Multi-scale seismic full waveform inversion in the frequency-domain with a multi-grid method

Although full waveform inversion in the frequency domain can overcome the local minima problem in the time direction, such problem still exists in the space direction because of the media subsurface complexity. Based on the optimal steep descent methods, we present an algorithm which combines the preconditioned bi-conjugated gradient stable method and the multi-grid method to compute the wave propagation and the gradient space. The multiple scale prosperity of the waveform inversion and the multi-grid method can overcome the inverse problems local minima defect and accelerate convergence. The local inhomogeneous three-hole model simulated results and the Marmousi model certify the algorithm effectiveness.

Multi-grid simulation of pedestrian counter flow with topological interaction

We investigate the dynamics of pedestrian counter flow by using a multi-grid topological pedestrian counter flow model. In the model, each pedestrian occupies multi- rather than only one grid, and interacts with others in the form of topological interaction, which means that a moving pedestrian interacts with a fixed number of those nearest neighbours coming from the opposite direction to determine his/her own moving direction. Thus the discretization of space and time are much finer, the decision making process of the pedestrian is more reliable, which all together makes the moving behaviour and boundary conditions much more realistic. When compared with field observations, it can be found that the modified model is able to reproduce well fitted pedestrian collective behaviour such as dynamical variation of lane formation, clustering of pedestrians in the same direction, etc. The fundamental diagram produced by the model fits also well with field data in thc frce flow region. Further analyses indicate that with the increase of the size of pedestrian counter flow system, it becomes harder for the system to transit into a jamming state, while the increase of interaction range does not change the transition point from free flow to jamming flow in the multi-grid topological counter flow model. It is also found that the asymmetry of the injection rate of pedestrians on the boundaries has direct influence on the process of transition from free flow to jamming flow, i.e., a symmetric injection makes it easier for the system to transit into jamming flow.

Research on a Multi-grid Model for Passenger Evacuation in Ships

In order to enhance the authenticity and accuracy of passenger evacuation simulation in ships, a new multi-grid model was proposed on the basis of a traditional cellular automata model. In the new model finer lattices were used, interaction of force among pedestrians or between pedestrians and constructions was considered, and static floor fields in a multi-level exit environment were simplified into cabin and exit static floor fields. Compared with the traditional cellular automata model, the multi-grid model enhanced the continuity of the passengers'track and the precision of the boundary qualifications. The functions of the dislocation distribution of passengers as well as partial overlap of tracks due to congestion were realized. Furthermore, taking the typical cabin environment as an example, the two models were used to analyze passenger evacuation under the same conditions. It was found that the laws of passenger evacuation simulated by the two models are similar, while the simulation's authenticity and accuracy are enhanced by the multi-grid model.

A MULTI-GRID ALGORITHM FOR MIXED PROBLEMS WITH PENALTY BY C°-PIECEWISE LINEAR ELEMENT APPROXIMATION

In this paper we describe a multi-grid algorithm for mixed problems with penalty by the linear finite element approximation. It is proved that the convergence rate of the algorithm is bound ed away from 1 independently of the meshsize. For convenience, we only discuss Jacobi relaxation as smoothing operator in detail.

ALGEBRAIC MULTI-GRID METHOD IN TWO-DIMENSION ELECTRICALLY LARGE PROBLEMS

In this paper the algebraic multi-grid principle is applied to the multilevel moment method, which makes the new multilevel method easier to implement and more adaptive to structure. Moreover, the error spectrum is analyzed, and the reason why conjugate gradient iteration is not a good relaxation scheme for multi-grid algorithm is explored. The numerical results show that our algebraic block Gauss Seidel multi-grid algorithm is very effective.

Study on Integral Expression in Measurement of Average Ion Velocity by Multi-Grid Probe

In order to improve the interference rejection performance in the measurement of average ion velocity by multi-grid probe, an integral expression is proposed. The integral expression, differing from other expressions for probe measurement, avoids the differential operation on the I-V characteristics of multi-grid probe measurement; and by this method, the ion average velocity can be figured out directly by the I-V characteristics of multi-grid probe measurement.

Application of Multi-Grid Method to the Computation of Electromagnetic Scattering Problems

The multi-grid method has been known as an efficient iterative method for the linear systems and nonlinear systems that arise from finite difference approximations for partial differential equations. In this paper, the multigrid method is extended to the application of solving integral equations which appear in electromagnetic scattering problems. The diakoptic theory is used for this purpose. Compared with other methods, the numerical results show that the multigrid method is powerful to solve electromagnetic scattering problems and can be used to compute electromagnetic scattering problems with electrically large bodies and complex structures.

Multi-focus Image Fusion Combined with CNN and Algebraic Multi-grid Method

The aim of the paper is to solve the problem of over-segmentation problem generated by Watershed segmentation algorithm or unstable clarity judgment by small areas in image fusion. A multi-focus image fusion algorithm is proposed based on CNN segmentation and algebraic multi-grid method (CNN-AMG). Firstly, the CNN segmentation result was utilized to instruct the merging process of the regions generated by the Watershed segmentation method. Then the clear regions were selected into the temporary fusion image and the final fusion process was performed according to the clarity evaluation index, which was computed with the algebraic multi-grid method (AMG). The experimental results show that the fused image quality obtained by the CNNAMG algorithm outperforms the traditional fusion methods such as DSIFT fusion method, CNN fusion method, ASR fusion method, GFF fusion method and so on with some evaluation indexes.

Dynamic limit equilibrium analysis of sliding block for rock slope based on nonlinear FEM

Traditional rigid body limit equilibrium method （RBLEM） was adopted for the stability evaluation and analysis of rock slope under earthquake scenario. It is not able to provide the real stress distribution of the structure, while the strength reduction method relies on the arbitrary decision on the failure criteria. The dynamic limit equilibrium solution was proposed for the stability analysis of sliding block based on 3-D multi-grid method, by incorporating implicit stepping integration FEM. There are two independent meshes created in the analysis： One original 3-D FEM mesh is for the simulation of target structure and provides the stress time-history, while the other surface grid is for the simulation of sliding surface and could be selected and designed freely. As long as the stress time-history of the geotechnical structure under earthquake scenario is obtained based on 3-D nonlinear dynamic FEM analysis, the time-history of the force on sliding surface could be derived by projecting the stress time-history from 3-D FEM mesh to surface grid. After that, the safety factor time-history of the sliding block will be determined through applying limit equilibrium method. With those information in place, the structure＇s aseismatic stability ean be further studied. The above theory and method were also applied to the aseismatic stability analysis of Dagangshan arch dam＇s right bank high slope and compared with the the result generated by Quasi-static method. The comparative analysis reveals that the method not only raises the FEM＇s capability in accurate simulation of complicated geologic structure, but also increases the flexibility and comprehensiveness of limit equilibrium method. This method is reliable and recommended for further application in other real geotechnical engineering.

FINITE ELEMENT METHOD ON NUMERICAL SIMULATION OF STRATUM CORNEUM'S PENETRATION PROPERTY

How the outer substance could penetrate through the skin lies in the stratum corneum, because it is the main barrier in the multi-layers of the skin. Supposing the keratin cell with a special geometry as tetrakaidecahedron, the penetration property of stratum corneum was the key problem which was numerically simulated with finite element method. At first the discretization of the stratum corneum region was given in two steps： first, the discretization of the keratin cell; second, the discretization of fattiness that surrounds the keratin. Then there was the work of numerical simulation. In this procedure, the finite element method and the multi-grid method were used. The former was to obtain the discretization of basic elements; the latter was to decrease the high frequency error. At last the visualization of the numerical simulation was shown.

Parallel programming characteristics of a DSP-based parallel system

This paper firstly introduces the structure and working principle of DSP-based parallel system, parallel accelerating board and SHARC DSP chip. Then it pays attention to investigating the system’s programming characteristics, especially the mode of communication, discussing how to design parallel algorithms and presenting a domain-decomposition-based complete multi-grid parallel algorithm with virtual boundary forecast (VBF) to solve a lot of large-scale and complicated heat problems. In the end, Mandelbrot Set and a non-linear heat transfer equation of ceramic/metal composite material are taken as examples to illustrate the implementation of the proposed algorithm. The results showed that the solutions are highly efficient and have linear speedup.

Effect of Sliding／Rolling Ratio on the Temperature Distribution and Traction Coefficient of Line Contact Thermal EHL of Helical Gears

By using multi-grid method, the simultaneous Reynolds, elasticily, film-thickness,rheology, energy and thermal interface temperature equations are solved, and the numerical solution of line-ontact thermal EHL is successfully obtained and presented in this paper.In addition, the influence of sliding/rolling ratio on the distribution of temperature within the film and on the solid surface. minimum film thickness and traction coefficient are also studied. The results show that the influence of temperature on film thickness is significant and unnegligible, All mentioned above may provide a basis for further investigation of thermal EHL of helical gears.

Flow and transport simulation of Madeira River using three depth-averaged two-equation turbulence closure models

This paper describes a numerical simulation in the Amazon water system, aiming to develop a quasi-three-dimensional numerical tool for refined modeling of turbulent flow and passive transport of mass in natural waters. Three depth-averaged two-equation turbulence closure models, k-ε,k-w, and k-w, were used to close the non-simplified quasi-three-dimensional hydrodynamic fundamental governing equations. The discretized equations were solved with the advanced multi-grid iterative method using non-orthogonal body-fitted coarse and fine grids with collocated variable arrangement. Except for steady flow computation, the processes of contaminant inpouring and plume development at the beginning of discharge, caused by a side-discharge of a tributary, have also been numerically investigated. The three depth-averaged two-equation closure models are all suitable for modeling strong mixing turbulence. The newly established turbulence models such as the k-w model, with a higher order of magnitude of the turbulence parameter, provide a possibility for improving computational precision.

Optimum Tactics of Parallel Multi-Grid Algorithm with Virtual Boundary Forecast Method Running on a Local Network with the PVM Platform

In this paper, an optimum tactic of multi-grid parallel algorithmwith virtual boundary forecast method is disscussed, and a two-stage implementationis presented. The numerical results of solving a non-linear heat transfer equationshow that the optimum implementation is much better than the non-optimum one.

Numerical simulations of self-propelled swimming of 3D bionic fish school

Numerical simulations of self-propelled swimming of a three dimensional bionic fish and fish school in a viscous fluid are carried out. This is done with the assistance of a parallel software package produced for 3D moving boundary problems. This computational fluid dynamics package combines the adaptive multi-grid finite volume method, the immersed boundary method and VOF (volume of fluid) method. By using the package results of the self-propelled swimming of a 3D bionic fish and fish school in a vis- cous fluid are obtained. With comparison to the existing experimental measurements of living fishes, the predicted structure of vortical wakes is in good agreement with the measurements.

Slope stability analysis based on a multigrid method using a nonlinear 3D finite element model

The rigid-body limit equilibrium method cannot reflect the actual stress distribution in a rock mass,and the finite-element-based strength reduction method also has some problems with respect to convergence.To address these problems,a multi-grid method was adopted in this study to establish a structural grid for finite element computation and a slip surface grid for computing slope stability safety factors.This method can be used to determine the stability safety factor for any slip surface or slide block through a combination of nonlinear finite element analysis and limit equilibrium analysis.An ideal elastic–plastic incremental analysis method based on the Drucker–Prager yield criterion was adopted in the nonlinear finite element computation.Elasto-plastic computation achieves good convergence for both small load steps and large load steps and can increase computation precision to a certain extent.To increase the scale and accuracy of the computation,TFINE,a finite element parallel computation program,was used to analyze the influence of grid density on the accuracy of the computation results and was then applied to analysis of the stability of the Jinping high slope.A comparison of the results with results obtained using the rigid-body limit equilibrium method showed that the slope stability safety factors determined using finite element analysis were greater than those obtained using the rigid-body limit equilibrium method and were in better agreement with actual values because nonlinear stress adjustment was considered in the calculation.

A New Algorithm for Total Variation Based Image Denoising

We propose a new algorithm for the total variation based on image denoising problem. The split Bregman method is used to convert an unconstrained minimization denoising problem to a linear system in the outer iteration. An algebraic multi-grid method is applied to solve the linear system in the inner iteration. Furthermore, Krylov subspace acceleration is adopted to improve convergence in the outer iteration. Numerical experiments demonstrate that this algorithm is efficient even for images with large signal-to-noise ratio.

Asymptotic expansions of finite element solutions to Robin problems in H^3 and their application in extrapolation cascadic multigrid method

For the Poisson equation with Robin boundary conditions,by using a few techniques such as orthogonal expansion(M-type),separation of the main part and the finite element projection,we prove for the first time that the asymptotic error expansions of bilinear finite element have the accuracy of O(h3)for u∈H3.Based on the obtained asymptotic error expansions for linear finite elements,extrapolation cascadic multigrid method(EXCMG)can be used to solve Robin problems effectively.Furthermore,by virtue of Richardson not only the accuracy of the approximation is improved,but also a posteriori error estimation is obtained.Finally,some numerical experiments that confirm the theoretical analysis are presented.

A NEWTON MULTIGRID METHOD FOR QUASILINEAR PARABOLIC EQUATIONS

A combination of the classical Newton Method and the multigrid method, i.e., a Newton multigrid method is given for solving quasilinear parabolic equations discretized by finite elements. The convergence of the algorithm is obtained for only one step Newton iteration per level. The asymptotically computational cost for quasilinear parabolic problems is O（NNk） similar to multigrid method for linear parabolic problems.

A Combination Model for Image Denoising

In this paper, we propose an efficient combination model of the second-order ROF model and a simple fourth-order partial differential equation （PDE） for image denoising. The split Bregman method is used to convert the nonlinear combination model into a linear system in the outer iteration, and an algebraic multigrid method is applied to solve the linear system in the inner iteration. Furthermore, Krylov subspace acceleration is adopted to improve convergence in the outer iteration. At the same time, we prove that the model is strictly convex and exists a unique global minimizer. We have also conducted a variety of numerical experiments to analyze the parameter selection criteria and discuss the performance of ~he fourth-order PDE in the combination model. The results show that our model can reduce blocky effects and our algorithm is efficient and robust to solve the proposed model.