Finite-difference Time-domain Propagation Research Articles

Pre-stack elastic reverse time migration in tunnels based on cylindrical coordinates

Seismic forward-prospecting in tunnels is an important step to ensure excavation safety. Nowadays, most advanced imaging techniques in seismic exploration involve calculating the solution of elastic wave equation in a certain coordinate system. However, considering the cylindrical geometry of common tunnel body, Cartesian coordinate system seemingly has limited applicability in tunnel seismic forward-prospecting. To accurately simulate the seismic signal received in tunnels, previous imaging method using decoupled non-conversion elastic wave equation is extended from Cartesian coordinates to cylindrical coordinates. The proposed method preserves the general finite-difference time-domain (FDTD) scheme in Cartesian coordinates, except for a novel wavefield calculation strategy addressing the singularity issue inherited at the cylindrical axis. Moreover, the procedure of cylindrical elastic reverse time migration (CERTM) in tunnels is introduced based on the decoupled non-conversion elastic wavefield. Its imaging effect is further validated via numerical experiments on typical tunnel models. As indicated in the synthetic examples, both the PP- and SS-images could clearly show the geological structure in front of the tunnel face without obvious crosstalk artifacts. Migration imaging using PP-waves can present satisfactory results with higher resolution information supplemented by the SS-images. The potential of applying the proposed method in real-world cases is demonstrated in a water diversion tunnel. In the end, we share our insights regarding the singularity treatment and further improvement of the proposed method.

Simulation of electromagnetic pulses generated by escaped electrons in a high-power laser chamber

Intensive electromagnetic pulses (EMPs) can be generated when a high-power laser strikes a target. The transient electromagnetic field can have an intensity of up to several hundred kV m−1 with a broad frequency of up to several gigahertz, which may affect diagnostics and interfere with, or even damage, electronic equipment. In this paper, the process in which hot electrons produced by the laser−target interaction radiate EMPs is studied and simulated. The physical process is divided into three stages which are: the production of hot electrons; the escape of hot electrons; and the generation of EMPs. Instead of using a general finite difference time domain (FDTD) method to solve the Maxwell equations, a particle-in-cell method together with a time-biased FDTD method is applied in EMP simulation to restrain high-frequency noise. The results show that EMPs are stronger with higher laser intensity and larger target size.

Finite-difference time-domain scheme for nonlinear acoustic waves in solids

Abstract A general finite-difference time-domain (FDTD) method for numerical simulation of the nonlinear acoustic wave in conservative (nondissipative) solids is presented. We apply the spatial derivatives of displacements instead of stress and particle velocity as the bases to discretize the governing partial differential equations. The mathematical model is completely compatible with its linear counterpart. The model solution keeps stable even very near to the formation of a shock wave. As numerical examples, the FDTD scheme is used to investigate the longitudinal and transverse plane waves in infinite isotropic material. In the case of longitudinal wave, a sinusoidal wave transforms into a wave with a sawtooth profile eventually. The distance for the formation of a discontinuity can be obtained directly. The primary and the high order harmonic waves vary with the travelling distance in a very complex way. In the case of transverse wave, high order transverse waves are neglectable and high order longitudinal waves are generated instead. This method dose not need linearization of the governing equations. It can also be used to deal with nonlinear acoustic wave in anisotropic solids without modification.

Optimization of transcostal phased-array refocusing using sparse semidefinite relaxation method.

Treating tumors in organs shadowed by the ribs is a challenge for high intensity focused ultrasound (HIFU). The ribs absorb energy from the ultrasound beams causing their temperature to rise, while also distorting the beams, and limiting the target heat deposition. Accordingly, it is necessary to devise focusing methods that address the difficulties presented by the ribs. In this paper, a new approach that reduces total power deposition on the region of interest (ROI) by removing transducer elements is introduced. The method builds on the limited power deposition (LPD) method, which took advantage of the semidefinite relaxation (SDR) method to relax nonconvex constraints into convex form. The method introduced in this paper induces sparsity using the one-norm squared. The results of using this method to focus a 1-MHz spherical phased array on a target in an inhomogeneous medium are presented and compared to the ray tracing (shadowing) approach [1]. A finite-difference time domain propagation model was used to model the wave propagation to the target. Temperature simulations that utilized the inhomogeneous bioheat transfer equation (BHTE) illustrate the advantages of the induced sparsity LPD method. Together, these simulation results illustrate the advantages of using optimization based on sparsity inducing techniques over the shadowing approach.

Bilinear Transform Implementation of the SC-PML for General Media and General FDTD Schemes

With the complex-frequency-shifted perfectly matched layer (CFS-PML) implemented based on both the stretched coordinates and the bilinear transform method as the absorbing boundary condition (ABC), a novel unified finite-difference time-domain (FDTD) algorithm is developed for general FDTD spatial schemes and general media. The proposed FDTD-PML algorithm employs a general expression for the permittivity of arbitrary linear dispersive media and also takes the nonlinear effects into account. The bilinear transform used in this paper has better accuracy than the frequently used forward, backward, and central difference schemes. Compared with the recursive convolution implementation of the CFS-PML, the bilinear transform implementation involves much simpler FDTD expressions and has better absorbing performance with the same computational cost. Several two-dimensional (2-D) and 3-D simulations involving the anisotropic media, the Debye media, the Drude media, and the Kerr nonlinear media have been done to validate the presented algorithm, and indicate the advantages of the bilinear transform implementation of the CFS-PML. A simulation involving the Lorentz media calculated with the proposed algorithm adopting the wavelet-based high-order FDTD scheme is also included to validate the accuracy and effectiveness of the developed method.

An absorbing boundary condition for general dispersive medium and general FDTD spatial scheme

Based on the stretched coordinate perfectly matched layer (SC-PML) formulation and the auxiliary differential equation method, an absorbing boundary condition for general dispersive medium is presented, and applied to both the standard finite difference time domain (FDTD) method and the high-order FDTD method. The proposed D-H formulations are completely independent of the material properties of the FDTD computational domain. Thus they can be directly applied to the simulations involving arbitrary dielectrics. Numerical results show that compared with the CPML, the proposed method is versatile, has an improved absorbing performance and low computational complexity, and can substantially reduce the computational time.

A general finite difference time domain method for hybrid dispersive media model

The shift operator finite difference time domain (SO-FDTD) method is developed to deal with a hybrid dispersive media model. First, we prove that the complex permittivity of the hybrid dispersive media model can be described by a rational polynomial fraction with respect to jω. Then, the relation between electric displacement D and electric field strength E is derived in the time domain by introducing zt as a shift operator. The constitutive relation in the discretized time domain and the recursive formulation of D and E available for FDTD computation are obtained. Finally, the reflection of the hybrid dispersive slab is computed. The computed results are in good agreement with that obtained by analytic method. This illustrates the generalization and the feasibility of the presented scheme.

General finite-difference time-domain solution of an arbitrary electromagnetic source interaction with an arbitrary dielectric surface

In this study, we develop a numerical algorithm to calculate the interaction of an arbitrary electromagnetic beam with an arbitrary dielectric surface as one of the tools necessary to design and build a detector network based on surface-enhanced Raman scattering (SERS). By using the scattered-field finite-difference time-domain (FDTD) method with incident source terms in the FDTD equations, this development enables an arbitrary incident beam to be implemented onto an arbitrary dielectric surface or particle. Most importantly, in this study a scattered-field uniaxial perfectly matched layer (SF-UPML) absorbing boundary condition (ABC) is developed to truncate the computational domain of the scattered-field FDTD grid. The novel SF-UPML for the scattered-field FDTD algorithm should have a numerical accuracy similar to that of the conventional uniaxial perfectly matched layer for the source-free FDTD equations. Using the new ABC, the scattered-field FDTD method can accurately calculate electromagnetic wave scattering by an arbitrary dielectric surface or particles illuminated by an arbitrary incident beam.

Analysis of thin-wire ground penetrating radar systems for buried target detection, using a hybrid MoM-FDTD technique

A hybrid method combining the finite difference time domain (FDTD) method and the method of moments (MoM) in the frequency domain is proposed to model the electromagnetic behavior of a realistic ground penetrating radar (GPR) system. The GPR is a non-destructive testing (NDT) technique. It consists of a broadband thin-wire vee-dipole antenna located in the vicinity of a lossy ground containing unexploded ordnances. In the solution of the problem, we identify two sub-problems, namely, the antenna problem and the ground buried object problem. Capabilities of the MoM for solution of the governing thin-wire electric field integral equation of the antenna problem and general FDTD solution of Maxwell's equations posed by the scattering of arbitrary shape objects in multilayered media are combined to efficiently and accurately simulate the electromagnetic operation of the system. The proposed simulation technique is validated against the original MoM solution of the problem. It is shown that the proposed hybrid technique exhibits superior performance based on both computation time and numerical accuracy compared with the conventional FDTD and MoM solution techniques. It is also shown that the position and size of the target, as well as the electromagnetic characteristics of the target, can be determined using a simple signal processing technique.

Generalized 3-D DSP-based FDTD algorithm for modelling the APML

A generalized method for implementing the diagonal anisotropic perfectly matched layer (APML) in the finite difference time domain (FDTD) algorithm is presented for truncating three-dimensional (3-D) open region domains. The method is based on incorporating the digital signal processing algorithms developed for digital filters into the APML formulations. In this method, the permittivity and the permeability tensors of the APML are modelled as a set of infinite impulse response digital filters by using the Bilinear transformation technique. The proposed method has the advantage of the simplicity as it allows direct FDTD implementation of Maxwell’s equations in the APML region and also can be used for modelling general FDTD domains such as lossy, dispersive, anisotropic, or nonlinear without any modifications. The new formulations are validated by analyzing 3-D radiation and guided-wave problems.

FDTD analysis of serial corner-fed square patch antennas for single- and dual-polarised applications

The finite-difference time-domain (FDTD) method is developed for the analysis of serial corner-fed square patch antennas. A special technique to model the slanted metallic boundaries of the patch antenna has been used in the general FDTD algorithm to avoid the staircase approximations. The method improves the accuracy of the original FDTD algorithm without increasing its complexity. Both the one-port and two-port cases are studied, which are for single- and dual-polarised applications, respectively. Several antenna elements are manufactured. An isolation of -25 dB is achieved by the two-port antenna, which makes it suitable for many dual-polarised applications. The numerical analysis is confirmed by the experimental results and by results published elsewhere.

Study of impedance and radiation properties of a concentric microstrip triangular-ring antenna and its modeling techniques using FDTD method

A concentric microstrip triangular-ring antenna structure using the log-periodic principle for increasing the impedance bandwidth of the microstrip patch antenna is described. The finite-difference time-domain (FDTD) method is applied to analyze the proposed structure. A special technique to model the slanted metallic boundaries of the triangular ring has been used in the general FDTD algorithm to avoid the staircase approximation. The method improves the accuracy of the original FDTD algorithm without increasing the complexity. The radiation patterns at different frequencies over a wide bandwidth are obtained experimentally.