Calculation Of Wave Propagation Research Articles

Comparison of finite element and discrete exterior calculus in computation of time-harmonic wave propagation with controllability

This paper discusses computation of time-harmonic wave problems using a mixed formulation and the controllability method introduced by Roland Glowinski. As an example, a scattering problem (in an exterior domain) is considered, and the continuous problem is first formulated in terms of differential forms. Based on the continuous formulation, we write the discrete problem and the controllability algorithm for methods based on both the finite element exterior calculus (FEEC) and the discrete exterior calculus (DEC). As the discrete exterior calculus method provides us with a diagonal “mass matrix”, time-stepping in the DEC approach is remarkably more efficient than in the FEEC approach. For the computations in this paper, we choose the lowest order Whitney elements (a.k.a. Raviart–Thomas elements) for the FEEC approach, and in the DEC discretization we use different diagonal approximations for the Hodge star. Especially, in the DEC approach, a “harmonic Hodge” approximation is used, the derivation of which is based on the time-harmonicity of the problem. Different type of grids are used to study the sensitivity of the solution to the quality of the grid. Putting an effort on meshes regular enough, the computed DEC-solution is as accurate as the FEEC-solution, but reached in the fraction of the time. Both methods seem to be able to keep the solution accuracy rather well in computations with a high wave number (corresponding to a high frequency and a small wave length).

Peridynamic computations of wave propagation and reflection at material interfaces

Peridynamics describes the material in a non-local form and is very suited for the simulation of dynamic fracture. However, one significant effect regarding dynamic fracture is the correct handling of elastic deformation, like the pressure and tension waves inside a body, due to dynamic boundary conditions like an impact or impulse. Many peridynamic material formulations have been developed with differences in this regard. This study investigates the elastic wave propagation characteristics of bond-based, ordinary state-based, continuum kinematics-inspired peridynamics and a local continuum consistent correspondence formulation. Multiple parameters of a longitudinal pressure wave inside an elastic bar are studied. While all formulations demonstrate adequate wave propagation handling, all except the correspondence formulation are sensitive to incomplete horizons. The local continuum consistent formulation does not suffer from the surface effect and models the wave propagation with perfect accuracy.

Numerical analysis of the phased array imaging with a stacked plate buffer

Abstract This paper discusses the imaging with a phased array transducer attached with a stacked thin plate buffer using the calculations of wave propagation. The buffer is designed to guarantee the performance of phased array transducer based on the properties of dispersion nature of the S0 mode of Lamb wave. First, numerical analyses showed the limitations of the imaging with a stacked plate buffer due to the multiple reflections at the buffer ends. Then the effective detecting region (EDR) of the phased array transducer with a stacked plate buffer was investigated theoretically and numerically. The imaging results of the numerical calculations agreed with the theoretical predictions on the EDR. Final numerical analyses also presented the longer buffer provides the wider EDR as predicted by the theoretical investigations.

Oceanic crust—seismic structure, lithology and the cause of the 2A Event at borehole 504B

SUMMARY This study focuses on the 3-D velocity structure and thickness of ∼7-Myr-old oceanic crust surrounding borehole 504B, located ∼235 km from the intermediate-spreading Costa Rica Rift (Panama Basin). It investigates how well seismic structure determined by 3-D tomography compares with actual lithology and, consequently, what the origin and cause might be of an amplitude anomaly, the 2A Event, that is observed in multichannel seismic data. Our P-wave model shows an ∼0.3-km-thick sediment layer of velocity between ∼1.6 and 1.9 km s−1 (gradient 1.0 s−1), bound at its base by a velocity step to 4.8 km s−1 at the top of oceanic crustal Layer 2. Layer 2 itself is subdivided into two main units (2A and 2B) by a vertical velocity gradient change at 4.5 km depth, with a gradient of 1.7 s−1 above (4.8–5.8 km s−1) and 0.7 s−1 below (5.8–6.5 km s−1). The base of Layer 2, in turn, is defined by a change in gradient at 5.6 km depth. Below this, Layer 3 has a velocity range of 6.5–7.5 km s−1 and a gradient of ∼0.3 s−1. Corresponding S-wave igneous layer velocities and gradients are: Layer 2A, 2.4–3.1 km s−1 and 1.0 s−1; Layer 2B, 3.1–3.7 km s−1 and 0.5 s−1; Layer 3, 3.7–4.0 km s−1 and 0.1 s−1. The 3-D tomographic models, coupled with gravity modelling, indicate that the crust is ∼6 km thick throughout the region, with a generally flat-lying Moho. Although the P- and S-wave models are smooth, their velocities and gradients are remarkably consistent with the main lithological layering subdivisions logged within 504B. Thus, using the change in velocity gradient as a proxy, Layer 2 is interpreted as ∼1.8 km thick and Layer 3 as ∼3.8 km thick, with little vertical variation throughout the 3-D volume. However, the strike of lateral gradient variation is not Costa Rica Rift-parallel, but instead follows the orientation of the present-day adjacent Ecuador Rift, suggesting a reorientation of the Costa Rica Rift spreading ridge axis. Having determined its consistency with lithological ground-truth, the resulting P-wave model is used as the basis of finite difference calculation of wave propagation to find the origin of the 2A Event. Our modelling shows that no distinct interface, or transition, is required to generate this event. Instead, it is caused by averaging of heterogeneous physical properties by the seismic wave as it propagates through Layer 2 and is scattered. Thus, we conclude that the 2A Event originates and propagates exclusively in the lower part of Layer 2A, above the mean depth to the top of the dykes of Layer 2B. From our synthetic data we conclude that using the 2A Event on seismic reflection profiles as a proxy to determine the Layer 2A/2B boundary's depth will result in an overestimate of up to several hundred metres, the degree of which being dependent on the specific velocity chosen for normal moveout correction prior to stacking.

High performance calculation of nonlinear wave propagation on GPU for focused ultrasound treatment planning

High intensity focused ultrasound (HIFU) is very promising new technology that has many therapeutic application, and among them are the treatment of cancer in different organs without major side effects. Some of the limitations of HIFU are the long treatment time and incomplete ablation. High performance computing can help in this regard. Simulation of nonlinear wave propagation in three dimensional geometry is very time consuming process especially when shocks are presented. In the current work, we are going to present three dimensional parallel solver on GPU. Some examples for the simulation in a patient specific geometry will be also presented. The presented results can be used for the optimization of the treatment. For the validation of the results, ex-vivo and in-vivo experiments have been performed. It has been shown that large volume can be ablated within a short period of time.

Evaluating Structural Details' Influence on Elastic Wave Propagation for Composite Structures via Ray Tracing.

This study presents a novel method based on ray tracing for analyzing wave propagation in composites specifically tailored for structural health monitoring applications. This method offers distinct advantages over the commonly used finite element method mainly in computational resource utilization, which has become a limiting factor for these kinds of analyses. The ray tracing method is evaluated against a number of example cases representing structural details such as thickness changes, stringers, or simulated damage, and the significance of ray tracing to study wave propagation under these conditions and how it can serve as a valuable tool for structural health monitoring are highlighted. This model has been developed as part of a complete SHM framework with the intention of being an efficient and simple way to calculate wave propagation and therefore it could be used as a way to determine relevant damage indicators or train an artificial intelligence model.

Simulation of wave propagation in austenitic stainless steel welds with solidification structure predicted by Cellular Automaton method

Austenitic stainless steel is widely used in nuclear power plants (NPPs) and a variety of occurrences of stress corrosion cracking (SCC) near its weld have been reported among NPPs. Ultrasonic testing is a critical technique for the detection and depth sizing of SCCs. However, such welds' anisotropic and heterogeneous properties cause difficulties in ultrasonic testing when ultrasonic waves propagate through welds. Deeply understanding the characteristics of ultrasonic waves with wave propagation simulation is effective to improve the accuracy of ultrasonic testing. To this end, it is necessary to take crystal orientation and grain boundary into account simultaneously in the numerical model. In this study, a model was developed so that the Cellular Automaton (CA) method can simulate the solidification structure from multilayer and multipass welding process, then the solidification structure of a 7-layer and 7-pass weld of austenitic stainless steel was predicted based on welding conditions. Finally, the finite element method was used to compute wave propagation in austenitic stainless steel weld with the solidification structure predicted. Numerical results of wave propagation in austenitic stainless steel weld were compared to those obtained by experiment.

A multi-GPU and CUDA-aware MPI-based spectral element formulation for ultrasonic wave propagation in solid media

In this paper, we introduce a new multi-GPU-based spectral element (SE) formulation for simulating ultrasonic wave propagation in solids. To maximize communication efficiency, we purposely developed, based on CUDA-aware MPI, two novel message exchange strategies which allow the common nodal forces of different subdomains to be shared between different GPUs in a direct manner, as opposed to via CPU hosts, during central difference-based time integration steps. The new multi-GPU and CUDA-aware MPI-based formulation is benchmarked against a multi-CPU core and classical MPI-based counterpart, demonstrating a remarkable acceleration in each and every stage of the computation of ultrasonic wave propagation, namely matrix assembly, time integration and message exchange. More importantly, both the computational efficiency and the degree-of-freedom limit of the new formulation are actually scalable with the number of GPUs used, potentially allowing larger structures to be computed and higher computational speeds to be realized. Finally, the new formulation was used to simulate the interaction between Lamb waves and randomly shaped thickness loss defects on plates, showing its potential to become an efficient, accurate and robust technique for addressing the propagation of ultrasonic waves in realistic engineering structures.

Fast automated quantitative phase reconstruction in digital holography with unsupervised deep learning

Digital holography can provide quantitative phase images related to the morphology and content of biological samples. To reconstruct an accurate phase image, several processes, such as phase unwrapping, focusing, and calculation of digital reference wave and numerical propagation, are essential. However, this process is time-consuming. We propose a model that performs phase reconstruction in one-step and two-step using an unsupervised image-to-image translation structure. The two-step reconstruction model translates the phase image, which is obtained by performing numerical propagation on the hologram, into an accurate phase image, whereas the one-step reconstruction model directly translates the hologram into an accurate phase image. The proposed model shows similar high-performance reconstruction to the supervised learning model used in many previous studies. However, since supervised learning is trained in strict pairs, many target domain data (accurate phase imagery) is required. Since the proposed model is trained by unsupervised learning, phase reconstruction can be performed with a small amount of target domain data. The proposed method can help to observe the morphology and movement of biological cells in real-time applications.

Wave Propagation in Laminated Cylinders with Internal Fluid and Residual Stress

Numerical computation of wave propagation in laminated cylinders with internal fluid and residual stress is obtained using a Wave Finite Element formulation for 2D waveguides. Only a very small segment of the system is modelled, resulting in a very low-order finite element (FE) model to which the theory of wave propagation in 2D periodic structures is applied. The method uses standard FE formulations and exploits the capability of commercial FE software to model both fluid and structure and their interaction, resulting in a very large reduction in computational time. The presented approach is general, and can be applied without the need to make assumptions related to shell theory or low-frequency analysis. In particular, the laminated structure is discretised using 3D solid elements, thus representing the through-thickness dynamics with high accuracy. Residual radial and hoop stresses are included in the model by adding the FE pre-stress stiffness matrix to the original stiffness matrix of the system. The method provides simultaneously a very substantial reduction of computational cost, accurate solutions up to very high frequency and prediction of the dispersion curves for selected circumferential orders without the need for any further analysis. Here, the formulation of the method is introduced and its application to laminated cylinders filled with an acoustic fluid is presented. A composite, reinforced rubber cylinder, pre-stressed by a circumferential tension, is also shown as an example of a laminated pipe for high-pressure applications.

A General ADE-WLP-FDTD Method With a New Temporal Basis for Wave Propagation

Based on an auxiliary differential equation (ADE) and a new temporal basis function, we propose a 3-D ADE finite-difference time-domain method (FDTD) with weighted Laguerre polynomials (WLPs), 3-D ADE-WLP-FDTD for short, to calculate wave propagation in general dispersive materials. Our proposed method introduces a linear combination of three WLPs as a temporal basis to improve computational efficiency and reduce memory usage. The ADE technique, which can effectively model dispersive media, was used to establish the relationship between the electric displacement vector and electric field intensity. Two numerical examples were presented to validate the advantages of the proposed approach. The simulation results reveal that compared with the conventional ADE-WLP-FDTD method, the proposed method can speed up the computational process and reduce memory usage with comparable accuracy.

A second-order distributed memory parallel fast sweeping method for the Eikonal equation

The Eikonal equation is used to calculate wave propagation and distance fields, and due to its complexity requires numerical treatment for its solution. We present a second-order distributed memory parallel fast sweeping method. The second-order solution switches on a two-point stencil when two upwind points are available, and reverts to first-order otherwise. In all examples, the second-order method improves the solution over the first-order, allowing for significant savings in memory while achieving the same accuracy. Parallelization over distributed memory saw good weak scaling with optimal convergence. The computational time for second-order was approximately 2.5 times slower than first-order, where the largest amount of mesh points ran on 144 cores (512 GB) was ≈20 billion. The savings in memory from the second-order method combined with the distributed memory algorithm result in the ability to solve problems much larger than are possible with the serial first-order method.

Representation of random media in acoustic scattering calculations

Turbulence, internal waves, surface roughness, and other environmental variations in the atmosphere and ocean randomly scatter sound. Realistic representation of these variations is important for numerical wave propagation calculations. In principle, there are two primary approaches to create these representations: (1) physics-based, dynamical models for the atmosphere or ocean and (2) kinematic synthesis of random fields with prescribed statistical properties that do not necessarily capture the medium dynamics. The most common kinematic approach involves synthesizing fields from randomly phased Fourier modes. For statistically inhomogeneous media, the Fourier modes generalize to empirical orthogonal functions. An alternative kinematic approach, called filtered Poisson processes, distribute spatially localized functions with randomized positions and orientations. Quasi-wavelets (QWs) are a filtered Poisson process intended for turbulence and other self-similar media. While both the Fourier and QW approaches can be formulated to reproduce specified second moments of the random field, if the representations are constructed too sparsely, higher-order moments such as the kurtosis will be unrealistic. The kinematic approaches also underlie phase screen methods, which can be quite useful when the Markov approximation is valid.

Systematic review on the use of digital terrain models in dam rupture simulations

The study of hypothetical dam failure simulates the flow of the volume released by a dam in partial or total collapse. The calculations of wave propagation over the ground downstream of the eroded dam are performed by fluid hydrodynamic simulation programs. In this sense, the input data of the simulation model can be summarized in the physical characteristics of the fluid, the propagation hydrograph and the digital terrain model (DTM). Thus, this systematic review aimed to seek current bibliographic sources around the topic of simulation of hypothetical dam failures, with emphasis on the topographic representation of the valley through which the wave propagates, as a subsidy for simulating the failure of Dam B1, in Brumadinho, MG, Brazil. The results were classified according to categories in order to better differentiate the multidisciplinary content of the topic addressed.

HTRSD: Hybrid Taylor Rayleigh-Sommerfeld diffraction.

Computing wave propagation is of the utmost importance in computational optics, especially three-dimensional optical imaging and computer-generated hologram. The angular spectrum method, based on fast Fourier transforms, is one of the efficient approaches; however, it induces sampling issues. We report a Hybrid Taylor Rayleigh-Sommerfeld diffraction (HTRSD) that achieves more accurate and faster wave propagation than the widely used angular spectrum method.

Enhanced ultrasonic total focusing imaging of CFRP corner with ray theory-based homogenization technique

Ultrasonic testing is effective in defect characterization and quality assurance of Carbon Fiber Reinforced Plastic (CFRP) components in the aerospace industry. Due to the coupling between complex shape and elastic anisotropy, the Phased Array Ultrasonic Testing (PAUT) and time-based Total Focusing Method (TFM) face significant challenges in the calculation of wave propagation. A wave velocity distribution model is established for a multidirectional convex corner of CFRP based on a homogenization theory and the above coupling effects are also incorporated. A ray-tracing method is proposed based on Dijkstra’s shortest path search algorithm. The predicted time of flight ensures that this technique, the homogenized TFM, could synthesize a high-quality focused image by post-processing on the full matrix capture data. Experiments on a laminate with three ϕ1.5 mm Side-Drilled Holes (SDHs) in different circumferential directions confirm a successful homogenized TFM imaging that all SDHs can be effectively detected. As compared to the isotropic scenario, the maximum positioning error is reduced to 0.12, 0.08, and 0.38 mm, and the Signal-to-Noise Ratios (SNRs) are increased by 2.1, 1.1, and 11.8 dB, respectively. It is suggested that the ray-tracing assisted TFM technique can effectively improve the imaging of corners in CFRP components.

Phase retrieval using hologram transformation with U-Net in digital holography

Digital holography is a method of recording light waves emitted from an object as holograms and then reconstructing the holograms using light wave propagation calculations to observe the object in three dimensions. However, a problem with digital holography is that unwanted images, such as conjugate images, are superimposed as the hologram is reconstructed to create an observed image. In particular, the superimposition of conjugate light on the observed image is caused by the imaging device’s ability to record just the intensity distribution of light rather than the phase distribution of light. In digital holography, it has been shown that unwanted light can be eliminated by the phase-shift method. However, it is difficult to apply the phase-shift method to digital holographic microscopy (DHM), which takes only one shot of light intensity. Alternatively, machine learning methods called deep learning have been actively studied in recent years for image-related problems, with image transformation as an example. Furthermore, a method that combines digital holography and deep learning has been proposed to perform image transformation to remove conjugate images using deep learning on the reconstructed image of a hologram. In this study, we generated a pair of holograms with only light intensity distribution and holograms with complex amplitude by simulating light wave propagation, trained U-Net to perform image transformation that adds phase information to the hologram with only light intensity distribution, and proposed a method for phase retrieval and conjugate image removal for holograms using the learned U-Net. To verify the effectiveness of the proposed method, we evaluated the image quality of the reconstructed image of holograms before and after processing by U-Net. Results showed that the peak signal-to-noise ratio (PSNR) increased by 8.37 [dB] in amplitude and 9.06 [dB] in phase. The amplitude and phase of the structural similarity index (SSIM) increased by 0.0566 and 0.0143, respectively. Furthermore, the results of applying the proposed method to holograms captured by actual digital holography optics showed the effectiveness of the proposed method in eliminating conjugate images in the reconstructed images. These results show that the proposed method is capable of phase retrieval of holograms in a single shot without the need for a complex optical system. This is expected to contribute to the field of portable DHMs and other applications that require compact and simple optical systems.

Regularized variational formulation for nonlinear dynamics of viscoplastic plates

In this work we present novel approach to Reissner–Mindlin plates, targeting the nonlinear dynamics applications and in particular robust scheme for improved performance in vibration and wave propagation computations, where the standard finite element isoparametric interpolations no longer provide the best approximation property. The first key ingredient of the present development is regularized variational formulation, recast in terms of stress resultants (bending moments and shear forces), which allows any convenient interpolations. The discrete approximation is here constructed by using the lowest order Raviart–Thomas vector space employed to discretize bending moment and shear force fields, providing the continuity of the stress resultants projections across the boundary between adjacent plate elements. The latter is of particular interest for dynamic analysis for it can capture smooth approximation for wave propagation phenomena. This particular space discrete approximation is further combined with the most appropriate time-integration schemes capable of enforcing either energy conservation or decay of high frequency modes, which delivers the schemes with higher stability and robustness in long-term computations. The developments are carried out for viscoplastic constitutive behavior of plate material, where the corresponding evolution equations are obtained by appealing to the penalty-like form of the principle of maximum plastic dissipation. The choice of viscoplasticity (rather than plasticity) is crucial in that allows development of second-order scheme by integrating simultaneously the momentum balance and viscoplastic strains evolution equations. Several numerical simulations are given to illustrate a very satisfying performance of the proposed hybrid-stress discrete approximation for thick plate element and of the energy conserving/decaying schemes.

X-ray phase contrast imaging model: application on tomography with a single 2D phase grating

In this paper, we propose a model dedicated to X-ray phase contrast imaging, which is well adapted to the characterization or inspection of low attenuating samples. We introduce a hybrid approach that combines a ray-tracing step with a wave propagation computation. The mathematical basis of our model is described and we present a comparison of the model to experimental results, for the case of an optical fiber sample, in the framework of a free-propagation phase technique. The extension to the 3D imaging is proposed on simulated data using a grating based technique or more precisely, a multilateral shearing interferometry. This technique uses a single 2D phase grating, which has the advantage of a simpler experimental setup and can be coupled with a standard micro-focus X-ray tube and a high-resolution detector. Our phase model was implemented on the CIVA CT simulation platform and used to generate easily different sets of projection data for any type of sample. While the method for 3D reconstruction has the same basis as the classical CT, we focus mainly on the intermediate processing steps, which are required for the phase retrieval and present the results for a phantom composed of spherical objects in different materials.

Backscattering Behavior of Vulnerable Road Users Based on High-Resolution RCS Measurements

Automotive radars, along with optical sensors such as cameras or lidars, offer a reliable way of obtaining the 3-D information about the environment. Of particular interest in autonomous driving (AD) is the reliable detection of particularly vulnerable road users (VRUs). Modern radar sensors are able to detect, distinguish, and track targets with high resolution. Relying on that, a backscattering model of complex traffic targets can be generated from the reflected signals of their scattering points (SPs). These models can be employed in the radar channel simulations for verification methods of advanced driver assistance systems. Therefore, in this work, different persons as the most vital VRUs are measured with high radial and high angular resolution. The necessary signal processing steps are explained in detail for the determination of the relevant SPs. Thus, the corresponding radar cross section (RCS) values can be assigned to certain body regions. In addition to real persons, further measurements are compared with a dummy of the corresponding size. Based on the measurement results, not only accurate models of road users can be derived, but also the measurement results can be employed for calculating wave propagation in traffic scenarios. From the measured SPs, the classification of the persons by size and stature is derived.