A novel method which integrates the topological flexibility of the level-set approach and the simplicity of point-sampled surfaces is proposed. The grid structure resulted from the level-set approach not only offers a...A novel method which integrates the topological flexibility of the level-set approach and the simplicity of point-sampled surfaces is proposed. The grid structure resulted from the level-set approach not only offers a wide range of powerful surface editing techniques for the point set surface editing, but also facilitates the topological change with ease. With the aid of point-based resampling, the method updates the surface shape of the point-based geometry quickly without worrying about point connectivity at all. The point set surface can also change its topology properly whenever a collision with other parts of itself is detected. The experiment demonstrates their effectiveness on several scanned objects and scan-converted models. Four examples of surface editing operations： smoothing, tapering, deforming, and Boolean operations, are presented.展开更多
Parameterized level-set method(PLSM)has been proposed and developed for many years,and is renowned for its efficacy in ad-dressing topology optimization challenges associated with intricate boundaries and nucleation o...Parameterized level-set method(PLSM)has been proposed and developed for many years,and is renowned for its efficacy in ad-dressing topology optimization challenges associated with intricate boundaries and nucleation of new holes.However,most pertinent investigations in the field rely predominantly on fixed background mesh,which is never remeshed.Consequently,the mesh element partitioned by material interface during the optimization process necessitates approximation by using artificial interpolation models to obtain its element stiffness or other properties.This paper introduces a novel approach to topology op-timization by integrating the PLSM with body-fitted adaptive mesh and Helmholtz-type filter.Primarily,combining the PLSM with body-fitted adaptive mesh enables the regeneration of mesh based on the zero level-set interface.This not only precludes the direct traversal of the material interface through the mesh element during the topology optimization process,but also improves the accuracy of calculation.Additionally,the incorporation of a Helmholtz-type partial differential equation filter,relying solely on mesh information essential for finite element discretization,serves to regulate the topological complexity and the minimum feature size of the optimized structure.Leveraging these advantages,the topology optimization program demonstrates its versa-tility by successfully addressing various design problems,encompassing the minimum mean compliance problem and minimum energy dissipation problem.Ultimately,the result of numerical example indicates that the optimized structure exhibits a dis-tinct and smooth boundary,affirming the effective control over both topological complexity and the minimum feature size of the optimized structure.展开更多
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 s...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 sound.When 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 singularities.When 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 amplitudes.The analysis bridges the low-frequency source inversion problem and the inverse problem of gravimetry.The proposed algorithms are validated and quantitatively evaluated with numerical experiments in 2D and 3D.展开更多
This work deals with the influences of nano-heterogeneities in the form of voids/cavities or cracks on the elastic (please confirm which word is correct. effective or elastic? According to the title of paper, I choose...This work deals with the influences of nano-heterogeneities in the form of voids/cavities or cracks on the elastic (please confirm which word is correct. effective or elastic? According to the title of paper, I choose elastic.) properties of a host medium. With a relatively large ratio of apparent-surface to volume and particularly strong physical interactions with the surrounding medium at nano-scale, nano-heterogeneities can potentially affect the elastic(effective or elastic?) properties of the parent medium (matrix) containing them in a significant manner. This has been reported by various theoretical and experimental studies, some of them are discussed in the present paper. To describe the positive (reinforcement) or negative (degradation) effect of the nano-heterogeneities from the modeling perspective, it is necessary to take into account the energy of interfaces/surfaces between nano-heterogeneities and the matrix which, by the fact of the relatively large extent of their apparent surface and their strong physical interaction with their neighborhood, can no longer be neglected compared to those of the volume energy. Thus, to account for the effects of interfaces/surfaces in a nanostructured heterogeneous medium, the coherent interface model is considered in the present investigation within a periodic homogenization procedure. In this interface/surface model, the displacement vector is assumed to be continuous across the interface while the stress vector is considered to be discontinuous and satisfying the Laplace-Young equations. To solve these equations coupled to the classical mechanical equilibrium problem, a numerical simulation tool is developed in a two-dimensional (2D) context using the eXtended Finite Element Method (XFEM) and the Level-Set functions. The developed numerical tool is then used to carry out a detailed analysis about the effect of nano-heterogeneities on the overall mechanical properties of a medium. The nano-heterogeneities are present in the medium initially as cylindrical cavities (circular in 2D) before being reduced to plane cracks (line in 2D) by successive flattenings.展开更多
A novel approach to extract flame fronts, which is called the conditioned level-set method with block division （CLSB）, has been developed. Based on a two-phase level-set formulation, the conditioned initialization a...A novel approach to extract flame fronts, which is called the conditioned level-set method with block division （CLSB）, has been developed. Based on a two-phase level-set formulation, the conditioned initialization and region-lock optimiza-tion appear to be beneficial to improve the efficiency and accuracy of the flame contour identification. The original block- division strategy enables the approach to be unsupervised by calculating local self-adaptive threshold values autonomously before binarization. The CLSB approach has been applied to deal with a large set of experimental data involving swirl- stabilized premixed combustion in diluted regimes operating at atmospheric pressures. The OH-PLIF measurements have been carried out in this framework. The resulting images are, thus, featured by lower signal-to-noise ratios （SNRs） than the ideal image; relatively complex flame structures lead to significant non-uniformity in the OH signal intensity; and, the mag- nitude of the maximum OH gradient observed along the flame front can also vary depending on flow or local stoichiometry. Compared with other conventional edge detection operators, the CLSB method demonstrates a good ability to deal with the OH-PLIF images at low SNR and with the presence of a multiple scales of both OH intensity and OH gradient. The robustness to noise sensitivity and intensity inhomogeneity has been evaluated throughout a range of experimental images of diluted flames, as well as against a circle test as Ground Truth （GT）.展开更多
文摘A novel method which integrates the topological flexibility of the level-set approach and the simplicity of point-sampled surfaces is proposed. The grid structure resulted from the level-set approach not only offers a wide range of powerful surface editing techniques for the point set surface editing, but also facilitates the topological change with ease. With the aid of point-based resampling, the method updates the surface shape of the point-based geometry quickly without worrying about point connectivity at all. The point set surface can also change its topology properly whenever a collision with other parts of itself is detected. The experiment demonstrates their effectiveness on several scanned objects and scan-converted models. Four examples of surface editing operations： smoothing, tapering, deforming, and Boolean operations, are presented.
基金supported by the National Natural Science Foundation of China(Grant Nos.12372200 and 12072242).
文摘Parameterized level-set method(PLSM)has been proposed and developed for many years,and is renowned for its efficacy in ad-dressing topology optimization challenges associated with intricate boundaries and nucleation of new holes.However,most pertinent investigations in the field rely predominantly on fixed background mesh,which is never remeshed.Consequently,the mesh element partitioned by material interface during the optimization process necessitates approximation by using artificial interpolation models to obtain its element stiffness or other properties.This paper introduces a novel approach to topology op-timization by integrating the PLSM with body-fitted adaptive mesh and Helmholtz-type filter.Primarily,combining the PLSM with body-fitted adaptive mesh enables the regeneration of mesh based on the zero level-set interface.This not only precludes the direct traversal of the material interface through the mesh element during the topology optimization process,but also improves the accuracy of calculation.Additionally,the incorporation of a Helmholtz-type partial differential equation filter,relying solely on mesh information essential for finite element discretization,serves to regulate the topological complexity and the minimum feature size of the optimized structure.Leveraging these advantages,the topology optimization program demonstrates its versa-tility by successfully addressing various design problems,encompassing the minimum mean compliance problem and minimum energy dissipation problem.Ultimately,the result of numerical example indicates that the optimized structure exhibits a dis-tinct and smooth boundary,affirming the effective control over both topological complexity and the minimum feature size of the optimized structure.
基金partially supported by the NSF(Grant Nos.2012046,2152011,and 2309534)partially supported by the NSF(Grant Nos.DMS-1715178,DMS-2006881,and DMS-2237534)+1 种基金NIH(Grant No.R03-EB033521)startup fund from Michigan State University.
文摘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 sound.When 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 singularities.When 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 amplitudes.The analysis bridges the low-frequency source inversion problem and the inverse problem of gravimetry.The proposed algorithms are validated and quantitatively evaluated with numerical experiments in 2D and 3D.
文摘This work deals with the influences of nano-heterogeneities in the form of voids/cavities or cracks on the elastic (please confirm which word is correct. effective or elastic? According to the title of paper, I choose elastic.) properties of a host medium. With a relatively large ratio of apparent-surface to volume and particularly strong physical interactions with the surrounding medium at nano-scale, nano-heterogeneities can potentially affect the elastic(effective or elastic?) properties of the parent medium (matrix) containing them in a significant manner. This has been reported by various theoretical and experimental studies, some of them are discussed in the present paper. To describe the positive (reinforcement) or negative (degradation) effect of the nano-heterogeneities from the modeling perspective, it is necessary to take into account the energy of interfaces/surfaces between nano-heterogeneities and the matrix which, by the fact of the relatively large extent of their apparent surface and their strong physical interaction with their neighborhood, can no longer be neglected compared to those of the volume energy. Thus, to account for the effects of interfaces/surfaces in a nanostructured heterogeneous medium, the coherent interface model is considered in the present investigation within a periodic homogenization procedure. In this interface/surface model, the displacement vector is assumed to be continuous across the interface while the stress vector is considered to be discontinuous and satisfying the Laplace-Young equations. To solve these equations coupled to the classical mechanical equilibrium problem, a numerical simulation tool is developed in a two-dimensional (2D) context using the eXtended Finite Element Method (XFEM) and the Level-Set functions. The developed numerical tool is then used to carry out a detailed analysis about the effect of nano-heterogeneities on the overall mechanical properties of a medium. The nano-heterogeneities are present in the medium initially as cylindrical cavities (circular in 2D) before being reduced to plane cracks (line in 2D) by successive flattenings.
文摘A novel approach to extract flame fronts, which is called the conditioned level-set method with block division （CLSB）, has been developed. Based on a two-phase level-set formulation, the conditioned initialization and region-lock optimiza-tion appear to be beneficial to improve the efficiency and accuracy of the flame contour identification. The original block- division strategy enables the approach to be unsupervised by calculating local self-adaptive threshold values autonomously before binarization. The CLSB approach has been applied to deal with a large set of experimental data involving swirl- stabilized premixed combustion in diluted regimes operating at atmospheric pressures. The OH-PLIF measurements have been carried out in this framework. The resulting images are, thus, featured by lower signal-to-noise ratios （SNRs） than the ideal image; relatively complex flame structures lead to significant non-uniformity in the OH signal intensity; and, the mag- nitude of the maximum OH gradient observed along the flame front can also vary depending on flow or local stoichiometry. Compared with other conventional edge detection operators, the CLSB method demonstrates a good ability to deal with the OH-PLIF images at low SNR and with the presence of a multiple scales of both OH intensity and OH gradient. The robustness to noise sensitivity and intensity inhomogeneity has been evaluated throughout a range of experimental images of diluted flames, as well as against a circle test as Ground Truth （GT）.
