scattering From Penetrable Objects

Method of moments (MoMs) solution of the electric and magnetic current combined-field integral equation (JMCFIE) for penetrable objects generally resorts to iterative solvers, which suffer from the problems of convergence rate and redundant computation for multiple right-hand-sides (RHSs). In this communication, an efficient direct solver based on the hierarchical ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}$ </tex-math></inline-formula> -) matrix technique is presented to solve these problems. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}$ </tex-math></inline-formula> -matrix formatted algorithms provide an efficient way to factorize the impedance matrix with low computational costs, which make the direct solution feasible. Examples of electromagnetic scattering from a dielectric object and optical scattering from a plasmonic nanostructure are shown to demonstrate the efficiency and accuracy of the proposed method.

A Novel JMCFIE-DDM for Analysis of EM Scattering and Radiation by Composite Objects

In this letter, a new integral equation domain decomposition method (IE-DDM) using electric and magnetic current combined-field integral equation (JMCFIE) is proposed for efficient electromagnetic analysis of composite objects. This method provides a flexible way to decompose a complex composite domain into several easily solvable nonoverlapping subdomains. In order to obtain a good approximation of the global solution, both electric and magnetic field interactions are considered at the subdomain interfaces, in addition to the traditional Robin-type transmission conditions. In this manner, the unphysical reflections at subdomain interfaces can be further suppressed. It is shown that the condition of the new JMCFIE-DDM system is much improved in this new implementation. Accuracy and efficiency of the proposed method are demonstrated through several numerical experiments.

Solutions of plasmonic structures using the multilevel fast multipole algorithm

We consider accurate full-wave solutions of plasmonic problems using the multilevel fast multipole algorithm (MLFMA). Metallic structures at optical frequencies are modeled by using the Lorentz-Drude model, formulated with surface integral equations, and analyzed iteratively via MLFMA. Among alternative choices, the electric and magnetic current combined-field integral equation (JMCFIE) and the combined tangential formulation (CTF), which are popular integral-equation formulations for penetrable objects, are discretized with the conventional Rao-Wilton-Glisson functions and used to model plasmonic structures. We discuss electromagnetic interactions in plasmonic media and show how far-field interactions may be omitted for improving the efficiency without sacrificing the accuracy of results. © 2016 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:335–341, 2016.

Scattering of a zero-order Bessel beam by arbitrarily shaped homogeneous dielectric particles

In this paper, we introduce an efficient numerical method based on surface integral equations to characterize the scattering of a zero-order Bessel beam by arbitrarily shaped homogeneous dielectric particles. The incident beam is described by vector expressions in terms of the electric and magnetic fields that perfectly satisfy Maxwell's equations. The scattering problems involving homogeneous dielectric particles with arbitrary shapes are formulated with the electric and magnetic current combined-field integral equation and modeled by using surface triangular patches. Solutions are performed iteratively by using the multilevel fast multipole algorithm. Some numerical results are included to illustrate the validity and capability of the proposed method. These results are also expected to provide useful insights into the scattering of a Bessel beam by complex-shaped particles.

Fast and accurate analysis of large-scale composite structures with the parallel multilevel fast multipole algorithm

Accurate electromagnetic modeling of complicated optical structures poses several challenges. Optical metamaterial and plasmonic structures are composed of multiple coexisting dielectric and/or conducting parts. Such composite structures may possess diverse values of conductivities and dielectric constants, including negative permittivity and permeability. Further challenges are the large sizes of the structures with respect to wavelength and the complexities of the geometries. In order to overcome these challenges and to achieve rigorous and efficient electromagnetic modeling of three-dimensional optical composite structures, we have developed a parallel implementation of the multilevel fast multipole algorithm (MLFMA). Precise formulation of composite structures is achieved with the so-called "electric and magnetic current combined-field integral equation." Surface integral equations are carefully discretized with piecewise linear basis functions, and the ensuing dense matrix equations are solved iteratively with parallel MLFMA. The hierarchical strategy is used for the efficient parallelization of MLFMA on distributed-memory architectures. In this paper, fast and accurate solutions of large-scale canonical and complicated real-life problems, such as optical metamaterials, discretized with tens of millions of unknowns are presented in order to demonstrate the capabilities of the proposed electromagnetic solver.

Solution of large-scale plasmonic problems with the multilevel fast multipole algorithm

A surface integral equation together with the multilevel fast multipole algorithm is successfully applied to fast and accurate resolution of plasmonic problems involving a large number of unknowns. The absorption, scattering, and extinction efficiencies of several plasmonic gold spheres of increasing size are efficiently obtained solving the electric and magnetic current combined-field integral equation. The numerical predictions are compared with reference analytic results to demonstrate the accuracy, suitability, and capabilities of this approach when dealing with large-scale plasmonic problems.

Fast and accurate solutions of electromagnetics problems involving lossy dielectric objects with the multilevel fast multipole algorithm

Fast and accurate solutions of electromagnetic scattering problems involving lossy dielectric objects are considered. Problems are formulated with two recently developed formulations, namely, the combined-tangential formulation (CTF) and the electric and magnetic current combined-field integral equation (JMCFIE), and solved iteratively using the multilevel fast multipole algorithm (MLFMA). Iterative solutions and accuracy of the results are investigated in detail for diverse geometries, frequencies, and conductivity values. It is demonstrated that CTF solutions are significantly accelerated as the conductivity increases to moderate values and CTF becomes comparable to JMCFIE in terms of efficiency. Considering also the superior accuracy of this formulation, CTF becomes suitable for fast and accurate analysis of scattering problems involving lossy dielectric objects.

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 multilevel 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.

Fast and Accurate Analysis of Homogenized Metamaterials With the Surface Integral Equations and the Multilevel Fast Multipole Algorithm

Fast and accurate analysis of double-negative materials (DNMs) with the surface integral equations and the multilevel fast multipole algorithm (MLFMA) is considered. DNMs, which are commonly used as simplified models of metamaterials at resonance frequencies, can be formulated with the surface integral equations. Two recently developed formulations-namely, the combined tangential formulation (CTF) and the electric and magnetic current combined-field integral equation (JMCFIE)-are used to formulate DNMs. Iterative solutions with MLFMA are investigated in detail to show that numerical results are consistent with those for ordinary materials. Accuracy and efficiency of the proposed implementation based on JMCFIE with high combination parameter and MLFMA are demonstrated on very large problems discretized with tens of millions of unknowns.

PARALLEL IMPLEMENTATION OF MLFMA FOR HOMOGENEOUS OBJECTS WITH VARIOUS MATERIAL PROPERTIES

We present a parallel implementation of the multilevel fast multipole algorithm (MLFMA) for fast and accurate solutions of electromagnetics problems involving homogeneous objects with diverse material properties. Problems are formulated rigorously with the electric and magnetic current combined-field integral equation (JMCFIE) and solved iteratively using MLFMA parallelized with the hierarchical partitioning strategy. Accuracy and efficiency of the resulting implementation are demonstrated on canonical problems involving perfectly conducting, lossless dielectric, lossy dielectric, and double-negative spheres.

Computational study of scattering from healthy and diseased red blood cells

We present a comparative study of scattering from healthy red blood cells (RBCs) and diseased RBCs with deformed shapes. Scattering problems involving three-dimensional RBCs are formulated accurately with the electric and magnetic current combined-field integral equation and solved efficiently by the multilevel fast multipole algorithm. We compare scattering cross section values obtained for different RBC shapes and different orientations. In this way, we determine strict guidelines to distinguish deformed RBCs from healthy RBCs and to diagnose various diseases using scattering cross section values. The results may be useful for designing new and improved flow cytometry procedures.

Comparison of Integral-Equation Formulations for the Fast and Accurate Solution of Scattering Problems Involving Dielectric Objects with the Multilevel Fast Multipole Algorithm

We consider fast and accurate solutions of scattering problems involving increasingly large dielectric objects formulated by surface integral equations. We compare various formulations when the objects are discretized with Rao-Wilton-Glisson functions, and the resulting matrix equations are solved iteratively by employing the multilevel fast multipole algorithm (MLFMA). For large problems, we show that a combined-field formulation, namely, the electric and magnetic current combined-field integral equation (JMCFIE), requires fewer iterations than other formulations within the context of MLFMA. In addition to its efficiency, JMCFIE is also more accurate than the normal formulations and becomes preferable, especially when the problems cannot be solved easily with the tangential formulations.