Three-dimensional magnetotellurics modeling using edgebased finite-element unstructured meshes

Three-dimensional forward modeling magnetotellurics （MT） problems. We present a is a challenge for geometrically complex new edge-based finite-element algorithm using an unstructured mesh for accurately and efficiently simulating 3D MT responses. The electric field curl-curl equation in the frequency domain was used to deduce the H （curl） variation weak form of the MT forward problem, the Galerkin rule was used to derive a linear finite-element equation on the linear-edge tetrahedroid space, and, finally, a BI-CGSTAB solver was used to estimate the unknown electric fields. A local mesh refinement technique in the neighbor of the measuring MT stations was used to greatly improve the accuracies of the numerical solutions. Four synthetic models validated the powerful performance of our algorithms. We believe that our method will effectively contribute to processing more complex MT studies.

Three-dimensional land FD-CSEM forward modeling using edge finite-element method

A modeling tool for simulating three-dimensional land frequency-domain controlled-source electromagnetic surveys,based on a finite-element discretization of the Helmholtz equation for the electric fields,has been developed.The main difference between our modeling method and those previous works is edge finite-element approach applied to solving the three-dimensional land frequency-domain electromagnetic responses generated by horizontal electric dipole source.Firstly,the edge finite-element equation is formulated through the Galerkin method based on Helmholtz equation of the electric fields.Secondly,in order to check the validity of the modeling code,the numerical results are compared with the analytical solutions for a homogeneous half-space model.Finally,other three models are simulated with three-dimensional electromagnetic responses.The results indicate that the method can be applied for solving three-dimensional electromagnetic responses.The algorithm has been demonstrated,which can be effective to modeling the complex geo-electrical structures.This efficient algorithm will help to study the distribution laws of3-D land frequency-domain controlled-source electromagnetic responses and to setup basis for research of three-dimensional inversion.

Indirect tension test of epoxy asphalt mixtureusing microstructural finite-element model

A finite-element model of the thermosetting epoxy asphalt mixture（EAM） microstructure is developed to simulate the indirect tension test（IDT）.Image techniques are used to capture the EAM microstructure which is divided into two phases：aggregates and mastic.A viscoelastic constitutive relationship,which is obtained from the results of a creep test,is used to represent the mastic phase at intermittent temperatures.Model simulation results of the stiffness modulus in IDT compare favorably with experimental data.Different loading directions and velocities are employed in order to account for their influence on the modulus and the localized stress of the microstructure model.It is pointed out that the modulus is not consistent when the loading direction changes since the heterogeneous distribution of the mixture internal structure,and the loading velocity affects the localized stress as a result of the viscoelasticity of the mastic.The study results can provide a theoretical basis for the finite-element method,which can be extended to the numerical simulations of asphalt mixture micromechanical behavior.

Perfectly matched layer-absorbing boundary condition for finite-element time-domain modeling of elastic wave equations

The perfectly matched layer （PML） is a highly efficient absorbing boundary condition used for the numerical modeling of seismic wave equation. The article focuses on the application of this technique to finite-element time-domain numerical modeling of elastic wave equation. However, the finite-element time-domain scheme is based on the second- order wave equation in displacement formulation. Thus, the first-order PML in velocity-stress formulation cannot be directly applied to this scheme. In this article, we derive the finite- element matrix equations of second-order PML in displacement formulation, and accomplish the implementation of PML in finite-element time-domain modeling of elastic wave equation. The PML has an approximate zero reflection coefficients for bulk and surface waves in the finite-element modeling of P-SV and SH wave propagation in the 2D homogeneous elastic media. The numerical experiments using a two-layer model with irregular topography validate the efficiency of PML in the modeling of seismic wave propagation in geological models with complex structures and heterogeneous media.

2.5D induced polarization forward modeling using the adaptive finite-element method

The conventional finite-element（FE） method often uses a structured mesh, which is designed according to the user’s experience, and it is not sufficiently accurate and flexible to accommodate complex structures such as dipping interfaces and rough topography. We present an adaptive FE method for 2.5D forward modeling of induced polarization（IP）. In the presented method, an unstructured triangulation mesh that allows for local mesh refinement and flexible description of arbitrary model geometries is used. Furthermore, the mesh refinement process is guided by dual error estimate weighting to bias the refinement towards elements that affect the solution at the receiver locations. After the final mesh is generated, the Jacobian matrix is used to obtain the IP response on 2D structure models. We validate the adaptive FE algorithm using a vertical contact model. The validation shows that the elements near the receivers are highly refined and the average relative error of the potentials converges to 0.4 % and 1.2 % for the IP response. This suggests that the numerical solution of the adaptive FE algorithm converges to an accurate solution with the refined mesh. Finally, the accuracy and flexibility of the adaptive FE procedure are also validated using more complex models.

Three-dimensional Computational Fluid Dynamics Modeling of Two-phase Flow in a Structured Packing Column

Characterizing the complex two-phase hydrodynamics in structured packed columns requires a power- ful modeling tool. The traditional two-dimensional model exhibits limitations when one attempts to model the de- tailed two-phase flow inside the columns. The present paper presents a three-dimensional computational fluid dy- namics （CFD） model to simulate the two-phase flow in a representative unit of the column. The unit consists of an CFD calculations on column packed with Flexipak 1Y were implemented within the volume of fluid （VOF） mathe- matical framework. The CFD model was validated by comparing the calculated thickness of liquid film with the available experimental data. Special attention was given to quantitative analysis of the effects of gravity on the hy- drodynamics. Fluctuations in the liquid mass flow rate and the calculated pressure drop loss were found to be quali- tatively in agreement with the experimental observations.

Three-Dimensional Tidal Model and Its Application to Numerical Simulation of Water Quality in Coastal Waters

The turbulence mechanism plays an important part in the mixing process and momentum transfer of turbulence. A three-dimensional Prandtl mixing length tidal model has been developed to simulate tidal flows and water quality. The eddy viscosities and diffusivities are computed from the Prandtl mixing length model. In order to model the water quality of an estuary or coastal area many interdependent processes need to be simulated. These may be conveniently separated into three main groups: transport and mixing processes, biochemical interaction of water quality variables and the utilization and re-cycling of nutrients by living matter. The model simulates full oxygen and nutrient balance, primary productivity and the transport, reaction mechanism and fate of pollutants over tidal time-scales. The model is applied to numerical simulation of tidal flows and water quality in Dalian Bay. The model has been calibrated against a limited data set of historical water quality observations and in general demonstrates excellent agreement with all available data.

Three-Dimensional and Cross-sectional Characteristics of Normal Grain Growth Based on Monte Carlo Simulation

An appropriate Monte Carlo method was developed to simulate the three-dimensional normal grain growth more completely. Comparative investigation on the three-dimensional and the cross-sectional characteristics of normal grain growth was done. It was found that the time exponent of grain growth determined from cross-section exhibits the same rule of increasing slowly with time and approaching the theoretical value n = 0.5 of steadygrain growth as the three-dimensional (3-D) system. From change of the number of grains per unit area with timemeasured in cross-section, the state of 3-D normal grain growth may be predicted. The gtain size distribution incross-section is different from that in 3-D system and can not express the evolution characteristic of the 3-D distribution. Furthermore, there exists statistical connection between the topological parameters in cross-section and thosein three-dimensions.

Three-dimensional frequency-domain full waveform inversion based on the nearly-analytic discrete method

The nearly analytic discrete(NAD)method is a kind of finite difference method with advantages of high accuracy and stability.Previous studies have investigated the NAD method for simulating wave propagation in the time-domain.This study applies the NAD method to solving three-dimensional(3D)acoustic wave equations in the frequency-domain.This forward modeling approach is then used as the“engine”for implementing 3D frequency-domain full waveform inversion(FWI).In the numerical modeling experiments,synthetic examples are first given to show the superiority of the NAD method in forward modeling compared with traditional finite difference methods.Synthetic 3D frequency-domain FWI experiments are then carried out to examine the effectiveness of the proposed methods.The inversion results show that the NAD method is more suitable than traditional methods,in terms of computational cost and stability,for 3D frequency-domain FWI,and represents an effective approach for inversion of subsurface model structures.

Acoustic reflection well logging modeling using the frequency-domain finite-element method with a hybrid PML

In this paper, we propose a hybrid PML （H-PML） combining the normal absorption factor of convolutional PML （C-PML） with tangential absorption factor of Mutiaxial PML （M-PML）. The H-PML boundary conditions can better suppress the numerical instability in some extreme models, and the computational speed of finite-element method and the dynamic range are greatly increased using this HPML. We use the finite-element method with a hybrid PML to model the acoustic reflection of the interface when wireline and well logging while drilling （LWD）, in a formation with a reflector outside the borehole. The simulation results suggests that the PS- and SP- reflected waves arrive at the same time when the inclination between the well and the outer interface is zero, and the difference in arrival times increases with increasing dip angle. When there are fractures outside the well, the reflection signal is clearer in the subsequent reflection waves and may be used to identify the fractured zone. The difference between the dominant wavelength and the model scale shows that LWD reflection logging data are of higher resolution and quality than wireline acoustic reflection logging.

Solution of shallow-water equations using least-squares finite-element method

A least-squares finite-element method （LSFEM） for the non-conservative shallow-water equations is presented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercritical flows, and flows with smooth and sharp gradient changes. Advantages of the model include： （1） sources terms, such as the bottom slope, surface stresses and bed frictions, can be treated easily without any special treatment; （2） upwind scheme is no needed; （3） a single approximating space can be used for all variables, and its choice of approximating space is not subject to the Ladyzhenskaya-Babuska-Brezzi （LBB） condition; and （4） the resulting system of equations is symmetric and positive-definite （SPD） which can be solved efficiently with the preconditioned conjugate gradient method. The model is verified with flow over a bump, tide induced flow, and dam-break. Computed results are compared with analytic solutions or other numerical results, and show the model is conservative and accurate. The model is then used to simulate flow past a circular cylinder. Important flow charac-teristics, such as variation of water surface around the cylinder and vortex shedding behind the cylinder are investigated. Computed results compare well with experiment data and other numerical results.

Least-squares finite-element method for shallow-water equations with source terms

Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include： the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.

The three-dimension model for the rock-breaking mechanism of disc cutter andanalysis of rock-breaking forces

To study the rock deformation with three- dimensional model under rolling forces of disc cutter, by car- rying out the circular-grooving test with disc cutter rolling around on the rock, the rock mechanical behavior under rolling disc cutter is studied, the mechanical model of disc cutter rolling around the groove is established, and the the- ory of single-point and double-angle variables is proposed. Based on this theory, the physics equations and geometric equations of rock mechanical behavior under disc cutters of tunnel boring machine （TBM） are studied, and then the bal- ance equations of interactive forces between disc cutter and rock are established. Accordingly, formulas about normal force, rolling force and side force of a disc cutter are de- rived, and their validity is studied by tests. Therefore, a new method and theory is proposed to study rock- breaking mech- anism of disc cutters.

Finite-element 3D modeling of stress patterns around a dipping fault

Stresses in a block around a dipping fracture simulating a damage zone of a fault are reconstructed by finite-element modeling. A fracture corresponding to a fault of different lengths, with its plane dipping at different angles, is assumed to follow a lithological interface and to experience either compression or shear. The stress associated with the destruction shows an asymmetrical pattern with different distances from the highest stress sites to the fault plane in the hanging and foot walls. As the dip angle decreases,the high-stress zone becomes wider in the hanging wall but its width changes negligibly in the foot wall.The length of the simulated fault and the deformation type affect only the magnitude of maximum stress,which remains asymmetrical relative to the fault plane. The Lh/Lfratio, where Lhand Lfare the widths of high-stress zones in the hanging and foot walls of the fault, respectively, is inversely proportional to the fault plane dip. The arithmetic mean of this ratio over different fault lengths in fractures subject to compression changes from 0.29 at a dip of 80°to 1.67 at 30°. In the case of shift displacement, ratios are increasing to 1.2 and 2.94, respectively.Usually they consider vertical fault planes and symmetry in a damage zone of faults. Following that assumption may cause errors in reconstructions of stress and fault patterns in areas of complex structural setting. According geological data, we know the structures are different and asymmetric in hanging and foot walls of fault. Thus, it is important to quantify zones of that asymmetry. The modeling results have to be taken into account in studies of natural faults, especially for practical applications in seismic risk mapping, engineering geology, hydrogeology, and tectonics.

Three-dimensional Finite Element Analysis on the Layer Steel Fiber Reinforced Concrete Pavement:A New Type of Pavement Material

An investigation was conducted on the design of layer steel fiberreinforced concrete (LSFRC) PAVEMENT. Finite element method wasapplied to the analysis on the stress distribution in order todetermine The thickness and segregation distance of LSFRC pavementslabs.

Dynamic Characteristic Mechanism of Atrial Septal Defect Using Real-Time Three-Dimensional Echocardiography and Evaluation of Right Ventricular Functions

The dynamic characteristics of the area of the atrial septal defect（ASD） were evaluated using the technique of real-time three-dimensional echocardiography（RT 3DE）, the potential factors responsible for the dynamic characteristics of the area of ASD were observed, and the overall and local volume and functions of the patients with ASD were measured. RT 3DE was performed on the 27 normal controls and 28 patients with ASD. Based on the three-dimensional data workstations, the area of ASD was measured at P wave vertex, R wave vertex, T wave starting point, and T wave terminal point and in the T-P section. The right atrial volume in the same time phase of the cardiac cycle and the motion displacement distance of the tricuspid annulus in the corresponding period were measured. The measured value of the area of ASD was analyzed. The changes in the right atrial volume and the motion displacement distance of the tricuspid annulus in the normal control group and the ASD group were compared. The right ventricular ejection fractions in the normal control group and the ASD group were compared using the RT 3DE long-axis eight-plane（LA 8-plane） method. Real-time three-dimensional volume imaging was performed in the normal control group and ASD group（n=30）. The right ventricular inflow tract, outflow tract, cardiac apex muscular trabecula dilatation, end-systolic volume, overall dilatation, end-systolic volume, and appropriate local and overall ejection fractions in both two groups were measured with the four-dimensional right ventricular quantitative analysis method（4D RVQ） and compared. The overall right ventricular volume and the ejection fraction measured by the LA 8-plane method and 4D RVQ were subjected to a related analysis. Dynamic changes occurred to the area of ASD in the cardiac cycle. The rules for dynamic changes in the area of ASD and the rules for changes in the right atrial volume in the cardiac cycle were consistent. The maximum value of the changes in the right atrial volume occurred in the end-systolic period when the peak of the curve appeared. The minimum value of the changes occurred in the end-systolic period and was located at the lowest point of the volume variation curve. The area variation curve for ASD and the motion variation curve for the tricuspid annulus in the cardiac cycle were the same. The displacement of the tricuspid annulus exhibited directionality. The measured values of the area of ASD at P wave vertex, R wave vertex, T wave starting point, T wave terminal point and in the T-P section were properly correlated with the right atrial volume（P〈0.001）. The area of ASD and the motion displacement distance of the tricuspid annulus were negatively correlated（P〈0.05）. The right atrial volumes in the ASD group in the cardiac cycle in various time phases increased significantly as compared with those in the normal control group（P=0.0001）. The motion displacement distance of the tricuspid annulus decreased significantly in the ASD group as compared with that in the normal control group（P=0.043）. The right ventricular ejection fraction in the ASD group was lower than that in the normal control group（P=0.032）. The ejection fraction of the cardiac apex trabecula of the ASD patients was significantly lower than the ejection fractions of the right ventricular outflow tract and inflow tract and overall ejection fraction. The difference was statistically significant（P=0.005）. The right ventricular local and overall dilatation and end-systolic volumes in the ASD group increased significantly as compared with those in the normal control group（P=0.031）. The a RVEF and the overall ejection fraction decreased in the ASD group as compared with those in the normal control group（P=0.0005）. The dynamic changes in the area of ASD and the motion curves for the right atrial volume and tricuspid annulus have the same dynamic characteristics. RT 3DE can be used to accurately evaluate the local and overall volume and functions of the right ventricle. The local and overall volume loads of the right ventricle in the ASD patients increase significantly as compared with those of the normal people. The right ventricular cardiac apex and the overall systolic function decrease.

Clinical Value of Stereoscopic Three-dimensional Echocardiography in Assessment of Atrial Septal Defects: Feasibility and Efficiency

Stereoscopic three-dimensional echocardiography（S-3DE） is a novel displaying technol-ogy based on real-time 3-dimensional echocardiography （RT-3DE）. Our study was to evaluate the feasibility and efficiency of S-3DE in the diagnosis of atrial septal defect （ASD） and its use in the guidance for transcatheter ASD occlusion. Twelve patients with secundum ASD underwent RT-3DE examination and 9 of the 12 were subjected to transcatheter closure of ASD. Stereoscopic vision was generated with a high-performance volume renderer with red-green stereoscopic glasses. S-3DE was compared with standard RT-3D display for the assessment of the shape, size, and the surrounding tis-sues of ASD and for the guidance of ASD occlusion. The appearance rate of coronary sinus and the mean formation time of the IVC, SVC were compared. Our results showed that S-3DE could measure the diameter of ASD accurately and there was no significant difference in the measurements between S-3DE and standard 3D display （2.89±0.73 cm vs 2.85±0.72 cm, P〉0.05; r=0.96, P〈0.05）. The appearance of coronary sinus for S-3DE was higher as compared with the standard 3D display （93.3% vs 100%）. The mean time of the IVC, SVC for S-3DE monitor was slightly shorter than that of the standard 3D display （11.0±3.8 s vs 10.3±3.6 s, P〉0.05）. The mean completion time of interven-tional procedure was shortened with S-3DE display as compared with standard 3D display （17.3±3.1 min vs 23.0±3.9 min, P〈0.05）. Stereoscopic three-dimensional echocardiography could improve the visualization of three-dimensional echocardiography, facilitate the identification of the adjacent structures, decrease the time required for interventional manipulation. It may be a feasible, safe, and efficient tool for guiding transcatheter septal occlusion or the surgical interventions.

Three-Dimensional Measurement and Reconstruction of Fabric Drape Shape

This paper introduces a new method of measuring the three-dimensional drape shape of fabrics with structural light. First, we apply parallel annular structural light to form light and shade alternating contour stripes on the surface of fabrics. We then collect the images of contour stripes using Charge Coupled Device (CCD). Subsequently, we process the images to identify the contour stripes and edges of fabrics, and obtain the fabric contour lines of curved surfaces. Finally, we apply three-dimensional curved surface modeling method based on a network of polar coordinates, and reconstruct the three-dimensional drape shape of fabrics. Experiments show that our method is effective in testing and reconstructing three-dimensional drape shape of fabrics.

Inversion of source mechanism of 1989 Loma Prieta earthquake by three-dimensional FEM Green's function

Based on three-dimensional joint finite element, this paper discusses the theory and methodology about inversionof geodetic data. The FEM and inversion formula is given in detail; also a related code is developed. By use of theGreen's function about 3-D FEM, we invert geodetic measurementS of coseismic deformation of the 1989 Ms=7. 1Loma Prieta earthquake to datermine itS source mechanism. The result indicates that the slip on the fault plane isvery heterogeneous. The maximum slip and shear stress are located about 10 kin to northwest of the eathquakesource, the stress drop is about more than 1 MPa.

Mesomechanics Finite-element Method for Determining the Shear Strength of Mudded Intercalation Materials

A new method regarding mesomechanics finite-element research is proposed to predict the peak shear strength of mudded intercalation materials on a mesoscopic scale. Based on geometric and mechanical parameters, along with the strain failure criteria obtained by sample＇s deformation characteristics, uniaxial compression tests on the sample were simulated through a finite-element model, which yielded values consistent with the data from the laboratory uniaxial compression tests, implying that the method is reasonable. Based on this model, a shear test was performed to calculate the peak shear strength of the mudded intercalation, consistent with values reported in the literature, thereby providing a new approach for investigating the mechanical properties of mudded intercalation materials.