Fast Inhomogeneous Plane Wave Algorithm Research Articles

Machine-Learning-Based Hybrid Method for the Multilevel Fast Multipole Algorithm

In this letter, a hybrid translation computation method for the multilevel fast multipole algorithm (MLFMA) is proposed based on machine learning. The hybrid method combines both generalized regression neural network (GRNN) and artificial neural network (ANN) to replace the traditional translation procedure during the solving process of the MLFMA. Based on the data corresponding to every one of the interaction list boxes at each level, the hybrid neural network is trained. Comparing with the previous machine learning method in this field, the proposed model is more general, and with lower complexity since it inherits the accuracy of the GRNN as well as the efficiency of the ANN. To the best of our knowledge, it is for the first time that the ANN is integrated into the MLFMA. Numerical examples are benchmarked to illustrate the reliability and capability, thus making it possible to solve similar problems during the fast inhomogeneous plane wave algorithm solving process in the multilayered medium.

Fast Solving Scattering From Multiple Bodies of Revolution With Arbitrarily Metallic-Dielectric Combinations

The accurate simulation of multiple bodies of revolution (MBoRs) is of great importance in many areas of engineering applications. The beauty of a single body of revolution (BOR) is that the 3-D problem can be reduced to a series of decoupled 2-D problems thereby not consuming large computational memory and time. However, for a multiple arbitrarily orientated bodies of revolution scattering problem, the modal Green's function (MGF) does not work. In this paper, an approach based on domain decomposition framework MBoRs (DDM-MBoRs) is proposed to solve electromagnetic scattering from MBoRs involving metallic and dielectric objects. First of all, the induced electric or magnetic currents in each single BoR are efficiently solved by a fast inhomogeneous plane wave algorithm (FIPWA). Then BoRs couple with each other via the far-field Green's function. In particular, a modified basis function mapping technique (BFMT) is utilized to project the BoR basis functions to constant vector basis functions, which further makes it flexible to employ multilevel fast multipole algorithm (MLFMA) to accelerate the mutual coupling of each BoR. In the proposed framework, MBoRs with arbitrarily metallic-dielectric combinations can be efficiently solved. Several numerical results are illustrated to demonstrate the accuracy and efficiency of the proposed method.

Fast Inhomogeneous Plane Wave Algorithm for Homogeneous Dielectric Body of Revolution

To solve the electromagnetic scattering problem for homogeneous dielectric bodies of revolution (BOR), a fast inhomogeneous plane wave algorithm is developed. By using the Weyl identity and designing a proper integration path, the aggregation and disaggregation factors can be derived analytically. Compared with the traditional method of moments (MoM), both thememory and CPU time requirements are reduced for large-scale homogeneous dielectric BOR problems. Numerical results are given to demonstrate the validity and the efficiency of the proposed method. AMS subject classifications: 35Q61, 74F15, 74J20, 83C50

Fast inhomogeneous plane wave algorithm for scattering from PEC body of revolution

AbstractTo solve large‐scale electromagnetic scattering problems for bodies of revolution, a fast inhomogeneous plane wave algorithm (FIPWA) is developed. By using the Weyl identity and designing a proper integral path, the aggregation and disaggregation factors can be computed efficiently in FIPWA. Both the memory and CPU time requirements are significantly reduced for large scale BOR problems over the method of moments. Numerical results are given to demonstrate the validity and the efficiency of the FIPWA method to perfect conductors, but the method can be extended to dielectric BORs. © 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 52: 1915–1922, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.25319

FAST INHOMOGENEOUS PLANE WAVE ALGORITHM FOR ANALYSIS OF COMPOSITE BODIES OF REVOLUTION

A fast inhomogeneous plane wave algorithm is developed for the electromagnetic scattering problem from the composite bodies of revolution (BOR). Poggio-Miller-Chang-Harrington-Wu (PMCHW) approach is used for the homogeneous dielectric objects, while the electric fleld integral equation (EFIE) is used for the perfect electric conducting objects. The aggregation and disaggregation factors can be expressed analytically by using the Weyl identity. Compared with the traditional method of moments (MoM), both the memory requirement and CPU time, are reduced for large-scale composite BOR problems. Numerical results are given to demonstrate the validity and the e-ciency of the proposed method.

An Efficient Implementation of the Combined Wideband MLFMA/LF-FIPWA

An efficient implementation of the low frequency fast inhomogeneous plane wave algorithm (LF-FIPWA) combined with the multilevel fast multipole algorithm (MLFMA) is presented. The seamless combination of the LF-FIPWA with the MLFMA renders a powerful method applicable for a wide frequency range. As the MLFMA is already well established we will describe possibilities for an efficient formulation of the LF-FIPWA: an implicit filtering reduces the bandwidth of the integrand. An interpolation of the excitation vectors is introduced which avoids dealing with the in general complex angles. An adaptive quadrature rule on the path in the complex plane further increases the efficiency. We present a simple but accurate interpolation and interpolation method on this path. In addition, for symmetric objects or for perfectly conducting ground the incorporation of a symmetry wall is described.

Error Bounds of the Fast Inhomogeneous Plane Wave Algorithm

The Green's function of free space for the fast inhomogeneous plane wave algorithm is represented by an integration in the complex plane. The error in the computational process is determined by the number of sampling points, the truncation of the integration path, and the extrapolation. Therefore, the error control method is different from that for the fast multipole method. We will discuss the worst-case interactions of the fast inhomogeneous plane wave algorithm for the box implementation and define the upper and lower bounds of the computational error.

Multipole‐Free Fast Inhomogeneous Plane Wave Algorithm

Solving radiation and scattering problems in the vicinity of a half‐space or stratified medium with integral equation methods is complicated, and slowed by computation of expensive Sommerfeld integrals. In this paper, a new formulation of the spectral layered media Green's function is presented. It is demonstrated for a simple scattering problem in the new fast algorithm called the Multipole‐Free Fast Inhomogeneous Plane Wave Algorithm (MF‐FIPWA). MF‐FIPWA is shown to scale as (N log N) in memory usage and processing time. Additional advantages include rigorous treatment of reflected contributions, simplicity in design, and mathematical insight into the fast algorithm.

Error Control for 2-D Fipwa in Complex, Homogeneous Media

This paper presents error control for the 2-D fast inhomogeneous planewave algorithm in lossy and active media. The error is explained, and control regions are defined according to the loss or gain. As a result, 2-D FIPWA is proposed for use in 3-D layered medium problems.

Low‐frequency fast inhomogeneous plane‐wave algorithm (LF‐FIPWA)

AbstractA new method, the low‐frequency fast inhomogeneous plane‐wave algorithm (LF‐FIPWA) is presented to extend the traditional multilevel fast multipole algorithm (MLFMA) and fast inhomogeneous plane‐wave algorithm (FIPWA) seamlessly into the low‐frequency range. It uses evanescent‐wave extrapolation and translation techniques to overcome the low‐frequency breakdown problem. The accuracy can be well controlled over a broad frequency range. Numerical examples show the effectiveness of this new algorithm. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 40: 117–122, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11302

Error analysis of the fast inhomogeneous plane wave algorithm for 2D free‐space cases

AbstractThe fast inhomogeneous plane wave algorithm is another approach of the diagonal factorization of the Green's function which is represented by the infinite integration. In this paper, we discuss the error analysis in terms of the truncation of the integration path and the indispensable extrapolation process. Finally, this algorithm will be shown to be error controllable. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 38: 300–304, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11043

Fast inhomogeneous plane wave algorithm for the analysis of electromagnetic scattering

The fast inhomogeneous plane wave algorithm has been developed to accelerate the solution of three‐dimensional electromagnetic scattering problems in free space. By expanding the kernel of the Green's function using the Weyl identity and choosing a proper steepest descent path, the diagonalization of the translation matrix is achieved after the interpolation and extrapolation techniques are applied. The proposed algorithm is implemented on top of the scalable multipole engine, a portable implementation of the dynamic multilevel fast multipole algorithm for distributed‐memory computers. The computational time per matrix vector multiplication is reduced to O(NlogN) and the memory requirement is reduced to O(N), where N is the number of unknowns in the discretized integral equation. The algorithm is validated by applying it to the solution of the electromagnetic scattering from the perfect electric conducting scatterers. This approach can be easily extended to more general problems with complicated Green's function expressed in terms of the plane wave spectral integrals, such as the ones encountered in the multilayered medium studies.

Fast inhomogeneous plane wave algorithm for scattering from objects above the multilayered medium

A previously developed fast inhomogeneous plane wave algorithm is adapted to the analysis of the scattering from the objects above a multilayered medium. Based on the similarity of the inhomogeneous plane wave expansion of the Green's function encountered in the layered medium study to its free space counterpart, the proper steepest descent path can be defined. By using the interpolation and extrapolation techniques, the translation matrix is diagonalized. The contributions of the pole and branch point, resulting from the deformation of the integration path, can be handled easily. Comparing with the previously developed methods in this area, this algorithm is simpler, more efficient, and more general. The multilevel fast inhomogeneous plane wave algorithm has been implemented and the numerical results show that O(N log N) computational complexity of the algorithm is achieved. The algorithm is validated by comparing the results from a conventional method of moments program.

Fast inhomogeneous plane wave algorithm for electromagnetic solutions in layered medium structures: Two‐dimensional case

An accurate and efficient algorithm is proposed for solving two‐dimensional electromagnetic scattering problems in a layered medium. As a natural extension of the previously developed fast inhomogeneous plane wave algorithm (FIPWA), this approach has several inherent merits, such as being simple, versatile, and error controllable. The basic idea is first to express the spatial Green's function, encountered in layered medium studies, as Sommerfeld‐type integrals. By observing the similarity of these integrals with the integral representation of the free space Green's function, FIPWA can be applied with ease to accelerate the matrix‐vector multiplication. The multilevel scheme has been implemented, and the computational complexity of O(N log N) is achieved. It is noted that the proposed approach is more accurate and more efficient than the existing fast multipole method coupled with the discrete complex image method.

Fast inhomogeneous plane wave algorithm for the fast analysis of two‐dimensional scattering problems

A novel algorithm, the fast inhomogeneous plane wave algorithm (FIPWA), has been developed to accelerate the solution of integral equations pertinent to the analysis of the scattering from two‐dimensional perfect electric conducting surfaces. Unlike the fast steepest descent path algorithm, the proposed technique directly interpolates the far‐field pattern of the source group and matches it along a modified steepest descent path. A novel approach, which results in a diagonal translator with built‐in interpolation coefficients, is proposed. The computational complexity per matrix‐vector multiplication of a two‐level implementation of the proposed FIPWA is O(N4/3) and the multilevel implementation further reduces the complexity to O(NlogN), where N is the number of unknowns in the discretized integral equation. It is shown that this technique outperforms the previously developed fast methods such as the fast mulitpole method and the ray‐propagation fast multipole algorithm.