Finite-element Time-domain Simulations Research Articles

Goal-Oriented 3-D Time-Domain Marine CSEM Modeling With Anisotropy and Topography

We have proposed a goal-oriented iteration algorithm with adaptive error estimation for the 3-D modeling of the time-domain marine controlled-source electromagnetic (CSEM) method. The algorithm is based on finite-element time-domain (FETD) formulations, and it updates both the time step and the mesh size in a staggered manner. With this scheme, the computational error is well suppressed, and the efficiency of the FETD simulation is guaranteed by adaptive time-stepping within each iteration. The verification results of an electric dipole radiation model and a synthetic 1-D marine CSEM model have shown that the proposed algorithm achieves a fine balance between computational accuracy and efficiency. Through numerical examples incorporated with stratum anisotropy and seafloor topography, we further conclude that both background anisotropy and topography impede the identification of submarine high-resistivity bodies with the electric field response. Contrarily, the time derivative of the magnetic field is sensitive to high-resistivity reservoirs over an extensive period of time in both anisotropic and topographic models. Based on this, we suggest that the magnetic field should be collected along with the electric field over the whole target area to reveal the anisotropic structure of submarine sediments and the existence of oil and gas reservoirs.

Emergence of stegotons in phononic materials with strongly nonlinear rough contacts

The incorporation of nonlinearity in phononic materials enables complex wave interactions in both space and time enriching the dynamic response of the underlying linear media. In this talk, we discuss the strongly nonlinear wave response of continuum phononic material with periodic and discrete nonlinearity. The studied phononic material is a periodic architecture of contact interfaces with rough surfaces, connecting linear elastic layers. These contacts exhibit strong nonlinearity, stemming from variable contact areas under compressive loads and their inability to support the tensile loads. We reveal the evolution of propagating waves using finite element time-domain simulations. The interplay of strong nonlinearity, and dispersion, in the presence of elastic layers, generate traveling localized waves, referred to as “stegotons.” Unlike classical solitons, these stagotons exhibit evolving spatial wave profiles and local variations in wave speed. Moreover, the elastodynamic effects arising from the nonlinearly coupled elastic layers enable strongly nonlinear energy transfer in the frequency domain by activating acoustic resonances of the layers. This study sheds light on the role of the strongly nonlinear coupling of linear media on the formation of traveling localized waves, and could open opportunities for enhanced dynamic response not possible with pure discrete or continuum phononic materials.

ZnO nanorod‐based Love wave delay line for high mass sensitivity: a finite element analysis

This study presents finite element time-domain simulation of a SiO 2 /36°-YX LiTaO 3 Love wave (LW) delay line to explore coupled resonance phenomenon with ZnO nanorods designed on the top surface of the device. The effect of variation in ZnO nanorods height on the propagation of LW, mode-transitions, area-averaged stress, insertion loss, and mass sensitivity of the device is studied. Simulation results show that at the critical height of ZnO nanorods, coupled resonance occurs that causes a sharp swing in the phase shift indicating a transition from inertial to elastic loading. Coupled resonance increases the acoustic impedance of the device and also the average stress between nanorod and substrate interface. Simulation of mass loading is performed by applying an incremental surface mass density on the active area of the device. A nanorod packing density of 1 μm -2 gives a high mass sensitivity of 728 m 2 kg -1 which is more than ten times the sensitivity of a plain LW device. At the coupled resonant height, the insertion loss of the sensor increases, and a swing of about 1 dB is observed with variation in the nanorod height.

Non-Split PML Boundary Condition for Finite Element Time-Domain Modeling of Ground Penetrating Radar

As a highly efficient absorbing boundary condition, Perfectly Matched Layer (PML) has been widely used in Finite Difference Time Domain (FDTD) simulation of Ground Penetrating Radar (GPR) based on the first order electromagnetic wave equation. However, the PML boundary condition is difficult to apply in GPR Finite Element Time Domain (FETD) simulation based on the second order electromagnetic wave equation. This paper developed a non-split perfectly matched layer (NPML) boundary condition for GPR FETD simulation based on the second order electromagnetic wave equation. Taking two-dimensional TM wave equation as an example, the second order frequency domain equation of GPR was derived according to the definition of complex extending coordinate transformation. Then it transformed into time domain by means of auxiliary differential equation method, and its FETD equation is derived based on Galerkin method. On this basis, a GPR FETD forward program based on NPML boundary condition is developed. The merits of NPML boundary condition are certified by compared with wave field snapshots, signal and reflection errors of homogeneous medium model with split and non-split PML boundary conditions. The comparison demonstrated that the NPML algorithm can reduce memory occupation and improve calculation efficiency. Furthermore, numerical simulation of a complex model verifies the good absorption effects of the NPML boundary condition in complex structures.

3D time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach

We present a finite-element time-domain (FETD) approach for the simulation of 3D electromagnetic (EM) diffusion phenomena. The finite-element algorithm efficiently simulates transient electric fields and the time derivatives of magnetic fields in general anisotropic earth media excited by multiple arbitrarily configured electric dipoles with various signal waveforms. To compute transient electromagnetic fields, the electric field diffusion equation is transformed into a system of differential equations via Galerkin’s method with homogeneous Dirichlet boundary conditions. To ensure numerical stability and an efficient time step, the system of the differential equations is discretized in time using an implicit backward Euler scheme. The resultant FETD matrix-vector equation is solved using a sparse direct solver along with a fill-in reduced ordering technique. When advancing the solution in time, the FETD algorithm adjusts the time step by examining whether or not the current step size can be doubled without unacceptably affecting the accuracy of the solution. To simulate a step-off source waveform, the 3D FETD algorithm also incorporates a 3D finite-element direct current (FEDC) algorithm that solves Poisson’s equation using a secondary potential method for a general anisotropic earth model. Examples of controlled-source FETD simulations are compared with analytic and/or 3D finite-difference time-domain solutions and are used to confirm the accuracy and efficiency of the 3D FETD algorithm.

Investigation of Radar Propagation in Buildings: A 10-Billion Element Cartesian-Mesh FETD Simulation

Large-scale full-wave simulations are performed to investigate radar wave propagation inside buildings. In principle, a radar system combined with sophisticated numerical methods for inverse problems can be used to determine the internal structure of a building. The composition of the walls (cinder block, rebar) may effect the propagation of the radar waves in a complicated manner. In order to provide a benchmark solution of radar propagation in buildings, including the effects of cinder block and rebar, we performed large-scale full-wave simulations using a finite-element time domain (FETD) method. This particular FETD implementation is tuned for the special case of an orthogonal Cartesian mesh and hence resembles finite-difference time domain (FDTD) in accuracy and efficiency. The method was implemented on a general-purpose massively parallel computer. In this paper we briefly describe the radar propagation problem, the FETD implementation, and we present results of simulations that used over 10-billion elements.

The low frequency reflection characteristics of the fundamental antisymmetric Lamb wave a0 from a rectangular notch in a plate.

An analysis of the reflection of the fundamental Lamb mode a0 from surface-breaking rectangular notches in isotropic plates is presented. The results are obtained from finite element time domain simulations together with experimental measurements. Good agreement is found between the simulations and the measurements. Results are shown for a range of notch widths and depths, including the special case of a crack, defined as a zero-width notch. The reflection coefficient, when plotted as a function of the notch width, exhibits a cosinusoidal periodic shape, and this is explained by interference between the separate reflections from the start and the end of the notch. The reflection coefficient, when plotted as a function of notch depth, shows that in general the reflection increases with both frequency and notch depth, but the shapes of the functions are complex and there are some surprising features. An analysis of the reflection from cracks using the S-parameter scattering approach and some simplified descriptions of the crack-opening behavior yields physical explanations of the nature of these reflection functions. It is found that opening of the crack can be described adequately by a quasistatic assumption only when the crack is small, and in other cases a ray theory approach is more representative. The reflection function is shown to be a result of contributions from both the axial stress and the shear stress in the wave, and the relative importance of these varies with the crack depth and the frequency.

Low-frequency reflection characteristics of the s0 lamb wave from a rectangular notch in a plate.

An analysis of the reflection of the fundamental Lamb mode s0 from surface-breaking rectangular notches in isotropic plates is presented. The results are obtained from finite element time domain simulations together with experimental measurements. Very good agreement is found between the simulations and the measurements. Results are shown for a range of notch widths and depths, including the special case of a crack, defined as a zero-width notch. An interference phenomenon is identified which explains the periodic nature of the reflection coefficient when plotted as a function of notch width. Finally, an analysis using the S-parameter approach and both low and high frequency asymptotic analyses yields physical explanations of the nature of the reflection behavior from the cracks. It is found that the low frequency (quasistatic) approximation may be used accurately for cracks up to about a quarter of the plate thickness, provided that the quasistatic crack-opening function is chosen such that bending of the plate is omitted. At higher frequencies and depths the functions tend towards the high frequency (ray theory) predictions but these are never accurate models within the nondispersive frequency range of the s0 mode.