Large Electromagnetic Problems Research Articles

Implementation of parallel GMRES(m) FFT method for solving large scale electromagnetic problems

AbstractIn this article, the parallel restarted generalized minimum residual [GMRES(m)] scheme has been implemented to solve large scale multilevel block Toeplitz matrix equations. The parallel fast Fourier transform has been used to accelerate the matrix‐vector multiplications in the iterative solver. The numerical results of electromagnetic scattering by cylindrical wire arrays demonstrate the accuracy and efficiency of the parallelization scheme. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 2084–2087, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24569

A New Method of Moments Solution Procedure to Solve Electrically Large Electromagnetic Scattering Problems

A New Method of Moments Solution Procedure to Solve Electrically Large Electromagnetic Scattering Problems

Numerical analysis of dielectric lens antennas using a ray-tracing method and HFSS software

In this paper, we use for the first time the ray-tracing method combined with the HFSS software to analyze lens antennas. HFSS is a very popular commercial tool that can provide very accurate results for the simulation of antennas. However, because of limitations on computational resources, it is hard to apply to solving large electromagnetic problems. In this paper, HFSS is used to simulate the fields of the feed part of a lens antenna. The ray tracing method is adopted for the lens part. This treatment makes the combined method feasible for solving large lens antennas. In using the ray-tracing method, cubicspline interpolation is exploited to fit the face of the lens and to solve for the derivatives at each point on the curved surface. Newton's method is applied to find the intercept between the ray and the curved surface. The numerical method proposed in this paper is very suitable for the analysis of dielectric lens antennas with arbitrary feeds and lens shapes. The validity of the idea is demonstrated by comparing the simulation results of this new method with those from using CST (Computer Simulation Technology) software. Very good agreement is achieved.

Heterogeneity and Loosely Coupled Systems in Electromagnetic Device Analysis

We present a system architecture and a set of control techniques that allow heterogeneous software analysis tools to collaborate intelligently and automatically. One of its distinguishing features is its ability to perform concurrent processing. Systems based on this architecture are able to effectively solve large electromagnetic (EM) analysis problems, particularly those that involve loose coupling between several areas of physics. The architecture can accept any existing software analysis tool, without requiring any modification or customization of the tool. This characteristic is produced in part by our use of a neutral virtual representation for storing problem data, including geometry and material definitions. We construct a system based on this architecture, using several circuit and finite-element analysis tools, and use it to perform EM analyses of several different devices. Our results show that our architecture and techniques allow practical problems to be solved effectively by heterogeneous tools.

An Iteration-Free MoM Approach Based on Excitation Independent Characteristic Basis Functions for Solving Large Multiscale Electromagnetic Scattering Problems

We describe a numerically efficient strategy for solving a linear system of equations arising in the Method of Moments for solving electromagnetic scattering problems. This novel approach, termed as the characteristic basis function method (CBFM), is based on utilizing characteristic basis functions (CBFs)-special functions defined on macro domains (blocks)-that include a relatively large number of conventional sub-domains discretized by using triangular or rectangular patches. Use of these basis functions leads to a significant reduction in the number of unknowns, and results in a substantial size reduction of the MoM matrix; this, in turn, enables us to handle the reduced matrix by using a direct solver, without the need to iterate. In addition, the paper shows that the CBFs can be generated by using a sparse representation of the impedance matrix-resulting in lower computational cost-and that, in contrast to the iterative techniques, multiple excitations can be handled with only a small overhead. Another important attribute of the CBFM is that it is readily parallelized. Numerical results that demonstrate the accuracy and time efficiency of the CBFM for several representative scattering problems are included in the paper.

A NOVEL DOMAIN DECOMPOSITION FINITE DIFFERENCE TIME DOMAIN SCHEME INCLUDING MULTIPLE REFLECTIONS

In this paper,we present a new domain decomposition technique which considers the effect of multiple reflections between the subdomains. This method has the ability to simulate accurately large electromagnetic problems that are difficult to handle using the direct application of the FDTD method. The results for the test examples considered in this paper compare well with the direct FDTD solution, and serve to validate the proposed scheme.

Massively Parallel Fast Multipole Method Solutions of Large Electromagnetic Scattering Problems

We describe a massively parallel version of the single-level fast multipole method (FMM) that employs the fast Fourier transform (FFT) for the translation stage. The proposed FMM-FFT method alleviates the communication bottleneck and has a lower complexity, O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4/3</sup> log <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2/3</sup> N), as compared to the conventional single level FMM which scales as O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3/2</sup> ), where N is the number of unknowns. Through numerical examples we demonstrate that the proposed parallel fast multipole method yields a faster solution time than its multilevel counterpart for very large problems in a distributed memory parallel setting.

A parallel method for large scale time domain electromagnetic inverse problems

In this work we consider the solution of 3D time domain electromagnetic inverse problems. Solving such problems is an open challenge as they require very high computational resources. We therefore explore a method to parallelize the inverse problem by using time decomposition. We show that our approach can reduce the computational time although it does not scale optimally.

Electromagnetic Scattering Using the Iterative Multiregion Technique

In this work, an iterative approach using the finite difference frequency domain method is presented to solve the problem of scattering from large-scale electromagnetic structures. The idea of the proposed iterative approach is to divide one computational domain into smaller subregions and solve each subregion separately. Then the subregion solutions are combined iteratively to obtain a solution for the complete domain. As a result, a considerable reduction in the computation time and memory is achieved. This procedure is referred to as the iterative multiregion (IMR) technique. Different enhancement procedures are investigated and introduced toward the construction of this technique. These procedures are the following: 1) a hybrid technique combining the IMR technique and a method of moment technique is found to be efficient in producing accurate results with a remarkable computer memory saving; 2) the IMR technique is implemented on a parallel platform that led to a tremendous computational time saving; 3) together, the multigrid technique and the incomplete lower and upper preconditioner are used with the IMR technique to speed up the convergence rate of the final solution, which reduces the total computational time. Thus, the proposed iterative technique, in conjunction with the enhancement procedures, introduces a novel approach to solving large open-boundary electromagnetic problems including unconnected objects in an efficient and robust way. Contents: Basics of the FDFD Method / IMR Technique for Large-Scale Electromagnetic Scattering Problems: 3D Case / IMR Technique for Large-Scale Electromagnetic Scattering Problems: 2D Case / The IMR Algorithm Using a Hybrid FDFD and Method of Moments Technique / Parallelization of the Iterative Multiregion Technique / Combined Multigrid Technique and IMR Algorithm / Concluding Remarks / Appendices

Efficient Method for Full-Wave Analysis of Large-Scale Finite-Sized Periodic Structures

A rigorous and efficient algorithm which combines the fast multipole method and conjugate gradient fast Fourier transform is presented for the full-wave analysis of large-scale finite-sized periodic structures. The memory requirement and computational complexity of the new algorithm are only of the order of O(N), where N denotes the number of unknowns. Hence the new method can handle very large electromagnetic problem of periodic structures. For example, a problem consisting of 12 millions unknowns can be solved in a personal computer. Numerical results prove the accuracy and efficiency of the new algorithm.

A new domain decomposition finite‐difference time domain for solving large electromagnetic problems

AbstractIn this paper, we present a novel domain decomposition finite‐difference time domain technique for solving large electromagnetic radiation and scattering problems. In this method the computational domain is divided into manageable, moderate‐sized subdomains with overlapping regions. PML layers are used for terminating the subdomains to absorb the outgoing waves. The tangential electric fields are stored on an interface plane to be used as a boundary condition to generate the field in the adjacent subdomain. These computations are applied in a serial manner to solve a problem that is too large to be solved in one step because of limitations in the available computational resources. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 2399–2405, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21962

Extending the Applicability of the Combined-Field Integral Equation to Geometries Containing Open Surfaces

In this letter, we consider the solution of large electromagnetics problems of composite structures with coexisting open and closed conductors. By modifying the construction of the combined-field integral equation (CFIE), we demonstrate a significant improvement in the iterative solution of these problems compared to the conventional electric-field formulation

Iterative multiregion technique for large‐scale electromagnetic scattering problems: Two‐dimensional case

One of the methods to solve large electromagnetic problems is to divide the computational domain into smaller subregions and solve each subregion separately. Then the subregion solutions are combined to obtain a solution for the complete domain. In this paper, an iterative approach using the finite difference frequency domain method is presented to solve the problems that can be divided into separated subregions.

A COMBINED BI-CGSTAB (1) AND WAVELET TRANSFORM METHOD FOR EM PROBLEMS USING METHOD OF MOMENTS

An efficient technique for the solution of large-scale electromagnetic radiation and scattering problems arising from the surface integral equations and the method of moments is developed. The conventional MoM basis and testing functions are used to discretize the integral equations resulting in a dense impedance matrix. A block-partitioned wavelet transform is then employed to sparsify the matrix. Full advantage is taken of the sparse nature of the mathematical model to solve the system of equations by means of the recently introduced Stabilized Bi-Conjugate Gradient method (Bi- CGSTAB (l)). Various problems are considered involving perfect electric conductor and dielectric material. Results are compared to the corresponding results obtained via the direct solution, or LU decomposition, of the original MoM dense matrix. Excellent results are obtained in a very efficient manner. By block partitioning the MoM impedance matrix as it is built and performing the wavelet transform on the matrix blocks, analysis of very large electromagnetic problems becomes possible in a very efficient and accurate manner.

Least squares spectral element method for 2D Maxwell equations in the frequency domain

We propose a high order numerical method for the first order Maxwell equations in the frequency domain, defined in media with arbitrary complex shape. Our approach is based on the combination of the least squares approach with the spectral element method. The former frees the solution from spurious modes, that can be found sometimes in classical finite element simulations. Many examples of such non-physical solutions exist in literature, and elimination of these spurious effects is a subject of great interest. Spectral elements are a numerical technique for solving partial differential equations which can be regarded as an extension of finite elements: they merge the flexibility of finite elements in dealing with complex geometries, and the better accuracy of spectral methods. Convergence to exact solution is improved by increasing (at run time) the polynomial degree, with no changes on the computational grid: this provides a significant advantage in respect to low order finite element, which necessarily have to resort to grid refinement. In the authors opinion this approach can be successfully used for the treatment of large scale electromagnetic problems or, alternatively, for applications where higher precision is required. We present a few numerical experiments which prove the capability of the method in object. Copyright © 2004 John Wiley & Sons, Ltd.

A fast wideband analysis of radiation and scattering problems by impedance‐matrix interpolation combined with progressive numerical method

AbstractIt has been shown that impedance‐matrix interpolation is a very direct and effective technique to speed up the wide‐band analysis of radiation and scattering problems. In view of the time‐costing problem of solving the large impedance matrix using impedance‐matrix interpolation and the good performance of the progressive numerical method (PNM) for dealing with large electromagnetic problems, a fast and effective wideband analysis of radiation and scattering problems by impedance‐matrix interpolation combined with a progressive numerical method is presented in this paper. Some numerical results are given to illustrate the effectiveness and the accuracy of the proposed method. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 43: 56–59, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20374

Efficient evaluation of macro‐basis‐function reaction terms in the subdomain multilevel approach

AbstractThis paper presents an improved subdomain multilevel approach (SMA), a technique efficiently used for solving large complex‐shaped antennas printed in multilayered media structure. In a large electromagnetic problem, where the memory occupation and computational time have been already significantly reduced using the SMA, the calculation of the macro basis function (MBF) reaction terms remains the most time‐consuming part of the procedure. In this paper, we present an efficient way of computing MBF reaction terms and reducing them to equivalent moments. The numerical results are compared with brute‐force computations, the SMA, and the measurements. They demonstrate conclusively the efficiency and power of the new proposed technique. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 42: 138–143, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20232

FAST SOLUTION FOR LARGE SCALE ELECTROMAGNETIC SCATTERING PROBLEMS USING WAVELET TRANSFORM AND ITS PRECONDITION - Abstract

Nowadays, electrically large complex electromagnetic problems exist in modern defence and communication industry. Accurate and efficient calculation for such electromagnetic radiation and scattering is a high computational complex task and a challenge to conventional electromagnetic solvers such as Method of Moment (MOM) where high memory and long computational time are required owing to its large size compared to operating wavelength. This paper presents the fast solution method with wavelet transform in the computation of scattering from large scale complex objects. Because of the vanishing moments, the moment matrices arising in these problems are sparsified by wavelet, and consequently, the induced current and equivalent magnetic current can be obtained quickly. Moreover, a precondition method is postulated and implemented in the fast solution of the transformed moment matrix equation with iteration methods.

New block ILU preconditioner scheme for numerical analysis of very large electromagnetic problems

Large electromagnetic scattering and radiation problems are tackled by iterative solvers, which require the use of huge preconditioners. Most often, the incomplete LU decomposition (ILU) of the preconditioner is applied to the system matrix at each iteration. However, the preconditioner ILU cannot be done in-core when the size of the preconditioning matrix exceeds the available memory. This paper presents a new preconditioning scheme to do the preconditioner ILU in small blocks that fit in core memory. The resulting approach allows the solution of very large problems in small computers.

Fast Solution for Large Scale Electromagnetic Scattering Problems Using Wavelet Transform and Its Precondition

Nowadays, electrically large complex electromagnetic problems exist in modern defence and communication industry. Accurate and efficient calculation for such electromagnetic radiation and scattering is a high computational complex task and a challenge to conventional electromagnetic solvers such as Method of Moment (MOM) where high memory and long computational time are required owing to its large size compared to operating wavelength. This paper presents the fast solution method with wavelet transform in the computation of scattering from large scale complex objects. Because of the vanishing moments, the moment matrices arising in these problems are sparsified by wavelet, and consequently, the induced current and equivalent magnetic current can be obtained quickly. Moreover, a precondition method is postulated and implemented in the fast solution of the transformed moment matrix equation with iteration methods.