Simulating Maxwell–Schrödinger Equations by High-Order Symplectic FDTD Algorithm

Authors: Guoda Xie ; Zhixiang Huang ; Ming Fang ; Wei E. I. Sha

In a numerical simulation of the interactions between high-intensity electromagnetic (EM) waves and plasma fluids, a good numerical resolution is required for all the physical quantities of interest, especially the plasma density distribution around the edge of the plasma bulk. Since the plasma formation and evolution is a dynamic process, it is difficult to predetermine the appropriate resolution at a given location. In this paper, we describe a discontinuous Galerkin time-domain (DGTD) based dynamic adaptation algorithm, which is able to adjust either the local mesh size or the local polynomial order in real time of a simulation to provide a sufficient numerical resolution of the physics while keeping the total computational cost low. To alleviate the constraint of the time step size of an explicit time integrator, a multirate time integration method is employed to advance the physics in time, which permits the application of different time step sizes in elements with different sizes or polynomial orders. With these techniques, the DGTD simulation of EM-plasma interactions can achieve a good accuracy and high efficiency.

DOI: 10.1109/JMMCT.2019.2920101

Incorporation of Ultrasonic Prior Information for Improving Quantitative Microwave Imaging of Breast

Nasim Abdollahi ; Douglas Kurrant ; Pedram Mojabi ; Muhammad Omer; Elise Fear; Joe LoVetri

Structural information derived via ultrasound is utilized as prior information for quantitative microwave imaging. The structural information is extracted from ray-based ultrasound reconstructions using a K-means clustering algorithm and consists of three tissue regions (skin, adipose, and fibroglandular). Tissue-specific complex permittivity values are assigned to each region (i.e., the complex permittivity is homogeneous over each region). The regions are then incorporated as an inhomogeneous numerical background in a quantitative microwave imaging algorithm (contrast source inversion). This new approach is assessed using synthetic data obtained from several anthropomorphic breast models of various densities derived from magnetic resonance imaging breast images, all containing tumors. Imaging results are quantitatively evaluated based on the algorithm’s ability to detect the tumors. The performance is tested with four different variations of the prior information: two variations of the structural information and two of the assigned permittivity values. The resulting ultrasound-microwave multimodality imaging approach substantially improves the fidelity and accuracy of the reconstructed internal structures relative to previous studies that used radar-based microwave techniques to extract the internal structural information. An improvement in the sensitivity of the imaging algorithm to malignant tissue is also observed.

DOI: 10.1109/JMMCT.2019.2905344

An Advanced EM-Plasma Simulator Based on the DGTD Algorithm With Dynamic Adaptation and Multirate Time Integration Techniques

Su Yan ; Jiwei Qian ; Jian-Ming Jin

In a numerical simulation of the interactions between high-intensity electromagnetic (EM) waves and plasma fluids, a good numerical resolution is required for all the physical quantities of interest, especially the plasma density distribution around the edge of the plasma bulk. Since the plasma formation and evolution is a dynamic process, it is difficult to predetermine the appropriate resolution at a given location. In this paper, we describe a discontinuous Galerkin time-domain (DGTD) based dynamic adaptation algorithm, which is able to adjust either the local mesh size or the local polynomial order in real time of a simulation to provide a sufficient numerical resolution of the physics while keeping the total computational cost low. To alleviate the constraint of the time step size of an explicit time integrator, a multirate time integration method is employed to advance the physics in time, which permits the application of different time step sizes in elements with different sizes or polynomial orders. With these techniques, the DGTD simulation of EM-plasma interactions can achieve a good accuracy and high efficiency.

DOI: 10.1109/JMMCT.2019.2901533

Computation of Electromagnetic Fields Scattered From Objects With Uncertain Shapes Using Multilevel Monte Carlo Method (Open Access)

Alexander Litvinenko ; Abdulkadir C. Yucel ; Hakan Bagci ; Jesper Oppelstrup; Eric Michielssen

Computational tools for characterizing electromagnetic scattering from objects with uncertain shapes are needed in various applications ranging from remote sensing at microwave frequencies to Raman spectroscopy at optical frequencies. Often, such computational tools use the Monte Carlo (MC) method to sample a parametric space describing geometric uncertainties. For each sample, which corresponds to a realization of the geometry, a deterministic electromagnetic solver computes the scattered fields. However, for an accurate statistical characterization, the number of MC samples has to be large. In this paper, to address this challenge, the continuation multilevel Monte Carlo (CMLMC) method is used together with a surface integral equation solver. The CMLMC method optimally balances statistical errors due to sampling of the parametric space and numerical errors due to the discretization of the geometry using a hierarchy of discretizations, from coarse to fine. The number of realizations of finer discretizations can be kept low, with most samples computed on coarser discretizations to minimize computational cost. Consequently, the total execution time is significantly reduced, in comparison to the standard MC scheme.

DOI: 10.1109/JMMCT.2019.2897490