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A rigorous surface integral equation approach is proposed to study the spontaneous emission of a quantum emitter embedded in a multilayered plasmonic structure with the presence of arbitrarily shaped metallic nanoscatterers. With the aid of the Fermi's golden rule, the spontaneous emission of the emitter can be calculated from the local density of states, which can be further expressed by the imaginary part of the dyadic Green's function of the whole electromagnetic system. To obtain this Green's function numerically, a surface integral equation is established taking into account the scattering from the metallic nanoscatterers. Particularly, the modeling of the planar multilayered structure is simplified by applying the layered medium Green's function to reduce the computational domain and hence the memory requirement. Regarding the evaluation of Sommerfeld integrals in the layered medium Green's function, the discrete complex image method is adopted to accelerate the evaluation process. This work offers an accurate and efficient simulation tool for analyzing complex multilayered plasmonic system, which is commonly encountered in the design of optical elements and devices.

The multilevel fast multipole algorithm (MLFMA) is extended to solve for acoustic wave scattering by very large objects with three-dimensional arbitrary shapes. Although the fast multipole method as the prototype of MLFMA was introduced to acoustics early, it has not been used to study acoustic problems with millions of unknowns. In this work, the MLFMA is applied to analyze the acoustic behavior for very large truncated ground with many trenches in order to investigate the approach for mitigating gun blast noise at proving grounds. The implementation of the MLFMA is based on the Nystrom method to create matrix equations for the acoustic boundary integral equation. As the Nystrom method has a simpler mechanism in the generation of far-interaction terms, which MLFMA acts on, the resulting scheme is more efficient than those based on the method of moments and the boundary element method (BEM). For near-interaction terms, the singular or near-singular integrals are evaluated using a robust technique, which differs from that in BEM. Due to the enhanced efficiency, the MLFMA can rapidly solve acoustic wave scattering problems with more than two million unknowns on workstations without involving parallel algorithms. Numerical examples are used to demonstrate the performance of the MLFMA with report of consumed CPU time and memory usage.

In this paper, we analyze the communication pattern and study the scalability of a distributed memory implementation of the multilevel fast multipole algorithm (MLFMA) called ScaleME. ScaleME uses the message passing interface (MPI) for communication between processors. The parallelization of MLFMA uses a novel a hybrid scheme for distributing the workload across the processors. We study the communication and computational behavior and demonstrate the effectiveness of the parallelization scheme using realistic problems. Index Terms--Electromagnetic scattering, fast multipole method (FMM), integral equations, parallel algorithms.

The simulation of antennas often necessitates modeling the effect of nearby electrically large structures. Such structures are often unsuitable for modeling with the same technique as used on the antenna because of the prohibitive required unknown count. First-principles models of antennas (or other key features) must then be augmented with approximate models of the larger auxiliary structures, usually with high-frequency asymptotic models. The surface equivalence principle is applied to linear-media multiple scattering without regard to the formulations used for each contained domain. A Schur complement is then applied to convert the homogeneous medium equivalent problem into a inhomogeneous medium equivalent problem. The Schur complement form supports application of approximate models and makes the scattering physics plain. The results are provided for two cases modeled with the equivalence principle algorithm (EPA) hybridized with physical optics (PO) approximation. [ABSTRACT FROM AUTHOR]

We propose a broadband multilevel fast multipole algorithm using hybridization of the plane wave and the multipole expansions of Green’s function in the analysis of 3-D electromagnetic problems. In the proposed method, the diagonal plane-wave expansion is used for low order harmonics, which captures most of the propagating spectrums, while the dense multipole expansion is used for high order harmonics, which captures most of the evanescent spectrums. By analyzing the errors and choosing the numbers of harmonics accordingly in the plane wave and the multipole expansions, the method is free of low-frequency breakdown and remains accurate at arbitrarily low frequencies, which is similar to the dense fast multipole algorithm (FMA). Meanwhile, the method reduces to the conventional diagonal FMA as the frequency increases. Therefore, it can be regarded as the generalization of the conventional dense and diagonal FMAs. Numerical studies in this paper show that very high accuracies can be achieved using the method. [ABSTRACT FROM AUTHOR]

A full-wave surface integral equation (SIE) method based on the augmented electric-field integral equation (A-EFIE) for dielectric objects with low-frequency stability is presented in this paper. Motivated by the A-EFIE formulation for perfect electric conductor (PEC), the internal and external problems are both augmented with the current continuity equation and renormalized to eliminate the low-frequency breakdown. Although the magnetic-field integral equation operator \mathcalK is free of low-frequency breakdown, its matrix form is ill-conditioned and unsolvable if the traditional Rao–Wilton–Glisson (RWG) basis function is used as the testing and basis functions. As a remedy, the Buffa–Christiansen (BC) basis function is introduced to alleviate this testing issue. After this treatment, the matrix form of operator \mathcalK is well conditioned. To solve problems with a large number of unknowns, a preconditioning scheme is introduced to accelerate the convergence and the mixed-form fast multipole algorithm (FMA) is adopted to accelerate the matrix vector product. [ABSTRACT FROM PUBLISHER]

ABSTRACT In this article, we describe a newly developed integral equation domain decomposition method for solving complex low frequency electromagnetic problems. This method is based on low frequency augmented equivalence principle algorithm (EPA) with the augmented electric field integral equation (A-EFIE). The A-EFIE provides a stable solution in the low-frequency regime as it includes both charge and current as unknowns to avoid the imbalance between the vector potential and the scalar potential. Based on similar idea, the augmented EPA can suppress the projection error resulting from low-frequency problems of the normal EPA. Combining these two methods, the proposed algorithm can be used in domain decomposition problems and is numerically stable at low frequencies. Several numerical examples are provided to verify its validity. © 2013 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:2475-2479, 2013 [ABSTRACT FROM AUTHOR]

Abstract: We propose a new fast solver for solving the augmented electric field integral equation (A-EFIE), which realizes memory savings for modeling low-frequency large-scale problems, compared with the low-frequency fast multipole algorithm (LF-FMA). The A-EFIE has been proposed to avoid the imbalance between the vector potential and the scalar potential at low frequencies by adding the charge to the unknown list. The corresponding low frequency fast multipole algorithm (LF-FMA) was also developed for solving the A-EFIE. Instead of the factorization of the scalar Greenʼs function by using the scalar addition theorem in the LF-FMA, we adopt the vector addition theorem for the factorization of the dyadic Greenʼs function to develop a vector fast multipole algorithm (VFMA) for solving the A-EFIE. The storage of radiation and receiving patterns of the VFMA, which becomes the main part of the total storage with the increasing scale of problems, can be reduced by 25 percent compared with that of the LF-FMA, although the storage for vector translators, which is independent of the number of unknowns, is larger than that of the LF-FMA. At last, some numerical results show the validity of the VFMA for solving A-EFIE. [Copyright &y& Elsevier]

This paper proposes an augmented electric field integral equation (A-EFIE) for layered medium Green's function. The newly developed matrix-friendly formulation of layered medium Green's function is applied in this method. By separating charge as extra unknown list, and enforcing the current continuity equation, the traditional EFIE can be cast into a generalized saddle-point system. Frequency scaling for the matrix-friendly formulation is analyzed when frequency tends to zero. Rank deficiency and the charge neutrality enforcement of the A-EFIE for layered medium Green's function is discussed in detail. The electrostatic limit of the A-EFIE is also analyzed. Without any topological loop-searching algorithm, electrically small conducting structures embedded in a general layered medium can be simulated by using this new A-EFIE formulation. Several numerical results are presented to validate this method at the end of this paper. [ABSTRACT FROM AUTHOR]

Abstract: This paper gives an overview of computational electromagnetics for simulating complex structures with a large number of unknowns using integral equation method. First, it discusses the pros and cons of differential equation solvers versus integral equation solvers. Then it gives an overview of different fast algorithms for solving integral equations. It also discusses the difficulty of solving electromagnetic problems in the “twilight zone” between static and full-wave electromagnetics. Finally, it discusses various methods for fast solutions of scattering and coupling problems involving layered media both for statics and dynamic problems, and presents some numerical results. To cite this article: W.C. Chew et al., C. R. Physique 6 (2005). [Copyright &y& Elsevier]

The translation matrix for the multilevel fast multipole algorithm (MLFMA) in an FISC (fast Illinois solver code) is calculated directly, and the complexity is O(N3/2), where N is the number of unknowns. For a problem with a small electrical size, the CPU time for calculating the translation matrix can be negligible. But for large problems, the calculation time increases significantly. In this paper, we use interpolation to calculate the translation matrix, and the complexity is reduced to O(N). Different interpolation techniques are tested, and it is found that the Lagrange polynomial interpolation with high sampling rates is the best. The saving factor is 10 for the VFY218 at 4 GHz. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 30: 109–114, 2001. [ABSTRACT FROM AUTHOR]

Presents information on a study which proposed a novel diffraction tomographic algorithm to detect two-dimensional dielectric cylinders buried under a lossy earth. Inversion algorithm; Numerical results; Conclusions.

A normalized two-dimensional (2-D) multilevel fast multipole algorithm (MLFMA) with a computational complexity of O(N) for the quasistatic (very low-frequency) case is developed. This normalized 2-D MLFMA can be used not only independently as in the quasi-static case, but also to solve large-scale structures with dense subgridded areas when combined with a dynamic algorithm. The null-space problem for boundary integral equations at very low frequencies is also studied. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 20: 306–311, 1999. [ABSTRACT FROM AUTHOR]

Presents a numerical algorithm for the reconstruction of the density and the compressibility of a biological body from ultrasonic scattering data. Algorithm implementation; Nonlinearity due to multiple scattering; Numerical examples of simulation data and real experimental data showing the capability of the algorithm; Conclusions.

In this work, a fast real-time convolution algorithm is proposed. By using this approach, the cost for real-time convolution in the presence of nonlinear terminations is reduced from O(N2) to O(N log2N). It is important to reduce the cost for the convolution operation because it usually dominates the computation time in a nonlinear circuit simulation. A nonlinearly-terminated microwave 3-port circuit, characterized by S parameters, is employed to demonstrate the efficiency of this fast algorithm. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 39: 280–282, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11190 [ABSTRACT FROM AUTHOR]