Dung Trinh-Xuan

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.

Solution of large-scale wideband EM wave scattering problems using Fast Fourier Transform and the Asymptotic Waveform Evaluation technique

The wideband electromagnetic wave scattering from arbitrarily shaped, three-dimensional (3D) dielectric objects is investigated using the Method of Moments (MoM) in conjunction with the Asymptotic Waveform Evaluation (AWE), Generalized Minimal Residual method (GMRES) and Fast Fourier Transform (FFT). Numerical results are presented which demonstrate the accuracy and computational efficiency of the technique in comparison with analytical and conventional numerical methods.

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.

Fast iterative method for computing electromagnetic scattering from randomly rough surfaces

A new iterative technique is proposed for the computation of electromagnetic scattering from randomly rough lossy surfaces. The proposed method is an extension of the improved forward backward method (IFBM), introduced by Brennan et al. The improvement step of the IFBM is modified for the use of multiple correction vectors instead of a single correction vector in the original technique. Spectral acceleration (SA) is applied in combination with a matrix splitting technique for a reduction of computational complexity from O(N2) to O(N). Numerical experiments are presented to compare to those techniques proposed in recent studies to demonstrate the efficiency of the proposed method. The modified improvement step significantly enhances the convergence rate of the forward backward method with negligible increases in storage requirements and computational complexity.

Rapid convergent iterative solver for computing two-dimensional random rough surface scattering

A novel technique is proposed to greatly enhance the convergence property of stationary iterative solvers applied for the solution of scattering from two-dimensional random rough surfaces. The proposed method extends the standard improvement step to enable the use of multiple correction vectors, leading to a significantly improved convergence rate of stationary iterative methods with negligible increases in computational complexity. Spectral acceleration technique is also applied to reduce a computational burden and storage requirements. Numerical results are shown to demonstrate the advantages of the proposed technique.

Improved Forward Backward Method with Spectral Acceleration for scattering from exponentially correlated rough lossy surfaces

This paper presents an efficient and precise iterative method for computing the electromagnetic (EM) wave scattering from dielectric rough surfaces described by exponential correlation functions. The proposed method is based on improving the convergence rate of the Forward Backward Method (FBM) [1]. Moreover, a matrix splitting technique is introduced to reduce the number of matrix-vector multiplications required by the correction step and Spectral Acceleration (SA) [2], [3] 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) and is compared to FBM-SA in terms of convergence rate and the run time required to achieve a desired relative error norm. The numerical analysis demonstrates that IFBM-SA has a much higher convergence rate than FBM-SA. Therefore, IFBM-SA can be efficiently used to compute the electromagnetic scattering from randomly rough surfaces.

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).