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.

The Application of Barr Numerical Method to Realize Abel Inversion

An 8-channel HCN laser interferometer will be installed on HL-2A in near term. In order to get the spatial profile of the electron density Barr numerical method is adopted to realize the Abel inversion. In this article the result of the Abel inversion by Matlab GUI is given which can be updated to process the measured data of the 8-channel laser interferometer and provide the spatial distribution of the electron density.

THEORETICAL STUDY OF THREE-DIMENSIONAL NUMERICAL MANIFOLD METHOD

The three-dimensional numerical manifold method（NMM） is studied on the basis of two-dimensional numerical manifold method. The three-dimensional cover displacement function is studied. The mechanical analysis and Hammer integral method of three-dimensional numerical manifold method are put forward. The stiffness matrix of three-dimensional manifold element is derived and the dissection rules are given. The theoretical system and the numerical realizing method of three-dimensional numerical manifold method are systematically studied. As an example, the cantilever with load on the end is calculated, and the results show that the precision and efficiency are agreeable.

A three-dimensional Eulerian method for the numerical simulation of high-velocity impact problems

In the present paper, a three-dimensional （3D） Eulerian technique for the 3D numerical simulation of high-velocity impact problems is proposed. In the Eulerian framework, a complete 3D conservation element and solution element scheme for conservative hyperbolic governing equations with source terms is given. A modified ghost fluid method is proposed for the treatment of the boundary conditions. Numerical simulations of the Taylor bar problem and the ricochet phenomenon of a sphere impacting a plate target at an angle of 60~ are carried out. The numerical results are in good agreement with the corresponding experimental observations. It is proved that our computational technique is feasible for analyzing 3D high-velocity impact problems.

Three-dimensional gravity inversion based on sparse recovery iteration using approximate zero norm

This research proposes a novel three-dimensional gravity inversion based on sparse recovery in compress sensing. Zero norm is selected as the objective function, which is then iteratively solved by the approximate zero norm solution. The inversion approach mainly employs forward modeling; a depth weight function is introduced into the objective function of the zero norms. Sparse inversion results are obtained by the corresponding optimal mathematical method. To achieve the practical geophysical and geological significance of the results, penalty function is applied to constrain the density values. Results obtained by proposed provide clear boundary depth and density contrast distribution information. The method's accuracy, validity, and reliability are verified by comparing its results with those of synthetic models. To further explain its reliability, a practical gravity data is obtained for a region in Texas, USA is applied. Inversion results for this region are compared with those of previous studies, including a research of logging data in the same area. The depth of salt dome obtained by the inversion method is 4.2 km, which is in good agreement with the 4.4 km value from the logging data. From this, the practicality of the inversion method is also validated.

Three-dimensional simulation method of multipactor in microwave components for high-power space application

Based on the particle-in-cell technology and the secondary electron emission theory, a three-dimensional simulation method for multipactor is presented in this paper. By combining the finite difference time domain method and the panicle tracing method, such an algorithm is self-consistent and accurate since the interaction between electromagnetic fields and particles is properly modeled. In the time domain aspect, the generation of multipactor can be easily visualized, which makes it possible to gain a deeper insight into the physical mechanism of this effect. In addition to the classic secondary electron emission model, the measured practical secondary electron yield is used, which increases the accuracy of the algorithm. In order to validate the method, the impedance transformer and ridge waveguide filter are studied. By analyzing the evolution of the secondaries obtained by our method, multipactor thresholds of these components are estimated, which show good agreement with the experimental results. Furthermore, the most sensitive positions where multipactor occurs are determined from the phase focusing phenomenon, which is very meaningful for multipactor analysis and design.

Analysis of Three-dimensional Crack Propagation by Using Displacement Discontinuity Method

A technique for modelling of three-dimensional(3D)quasi-statically propagating cracks in elastic bodies by the displacement discontinuity method(DDM)was described.When the crack is closed,the Mohr-coulomb rule on the two contacted surfaces of the crack must be satisfied.A simple iterative method was adopted in order to consider three different states of cracks.Under the assumption that the advance of the point on the crack front would occur only in the normal plane which is through this edge point,the maximum energy release rate criterion is modified to be used as the criterion for the crack growth.With discretization,the process of crack propagation can be seen as the advance of the vertices of the crack front.The program MCP3D was developed based on these theories to simulate the 3D quasi-static crack propagation.A numerical example of a penny-shaped crack subject to tension and compression in an infinite elastic media was analyzed with MCP3D,and the results in comparison with others' show that the present method for 3D crack propagation is effective.

Existence and Uniqueness of 2π-Periodic Solution About Duffing Equation and Its Numerical Method

A new provement of the existence and uniqueness about periodic boundary value Duffing equation is established by using global inverse function theorem. An algorithm for solving differential equation that has a large convergence domain is given. Finally, a numerical example is given.

Nonlinear Inversion for Complex Resistivity Method Based on QPSO-BP Algorithm

The significant advantage of the complex resistivity method is to reflect the abnormal body through multi-parameters, but its inversion parameters are more than the resistivity tomography method. Therefore, how to effectively invert these spectral parameters has become the focused area of the complex resistivity inversion. An optimized BP neural network (BPNN) approach based on Quantum Particle Swarm Optimization (QPSO) algorithm was presented, which was able to improve global search ability for complex resistivity multi-parameter nonlinear inversion. In the proposed method, the nonlinear weight adjustment strategy and mutation operator were used to enhance the optimization ability of QPSO algorithm. Implementation of proposed QPSO-BPNN was given, the network had 56 hidden neurons in two hidden layers (the first hidden layer has 46 neurons and the second hidden layer has 10 neurons) and it was trained on 48 datasets and tested on another 5 synthetic datasets. The training and test results show that BP neural network optimized by the QPSO algorithm performs better than the BP neural network without initial optimization on the inversion training and test models, and the mean square error distribution is better. At the same time, a double polarized anomalous bodies model was also used to verify the feasibility and effectiveness of the proposed method, the inversion results show that the QPSO-BP algorithm inversion clearly characterizes the anomalous boundaries and is closer to the values of the parameters.

A SEMI-ANALYTICAL AND SEMI-NUMERICAL METHOD FOR SOLVING 2-D SOUND-STRUCTURE INTERACTION PROBLEMS

Based on the transfer matrix method and the virtual source simulation technique, this paper proposes a novel semi-analytical and semi-numerical method for solving 2-D sound- structure interaction problems under a harmonic excitation.Within any integration segment, as long as its length is small enough,along the circumferential curvilinear coordinate,the non- homogeneous matrix differential equation of an elastic ring of complex geometrical shape can be rewritten in terms of the homogeneous one by the method of extended homogeneous capacity proposed in this paper.For the exterior fluid domain,the multi-circular virtual source simulation technique is adopted.The source density distributed on each virtual circular curve may be ex- panded as the Fourier's series.Combining with the inverse fast Fourier transformation,a higher accuracy and efficiency method for solving 2-D exterior Helmholtz's problems is presented in this paper.In the aspect of solution to the coupling equations,the state vectors of elastic ring induced by the given harmonic excitation and generalized forces of coefficients of the Fourier series can be obtained respectively by using a high precision integration scheme combined with the method of extended homogeneous capacity put forward in this paper.According to the superposition princi- ple and compatibility conditions at the interface between the elastic ring and fluid,the algebraic equation of system can be directly constructed by using the least square approximation.Examples of acoustic radiation from two typical fluid-loaded elastic rings under a harmonic concentrated force are presented.Numerical results show that the method proposed is more efficient than the mixed FE-BE method in common use.

A stable one-point quadrature rule for three-dimensional numerical manifold method

We present a numerically stable one-point quadrature rule for the stiffness matrix and mass matrix of the three-dimensional numerical manifold method(3D NMM).The rule simplifies the integration over irregularly shaped manifold elements and overcomes locking issues,and it does not cause spurious modes in modal analysis.The essential idea is to transfer the integral over a manifold element to a few moments to the element center,thereby deriving a one-point integration rule by the moments and making modifications to avoid locking issues.For the stiffness matrix,after the virtual work is decomposed into moments,higher-order moments are modified to overcome locking issues in nearly incompressible and bending-dominated conditions.For the mass matrix,the consistent and lumped types are derived by moments.In particular,the lumped type has the clear advantage of simplicity.The proposed method is naturally suitable for 3D NMM meshes automatically generated from a regular grid.Numerical tests justify the accuracy improvements and the stability of the proposed procedure.

Three-dimensional numerical manifold method for heat conduction problems with a simplex integral on the boundary

The three-dimensional numerical manifold method(3D-NMM),which is based on the derivation of Galerkin's variation,is a powerful calculation tool that uses two cover systems.The 3D-NMM can be used to handle continue-discontinue problems and extend to THM coupling.In this study,we extended the 3D-NMM to simulate both steady-state and transient heat conduction problems.The modelling was carried out using the raster methods(RSM).For the system equation,a variational method was employed to drive the discrete equations,and the crucial boundary conditions were solved using the penalty method.To solve the boundary integral problem,the face integral of scalar fields and two-dimensional simplex integration were used to accurately describe the integral on polygonal boundaries.Several numerical examples were used to verify the results of 3D steady-state and transient heat-conduction problems.The numerical results indicated that the 3D-NMM is effective for handling 3D both steadystate and transient heat conduction problems with high solution accuracy.

Application of inverse method to estimation of boundary conditions during investment casting simulation

Inverse method was used in single crystal superalloy DD6 processing simulation during solidification. Numerical modeling coupled with experiments has been used to estimate the interface heat transfer coefficient （IHTC） between the surface of slab casting and inner mold. Calculated temperature dependent values of IHTC were obtained from a numerical solution. The calculated temperatures agreed well with the measurement of cooling profile.

Multi-parameter numerical simulation of dynamic monitoring of rock deformation in deep mining

The level of deformation development of surrounding rocks is a vital predictor to evaluate impending coal mine disasters and it is important to establish accurate measurements of the deformed status to ensure coal mine safety. Traditional deformation monitoring methods are mostly based on single parameter, in this paper, multiple approaches are integrated: firstly, both electric and elastic models are established,from which electric field distribution and seismic wave recording are calculated and finally, the resistivity profiles and source position information are determined using inversion methods, from which then the deformation and failure of mine floor are evaluated. According to the inversion results of both electric and seismic field signals, multiple-parameter dynamic monitoring of surrounding rock deformation in deep mine can be performed. The methodology is validated using numerical simulation results which shows that the multi-parameter dynamic monitoring methods have better results for surrounding rock deformation in deep mine monitoring than single parameter methods.

Numerical Simulation of Interaction Between Laminar Flow and Elastic Sheet

A numerical simulation of the interaction between laminar flow with low Reynolds number and a highly flexible elastic sheet is presented. The mathematical model for the simulation includes a three-dimensional finitevolume based fluid solver for incompressible viscous flow and a combined finite-discrete element method for the three-dimensional deformation of solid. An immersed boundary method is used to couple the simulation of fluid and solid. It is implemented through a set of immersed boundary points scattered on the solid surface. These points provide a deformable solid wall boundary for the fluid by adding body force to Navier-Stokes equations. The force from the fluid is also obtained for each point and then applied on the boundary nodes of the solid. The vortex-induced vibration of the highly flexible elastic sheet is simulated with the established mathematical model. The simulated results for both swing pattern and oscillation frequency of the elastic sheet in low Reynolds number flow agree well with experimental data.

Precise integration method without inverse matrix calculation for structural dynamic equations

The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise when the algorithm is used for non-homogeneous dynamic systems due to the inverse matrix calculation required. In this paper, the structural dynamic equalibrium equations are converted into a special form, the inverse matrix calculation is replaced by the Crout decomposition method to solve the dynamic equilibrium equations, and the precise integration method without the inverse matrix calculation is obtained. The new algorithm enhances the present precise integration method by improving both the computational accuracy and efficiency. Two numerical examples are given to demonstrate the validity and efficiency of the proposed algorithm.

A numerical simulation of surface wave excitation in a rectangular planar-type plasma source

The principle of surface wave plasma discharge in a rectangular cavity is introduced simply based on surface plasmon polariton theory. The distribution of surface-wave electric field at the interface of the plasma-dielectric slab is investigated by using the three-dimensional finite-difference time-domain method （3D-FDTD） with different slotantenna structures. And the experimental image of discharge with a novel slot antenna array and the simulation of the electric field with this slot antenna array are both displayed. Combined with the distribution of surface wave excitation and experimental results, the numerical simulation performed by using 3D-FDTD is shown to be a useful tool in the computer-aided antenna design for large area planar-type surface-wave plasma sources.

Simulation of Fully Nonlinear 3-D Numerical Wave Tank

A fully nonlinear numerical wave tank (NWT) has been simulated by use of a three-dimensional higher order boundary element method (HOBEM) in the time domain. Within the frame of potential flow and the adoption of simply Rankine source, the resulting boundary integral equation is repeatedly solved at each time step and the fully nonlinear free surface boundary conditions are integrated with time to update its position and boundary values. A smooth technique is also adopted in order to eliminate the possible saw-tooth numerical instabilities. The incident wave at the uptank is given as theoretical wave in this paper. The outgoing waves are absorbed inside a damping zone by spatially varying artificial damping on the free surface at the wave tank end. The numerical results show that the NWT developed by these approaches has a high accuracy and good numerical stability.

Optimal Evacuation Scheme Based on Dam-Break Flood Numerical Simulation

The optimal evacuation scheme is studied based on the dam-break flood numerical simulation. A three- dimensional dam-break mathematical model combined with the volume of fluid （VOF） method is adopted. According to the hydraulic information obtained from numerical simulation and selecting principles of evacuation emergency scheme, evacuation route analysis model is proposed, which consists of the road right model and random degree model. The road right model is used to calculate the consumption time in roads, and the random degree model is used to judge whether the roads are blocked. Then the shortest evacuation route is obtained based on Dijstra algorithm. Gongming Reservoir located in Shenzhen is taken as a case to study. The results show that industrial area I is flooded at 2 500 s, and after 5 500 s, most of industrial area II is submerged. The Hushan, Loucun Forest and Chaishan are not flooded around industrial area I and II. Based on the above analysis, the optimal evacuation scheme is determined.

In-Place Matrix Inversion by Modified Gauss-Jordan Algorithm

The classical Gauss-Jordan method for matrix inversion involves augmenting the matrix with a unit matrix and requires a workspace twice as large as the original matrix as well as computational operations to be performed on both the original and the unit matrix. A modified version of the method for performing the inversion without explicitly generating the unit matrix by replicating its functionality within the original matrix space for more efficient utilization of computational resources is presented in this article. Although the algorithm described here picks the pivots solely from the diagonal which, therefore, may not contain a zero, it did not pose any problem for the author because he used it to invert structural stiffness matrices which met this requirement. Techniques such as row/column swapping to handle off-diagonal pivots are also applicable to this method but are beyond the scope of this article.