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Imaging disturbance zones ahead of a tunnel by elastic full-waveform inversion:Adjoint gradient based inversion *** space reduction using a level-set method

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Underground Space 2018年第1期3卷 21-33页

作者： Andre Lamert Luan T.Nguyen Wolfgang Friederich Tamara Nestorovic Seismology Institute of GeologyMineralogy and GeophysicsRuhr-Uniersity BochumGermany Reservoir Engineering and Rock Physics International Geothermal CenterBochuon University of Applied SciencesGermany Mechanics of Adaptive Systems Institute of Computational EngineeringRudhr-Umiversity BochumGermany

We present and compare twoﬂexible and effective methodologies to predict disturbance zones ahead of underground tunnels by using elastic full-waveform *** methodology uses a linearized,iterative approach based on misﬁt gradients computed with the adjoint method while the other uses iterative,gradient-free unscented Kalmanﬁltering in conjunction with a level-set *** the former does not involve a priori assumptions on the distribution of elastic properties ahead of the tunnel,the latter intro-duces a massive reduction in the number of explicit model parameters to be inverted for by focusing on the geometric form of potential disturbances and their average elastic *** imaging methodologies are validated through successful reconstructions of simple *** an application,we consider an elastic multiple disturbance *** using identical synthetic time-domain seismo-grams as test data,we obtain satisfactory,albeit different,reconstruction results from the two inversion *** computa-tional costs of both approaches are of the same order of magnitude,with the gradient-based approach showing a slight *** model parameter space reduction approach compensates for this by additionally providing a posteriori estimates of model parameter uncertainty.

关键词： Tunnel seismics Full waveform inversion Seismic waves level-set method Adjoint method Kalman filter

An Adaptive Semi-Lagrangian level-set method for Convection-Diffusion Equations on Evolving Interfaces

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Advances in Applied Mathematics and Mechanics 2017年第6期9卷 1364-1382页

作者： Weidong Shi Jianjun Xu Shi Shu School of Mathematical and Computational Sciences Xiangtan UniversityXiangtanHunan 411105China Chongqing Institute of Green and Intelligent Technology Chinese Academy of SciencesChongqing 400714China

A new Semi-Lagrangian scheme is proposed to discretize the surface convection-diffusion *** other involved equations including the the levelset convection equation,the re-initialization equation and the extension equation are also solved by S-L *** S-L method removes both the CFL condition and the stiffness caused by the surface Laplacian,allowing larger time step than the Eulerian *** method is extended to the block-structured adaptive *** examples are given to demonstrate the efficiency of the S-L method.

关键词： Convection-diffusion equation semi-Lagrangian method level-set method blockstructured adaptive mesh finite difference method

Model the Solvent-Excluded Surface of 3D Protein Molecular Structures Using Geometric PDE-Based level-set method

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Communications in Computational Physics 2009年第9期6卷 777-792页

作者： Qing Pan Xue-Cheng Tai College of Mathematics and Computer Science Hunan Normal UniversityChangsha410081China Division of Mathematical Sciences School of Physical and Mathematical SciencesNanyang Technological UniversitySingapore Department of Mathematics University of BergenNorway

This paper presents an approach to model the solvent-excluded surface(SES)of 3D protein molecular structures using the geometric PDE-based level-set *** level-set method embeds the shape of 3D molecular objects as an isosurface or level set corresponding to some isovalue of a scattered dense scalar field,which is saved as a discretely-sampled,rectilinear grid,i.e.,a volumetric *** level-set model is described as a class of tri-cubic tensor product B-spline implicit surface with control point values that are the signed distance *** geometric PDE is evolved in the discrete *** geometric PDE we use is the mean curvature specified flow,which coincides with the definition of the SES and is geometrically *** technique of speeding up is achieved by use of the narrow band strategy incorporated with a good initial approximate construction for the *** get a very desirable approximate surface for the SES.

关键词： Solvent-excluded surface implicit surface mean curvature specified flow level-set method

A Simple Implementation of the Semi-Lagrangian level-set method

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Advances in Applied Mathematics and Mechanics 2017年第1期9卷 104-124页

作者： Weidong Shi Jian-Jun Xu Shi Shu School of Mathematical and Computational Sciences Xiangtan UniversityXiangtanHunan 411105China Chongqing Institute of Green and Intelligent Technology Chinese Academy of SciencesChongqing 400714China

Semi-Lagrangian(S-L)methods have no CFL stability constraint,and are more stable than the Eulerian *** the literature,the S-L method for the levelset re-initialization equation was complicated,which may be *** the re-initialization procedure is auxiliary,we propose to use the first-order S-L scheme coupled with a projection technique to improve the accuracy at the grid points just adjacent to the *** second-order S-L method is used for evolving the level-set convection *** implementation is simple,including on the block-structured adaptive *** efficiency of the S-L method is demonstrated by extensive numerical examples including passive convection of interfaces with corners/kinks/large deformation under given velocity fields,a geometrical flow with topological changes,simulations of bubble/droplet dynamics in incompressible twophase *** terms of accuracy it is comparable to the other existing methods.

关键词： Semi-Lagrangian method level-set method interface motion two-phase flow bubble/droplet dynamics block-structured adaptive mesh

Piecewise Acoustic Source Imaging with Unknown Speed of Sound Using a level-set method

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Communications on Applied Mathematics and Computation 2024年第2期6卷 1070-1095页

作者： Guanghui Huang Jianliang Qian Yang Yang Petroleum Geo-Services HoustonTX 77079USA Department of Mathematics Michigan State UniversityEast LansingMI 48824USA Department of Computational Mathematics Science and EngineeringMichigan State UniversityEastLansingMI48824USA

We investigate the following inverse problem:starting from the acoustic wave equation,reconstruct a piecewise constant passive acoustic source from a single boundary temporal measurement without knowing the speed of *** the amplitudes of the source are known a priori,we prove a unique determination result of the shape and propose a level set algorithm to reconstruct the *** the singularities of the source are known a priori,we show unique determination of the source amplitudes and propose a least-squares fitting algorithm to recover the source *** analysis bridges the low-frequency source inversion problem and the inverse problem of *** proposed algorithms are validated and quantitatively evaluated with numerical experiments in 2D and 3D.

关键词： Inverse gravimetry Acoustic source imaging Inversion of sound speed level-set method Inverse problem

A level set Representation method for N-Dimensional Convex Shape and Applications

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Communications in Mathematical Research 2021年第2期37卷 180-208页

作者： Lingfeng Li Shousheng Luo Xue-Cheng Tai Jiang Yang Department of Mathematics of Hong Kong Baptist University Hong KongSARChina Department of Mathematics of Southern University of Science and Technology ShenzhenChina School of Mathematics and Statistics Henan Engineering Research Center for Artificial Intelligence Theory and AlgorithmsHenan UniversityKaifengChina

In this work,we present a new method for convex shape representation,which is regardless of the dimension of the concerned objects,using level-set *** the best of our knowledge,the proposed prior is the first one which can work for high dimensional *** prior is very useful for object completion in computer *** is a very challenging task to represent high dimensional convex *** this paper,we first prove that the convexity of the considered object is equivalent to the convexity of the associated signed distance ***,the second order condition of convex functions is used to characterize the shape convexity *** apply this new method to two applications:object segmentation with convexity prior and convex hull problem(especially with outliers).For both applications,the involved problems can be written as a general optimization problem with three *** algorithm based on the alternating direction method of multipliers is presented for the optimization *** experiments are conducted to verify the effectiveness of the proposed representation method and algorithm.

关键词： Convex shape prior level-set method image segmentation convex hull ADMM

Application of the level-set Model with Constraints in Image Segmentation

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Numerical Mathematics(Theory,methods and Applications) 2016年第1期9卷 147-168页

作者： Vladimiır Klement Tomas Oberhuber Daniel Sevcovic Department of Mathematics Faculty of Nuclear Sciences and Physical EngineeringCzech Technical University in PragueTrojanova 13Praha 212000Czech Republic Department of Applied Mathematics and Statistics Comenius University84248 BratislavaSlovakia

We proposeand analyze a constrained level-set method forsemi-automatic image *** level-set model with constraints on the level-set function enables us to specify which parts of the image lie inside respectively outside the segmented *** a-priori information can be expressed in terms of upper and lower constraints prescribed for the level-set *** have the same conceptual meaning as initial seeds of the popular graph-cuts based meth-ods for image segmentation.A numerical approximation scheme is based on the complementary-finite volumes method combined with the Projected successive over-relaxation method adopted for solving constrained linear complementarity *** advantage of the constrained level-set method is demonstrated on several artificial images as well as on cardiac MRI data.

关键词： linear complementarity image processing segmentation level-set method projected successive over-relaxation method

Numerical Study of Surfactant-Laden Drop-Drop Interactions

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Communications in Computational Physics 2011年第7期10卷 453-473页

作者： Jian-Jun Xu Zhilin Li John Lowengrub Hongkai Zhao School of Mathematical and Computational Sciences Xiangtan UniversityXiangtanHunan 411105China Department of Mathematics North Carolina State UniversityRaleighNC27695USA Department of Mathematics University of California IrvineIrvineCA92697USA

In this paper,we numerically investigate the effects of surfactant on dropdrop interactions in a 2D shear flow using a coupled level-set and immersed interface approach proposed in(Xu et al.,***.,212(2006),590–616).We find that surfactant plays a critical and nontrivial role in drop-drop *** particular,we find that the minimum distance between the drops is a non-monotone function of the surfactant coverage and Capillary *** non-monotonic behavior,which does not occur for clean drops,is found to be due to the presence of Marangoni forces along the drop *** suggests that there are non-monotonic conditions for coalescence of surfactant-laden drops,as observed in recent experiments of Leal and *** our study is two-dimensional,we believe that drop-drop interactions in three-dimensional flows should be qualitatively similar as the Maragoni forces in the near contact region in 3D should have a similar effect.

关键词： Surfactants drops coalescence surface tension Marangoni effect level-set method immersed interface method Stokes flow

On the Transient Numerical Simulation of Solid Rocket Motor by Coupling Quasi One-dimension Internal Flow with Three-dimension Propellant Grain Burnback

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Journal of Harbin Institute of Technology(New series) 2020年

作者： JuanDuan YongliangXiong NingdongHu DepartmentofMechanics HuazhongUniversityofScienceandTechnology HubeiKeyLaboratoryofEngineeringStructuralAnalysisandSafetyAssessment

The quasi one-dimension compressible flowfield coupled to the three-dimension propellant grain regression solved by the level-set method was used to simulate the transient internal ballistics of solid rocket motor. One-dimension flowfield instead of three-dimension can save computational cost on the premise of calculation accuracy because the radial and azimuthal variations parameters have little contribution to the internal flowfield. The grain regression in real-time could provide accurate geometrical information for simulation. A combination of flowfluid solver and grain regression can reappear in a relatively real internal ballistic flowfield, so it is good for further studying the instability of solid rocket motor. For level-set equations, the total variation-diminishing second-order Runge-Kutta method for temporal derivatives and a fifth-order weighted-essentially-non-oscillatory scheme for spatial derivatives were used. The total variation-diminishing MacCormack method was used to discrete the Euler equations in flowfield solver. Two modules of this code were tested in this study: one is the burning rate module and the other is the nozzle erosion module. Results show that the burning rate influenced the solid rocket motor efficiency, and the velocity profile in the chamber was affected by the nozzle shape, and the nozzle erosion could influence the head-end pressure spike.

关键词： transient compressible solver internal ballistics simulation level-set method solid rocket motor