Patrick Bradley

Efficient Wideband Electromagnetic Scattering Computation for Frequency Dependent Lossy Dielectrics Using WCAWE

This paper presents a model order reduction algorithm for the volume electric field integral equation (EFIE) formulation, that achieves fast and accurate frequency sweep calculations of electromagnetic wave scattering. An inhomogeneous, two-dimensional, lossy dielectric object whose material is characterized by a complex permittivity which varies with frequency is considered. The variation in the dielectric properties of the ceramic BaxLa4Ti 2+xO 12+3x in the <1 GHz frequency range is investigated for various values of x in a frequency sweep analysis. We apply the well-conditioned asymptotic waveform evaluation (WCAWE) method to circumvent the computational complexity associated with the numerical solution of such formulations. A multipoint automatic WCAWE method is also demonstrated which can produce an accurate solution over a much broader bandwidth. Several numerical examples are given on order to illustrate the accuracy and robustness of the proposed methods.

Improved Forward Backward Method With Spectral Acceleration for Scattering From Randomly Rough Lossy Surfaces

An efficient and accurate iterative method is proposed for computing electromagnetic (EM) scattering from 1-D dielectric rough surfaces. The communication improves the convergence of forward backward method, applying it to the problem of 2D wave scattering from random lossy rough surfaces using a coupled surface integral equation formulation. A matrix splitting technique is introduced to reduce the number of matrix-vector multiplications required by the correction step and Spectral Acceleration (SA) is applied to reduce the computational complexity of each matrix-vector product from O(N2) to O(N). The proposed method is called the improved forward backward method with spectral acceleration (IFBM-SA). The numerical analysis demonstrates that IFBM-SA has a higher convergence rate than FBM-SA and a recent technique which is used as a reference method. Moreover, IFBM-SA is more robust than the reference method and has smaller storage requirements meaning that it can readily scale to larger problems. In addition an eigenvalue based analysis is provided illustrating how the improvement step works.

Fast Fourier Transform Based Iterative Method for Electromagnetic Scattering From 1D Flat Surfaces

An efficient iterative method is proposed for computing the electromagnetic fields scattered from a one dimensional (1D) flat surface. The new iterative method is based on a similar implementation to the Conjugate Gradient Fast Fourier Transform (CG-FFT), where acceleration of the matrix-vector multiplications is achieved using fast Fourier transforms (FFT). However, the iterative method proposed is not based on Krylov subspace expansions and is shown to converge faster than GMRES-FFT and CGNE-FFT while maintaining the computational complexity and memory usage of those methods. Analysis is presented deriving an explicit convergence criterion.

Arnoldi model order reduction for electromagnetic wave scattering computation

This paper presents a model order reduction (MOR) algorithm for the volume integral equation formulation of electromagnetic wave scattering. We apply the Arnoldi algorithm to circumvent the computational complexity associated with the numerical solution of such formulations. An approximate extension of the Arnoldi algorithm to the problem of wave scattering from an inhomogeneous body is introduced and implemented. Numerical examples are presented to demonstrate the accuracy of our approximate extension.

Accelerated Source-Sweep Analysis Using a Reduced-Order Model Approach

This communication is concerned with the development of a model-order reduction (MOR) approach for the acceleration of a source-sweep analysis using the volume electric field integral equation (EFIE) formulation. In particular, we address the prohibitive computational burden associated with the repeated solution of the two-dimensional electromagnetic wave scattering problem for source-sweep analysis. The method described within is a variant of the Krylov subspace approach to MOR, that captures at an early stage of the iteration the essential features of the original system. As such these approaches are capable of creating very accurate low-order models. Numerical examples are provided that demonstrate the speed-up achieved by utilizing these MOR approaches when compared against a method of moments (MoM) solution accelerated by use of the fast Fourier transform (FFT).

Well-Conditioned Asymptotic Waveform Evaluation for Efficient Computation of Wave-Scattering from Perfectly Conducting Bodies

This paper presents a model order reduction algorithm for the surface electric field integral equation (EFIE) formulation of the electromagnetic wave scattering problem. The method allows fast and accurate frequency sweep calculations of electromagnetic wave scattering from a perfectly conducting (PEC) three-dimensional object. We apply the well-conditioned asymptotic waveform evaluation (WCAWE) method to circumvent the computational complexity associated with the numerical solution of such formulations. Practical implementation issues are addressed with numerical examples given to illustrate the accuracy and robustness of the proposed methods.

Extension of fast far field algorithm to propagation over lossy dielectric terrain and buildings

In this paper the Fast Far-Field Approximation (FAFFA) is extended to 2D problems involving EM wave propagation over lossy terrain and over concrete buildings. A coupled surface electric field integral equation formulation is used and solved using the method of moments. The unknowns corresponding to the unknown electric and magnetic fields are interleaved to facilitate the use of the forward-backward method (FBM) and the block forward-backward method (BFBM). Results show good agreement with measured data in the case of propagation over terrain. The FAFFA-accelerated fields are in good agreement with a slow reference solution in the case of propagation over buildings. Convergence of the FBM is investigated.

Accelerated forward backward iterative solution for scattering from randomly rough lossy surfaces

This paper extends the method developed in [1] to the problem of 2D wave scattering from lossy dielectric randomly rough surfaces using a coupled surface integral equation formulation. Moreover, a similar implementation to BMIA/CAG [2] is used to split the impedance matrix into a sparse strong interaction matrix and a dense weak interaction matrix. Taylor series expansions and FFTs are applied to compute matrix vector products involving the weak interaction matrix. By doing this the complexity of the optimisation step is reduced from order of O(N2) to order of O(N logN).