scholarly journals Parallel Integral Equation-Based Nonoverlapping DDM for Solving Challenging Electromagnetic Scattering Problems of Two Thousand Wavelengths

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Qin Su ◽  
Yingyu Liu ◽  
Xunwang Zhao ◽  
Zongjing Gu ◽  
Chang Zhai ◽  
...  
Keyword(s):  
Integral Equation ◽  
Electromagnetic Scattering ◽  
Domain Decomposition Method ◽  
Near Field ◽  
Limited Resources ◽  
Accurate Analysis ◽  
Scattering Problems ◽  
Fast Multipole Algorithm ◽  
Matrix Vector ◽  
Field Integral

In this paper, a parallel nonoverlapping and nonconformal domain decomposition method (DDM) is proposed for fast and accurate analysis of electrically large objects in the condition of limited resources. The formulation of nonoverlapping DDM for PEC bodies is derived from combined-field integral equation (CFIE), and an explicit boundary condition is applied to ensure the continuity of electric currents across the boundary. A parallel multilevel fast multipole algorithm (MLFMA) is extended to accelerate matrix-vector multiplications of subdomains as well as the coupling between them, and the coupling between different subdomains is computed in the manner of near field to avoid the storage of the mutual impedance. An improved adaptive direction partitioning scheme is applied to the oct-tree of MLFMA to achieve high parallel efficiency. Numerical examples demonstrate that the proposed method is able to simulate realistic problems with a maximum dimension greater than 2000 wavelengths.

scholarly journals P-FFT Accelerated EFIE with a Novel Diagonal Perturbed ILUT Preconditioner for Electromagnetic Scattering by Conducting Objects in Half Space

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Lan-Wei Guo ◽  
Yongpin Chen ◽  
Jun Hu ◽  
Joshua Le-Wei Li
Keyword(s):  
Integral Equation ◽  
Electric Field ◽  
Half Space ◽  
Electromagnetic Scattering ◽  
High Performance ◽  
Three Dimensional ◽  
Scattering Problems ◽  
Geometrical Structures ◽  
Incomplete Lu Factorization ◽  
Field Integral

A highly efficient and robust scheme is proposed for analyzing electromagnetic scattering from electrically large arbitrary shaped conductors in a half space. This scheme is based on the electric field integral equation (EFIE) with a half-space Green’s function. The precorrected fast Fourier transform (p-FFT) is first extended to a half space for general three-dimensional scattering problems. A novel enhanced dual threshold incomplete LU factorization (ILUT) is then constructed as an effective preconditioner to improve the convergence of the half-space EFIE. Inspired by the idea of the improved electric field integral operator (IEFIO), the geometrical-optics current/principle value term of the magnetic field integral equation is used as a physical perturbation to stabilize the traditional ILUT perconditioning matrix. The high accuracy of EFIE is maintained, yet good calculating efficiency comparable to the combined field integral equation (CFIE) can be achieved. Furthermore, this approach can be applied to arbitrary geometrical structures including open surfaces and requires no extra types of Sommerfeld integrals needed in the half-space CFIE. Numerical examples are presented to demonstrate the high performance of the proposed solver among several other approaches in typical half-space problems.

The efficient implementation of IE-FFT algorithm with combined field integral equation for solving electromagnetic scattering problems

2020 ◽  
pp. 1-7
Author(s):  
Seung Mo Seo
Keyword(s):  
Integral Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Electromagnetic Scattering ◽  
Cartesian Grid ◽  
Memory Storage ◽  
Scattering Problems ◽  
Cpu Time ◽  
Interaction Terms ◽  
Field Integral

Abstract An integral equation-fast Fourier transform (IE-FFT) algorithm is applied to the electromagnetic solutions of the combined field integral equation (CFIE) for scattering problems by an arbitrary-shaped three-dimensional perfect electric conducting object. The IE-FFT with CFIE uses a Cartesian grid for known Green's function to considerably reduce memory storage and speed up CPU time for both matrix fill-in and matrix vector multiplication when used with a generalized minimal residual method. The uniform interpolation of the Green's function on an equally spaced Cartesian grid allows a global FFT for field interaction terms. However, the near interaction terms do not take care for the singularity of the Green's function and should be adequately corrected. The IE-FFT with CFIE does not always require a suitable preconditioner for electrically large problems. It is shown that the complexity of the IE-FFT with CFIE is found to be approximately O(N1.5) and O(N1.5log N) for memory and CPU time, respectively.

scholarly journals ANALYSIS OF COMPOSITE DIELECTRIC METAMATERIALS USING INTEGRAL EQUATION TECHNIQUES

2020 ◽  
Author(s):  
John Stevenson
Keyword(s):  
Integral Equation ◽  
Method Of Moments ◽  
Electromagnetic Scattering ◽  
Three Dimensional ◽  
Surface Integral ◽  
Integral Equation Formulation ◽  
The Matrix ◽  
Speed Up ◽  
Fast Multipole Algorithm ◽  
Matrix Vector

We study numerically the electromagnetic scattering properties of three dimensional (3D),arbitrary shaped composite dielectric metamaterials. Using integral equation techniques, we firstderive a surface integral equation formulation which produces well-conditioned matrix equation.To solve the obtained integral equations, we apply a Galerkin scheme and choose the basis andtesting functions as Rao-Wilton-Glisson defined on planar patches. We then develop an algorithmto speed up the matrix-vector multiplications by employing the well-known method of moments(MoM) and the multilevel fast multipole algorithm on personal computer (PC) clusters. Some 3Dnumerical examples are presented to demonstrate the validity and accuracy of the proposedapproach.

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