The Experts below are selected from a list of 20340 Experts worldwide ranked by ideXlab platform
Ronald Fedkiw - One of the best experts on this subject based on the ideXlab platform.
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Particle Level Set Method
Applied Mathematical Sciences, 2020Co-Authors: Stanley Osher, Ronald FedkiwAbstract:The great success of Level Set Methods can in part be attributed to the role of curvature in regularizing the Level Set function such that the proper vanishing viscosity solution is obtained. It is much more difficult to obtain vanishing viscosity solutions with Lagrangian Methods that faithfully follow the characteristics. For these Methods one usually has to delete (or add) characteristic information “by hand” when a shock (or rarefaction) is detected. This ability of Level Set Methods to identify and delete merging characteristics is clearly seen in a purely geometrically driven flow where a curve is advected normal to itself at constant speed, as shown in Figures 9.1 and 9.2. In the corners of the square, the flow field has merging characteristics that are appropriately deleted by the Level Set Method. We demonstrate the difficulties associated with a Lagrangian calculation of this interface motion by initially seeding some marker particles interior to the interface, as shown in Figure 9.3 and passively advecting them with \( {\overrightarrow x_t} = \overrightarrow V \left( {\overrightarrow x, t} \right) \) where the velocity field V↦(x↦ t) is determined from the Level Set solution. Figure 9.4 illustrates that a number of particles incorrectly escape from inside the Level Set solution curve in the corners of the square where the characteristic information (represented by the particles themselves) needs to be deleted so that the correct vanishing viscosity solution can be obtained.
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a fast and accurate semi lagrangian particle Level Set Method
Computers & Structures, 2005Co-Authors: Douglas Enright, Frank Losasso, Ronald FedkiwAbstract:In this paper, we present an efficient semi-Lagrangian based particle Level Set Method for the accurate capturing of interfaces. This Method retains the robust topological properties of the Level Set Method with- out the adverse effects of numerical dissipation. Both the Level Set Method and the particle Level Set Method typically use high order accurate numerical discretizations in time and space, e.g. TVD Runge-Kutta and HJ-WENO schemes. We demonstrate that these computationally expensive schemes are not required. Instead, fast, low order accurate numerical schemes suffice. That is, the addition of particles to the Level Set Method not only removes the difficulties associated with numerical diffusion, but also alleviates the need for computationally expensive high order accurate schemes. We use an efficient, first order accurate semi-Lagrangian advection scheme coupled with a first order accurate fast marching Method to evolve the Level Set function. To accurately track the underlying flow characteristics, the particles are evolved with a second order accurate Method. Since we avoid complex high order accurate numerical Methods, extending the algorithm to arbitrary data structures becomes more feasible, and we show preliminary results obtained with an octree-based adaptive mesh.
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a hybrid particle Level Set Method for improved interface capturing
Journal of Computational Physics, 2002Co-Authors: Douglas Enright, Ronald Fedkiw, Joel H Ferziger, Ian M MitchellAbstract:In this paper, we propose a new numerical Method for improving the mass conservation properties of the Level Set Method when the interface is passively advected in a flow field. Our Method uses Lagrangian marker particles to rebuild the Level Set in regions which are underresolved. This is often the case for flows undergoing stretching and tearing. The overall Method maintains a smooth geometrical description of the interface and the implementation simplicity characteristic of the Level Set Method. Our Method compares favorably with volume of fluid Methods in the conservation of mass and purely Lagrangian schemes for interface resolution. The Method is presented in three spatial dimensions.
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fast surface reconstruction using the Level Set Method
Proceedings IEEE Workshop on Variational and Level Set Methods in Computer Vision, 2001Co-Authors: Hongkai Zhao, Stanley Osher, Ronald FedkiwAbstract:We describe new formulations and develop fast algorithms for implicit surface reconstruction based on variational and partial differential equation (PDE) Methods. In particular we use the Level Set Method and fast sweeping and tagging Methods to reconstruct surfaces from a scattered data Set. The data Set might consist of points, curves and/or surface patches. A weighted minimal surface-like model is constructed and its variational Level Set formulation is implemented with optimal efficiency. The reconstructed surface is smoother than piecewise linear and has a natural scaling in the regularization that allows varying flexibility according to the local sampling density. As is usual with the Level Set Method we can handle complicated topology and deformations, as well as noisy or highly nonuniform data Sets easily. The Method is based on a simple rectangular grid, although adaptive and triangular grids are also possible. Some consequences, such as hole filling capability, are demonstrated, as well as the viability and convergence of our new fast tagging algorithm.
Stanley Osher - One of the best experts on this subject based on the ideXlab platform.
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Particle Level Set Method
Applied Mathematical Sciences, 2020Co-Authors: Stanley Osher, Ronald FedkiwAbstract:The great success of Level Set Methods can in part be attributed to the role of curvature in regularizing the Level Set function such that the proper vanishing viscosity solution is obtained. It is much more difficult to obtain vanishing viscosity solutions with Lagrangian Methods that faithfully follow the characteristics. For these Methods one usually has to delete (or add) characteristic information “by hand” when a shock (or rarefaction) is detected. This ability of Level Set Methods to identify and delete merging characteristics is clearly seen in a purely geometrically driven flow where a curve is advected normal to itself at constant speed, as shown in Figures 9.1 and 9.2. In the corners of the square, the flow field has merging characteristics that are appropriately deleted by the Level Set Method. We demonstrate the difficulties associated with a Lagrangian calculation of this interface motion by initially seeding some marker particles interior to the interface, as shown in Figure 9.3 and passively advecting them with \( {\overrightarrow x_t} = \overrightarrow V \left( {\overrightarrow x, t} \right) \) where the velocity field V↦(x↦ t) is determined from the Level Set solution. Figure 9.4 illustrates that a number of particles incorrectly escape from inside the Level Set solution curve in the corners of the square where the characteristic information (represented by the particles themselves) needs to be deleted so that the correct vanishing viscosity solution can be obtained.
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efficient algorithm for Level Set Method preserving distance function
IEEE Transactions on Image Processing, 2012Co-Authors: Virginia Estellers, Stanley Osher, Dominique Zosso, Jeanphilippe Thiran, Xavier BressonAbstract:The Level Set Method is a popular technique for tracking moving interfaces in several disciplines, including computer vision and fluid dynamics. However, despite its high flexibility, the original Level Set Method is limited by two important numerical issues. First, the Level Set Method does not implicitly preserve the Level Set function as a distance function, which is necessary to estimate accurately geometric features, s.a. the curvature or the contour normal. Second, the Level Set algorithm is slow because the time step is limited by the standard Courant-Friedrichs-Lewy (CFL) condition, which is also essential to the numerical stability of the iterative scheme. Recent advances with graph cut Methods and continuous convex relaxation Methods provide powerful alternatives to the Level Set Method for image processing problems because they are fast, accurate, and guaranteed to find the global minimizer independently to the initialization. These recent techniques use binary functions to represent the contour rather than distance functions, which are usually considered for the Level Set Method. However, the binary function cannot provide the distance information, which can be essential for some applications, s.a. the surface reconstruction problem from scattered points and the cortex segmentation problem in medical imaging. In this paper, we propose a fast algorithm to preserve distance functions in Level Set Methods. Our algorithm is inspired by recent efficient l1 optimization techniques, which will provide an efficient and easy to implement algorithm. It is interesting to note that our algorithm is not limited by the CFL condition and it naturally preserves the Level Set function as a distance function during the evolution, which avoids the classical re-distancing problem in Level Set Methods. We apply the proposed algorithm to carry out image segmentation, where our Methods prove to be 5-6 times faster than standard distance preserving Level Set techniques. We also present two applications where preserving a distance function is essential. Nonetheless, our Method stays generic and can be applied to any Level Set Methods that require the distance information.
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fast surface reconstruction using the Level Set Method
Proceedings IEEE Workshop on Variational and Level Set Methods in Computer Vision, 2001Co-Authors: Hongkai Zhao, Stanley Osher, Ronald FedkiwAbstract:We describe new formulations and develop fast algorithms for implicit surface reconstruction based on variational and partial differential equation (PDE) Methods. In particular we use the Level Set Method and fast sweeping and tagging Methods to reconstruct surfaces from a scattered data Set. The data Set might consist of points, curves and/or surface patches. A weighted minimal surface-like model is constructed and its variational Level Set formulation is implemented with optimal efficiency. The reconstructed surface is smoother than piecewise linear and has a natural scaling in the regularization that allows varying flexibility according to the local sampling density. As is usual with the Level Set Method we can handle complicated topology and deformations, as well as noisy or highly nonuniform data Sets easily. The Method is based on a simple rectangular grid, although adaptive and triangular grids are also possible. Some consequences, such as hole filling capability, are demonstrated, as well as the viability and convergence of our new fast tagging algorithm.
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regular article a pde based fast local Level Set Method
Journal of Computational Physics, 1999Co-Authors: Danping Peng, Barry Merriman, Stanley Osher, Hongkai Zhao, Myungjoo KangAbstract:We develop a fast Method to localize the Level Set Method of Osher and Sethian (1988, J. Comput. Phys.79, 12) and address two important issues that are intrinsic to the Level Set Method: (a) how to extend a quantity that is given only on the interface to a neighborhood of the interface; (b) how to reSet the Level Set function to be a signed distance function to the interface efficiently without appreciably moving the interface. This fast local Level Set Method reduces the computational effort by one order of magnitude, works in as much generality as the original one, and is conceptually simple and easy to implement. Our approach differs from previous related works in that we extract all the information needed from the Level Set function (or functions in multiphase flow) and do not need to find explicitly the location of the interface in the space domain. The complexity of our Method to do tasks such as extension and distance reinitialization is O(N), where N is the number of points in space, not O(N log N) as in works by Sethian (1996, Proc. Nat. Acad. Sci. 93, 1591) and Helmsen and co-workers (1996, SPIE Microlithography IX, p. 253). This complexity estimation is also valid for quite general geometrically based front motion for our localized Method.
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Island dynamics and the Level Set Method for epitaxial growth
Applied Mathematics Letters, 1999Co-Authors: Russel E. Caflisch, M. F. Gyure, Barry Merriman, Stanley Osher, Christian Ratsch, Dimitri D. Vvedensky, Jennifer J. ZinckAbstract:Abstract We adapt the Level Set Method to simulate the growth of thin films described by the motion of island boundaries. This island dynamics model involves a continuum in the lateral directions, but retains atomic scale discreteness in the growth direction. Several choices for the island boundary velocity are discussed, and computations of the island dynamics model using the Level Set Method are presented.
Petros Koumoutsakos - One of the best experts on this subject based on the ideXlab platform.
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a lagrangian particle Level Set Method
Journal of Computational Physics, 2005Co-Authors: Simone E Hieber, Petros KoumoutsakosAbstract:We present a novel particle Level Set Method for capturing interfaces. The Level Set equation is solved in a Lagrangian frame using particles that carry the Level Set information. A key aspect of the Method involves a consistent remeshing procedure for the regularization of the particle locations when the particle map gets distorted by the advection field. The Lagrangian description of the Level Set Method is inherently adaptive and exact in the case of solid body motions. The efficiency and accuracy of the Method is demonstrated in several benchmark problems in two and three dimensions involving pure advection and curvature induced motion of the interface. The simplicity of the particle description is shown to be well suited for real time simulations of surfaces involving cutting and reconnection as in virtual surgery environments.
Douglas Enright - One of the best experts on this subject based on the ideXlab platform.
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a fast and accurate semi lagrangian particle Level Set Method
Computers & Structures, 2005Co-Authors: Douglas Enright, Frank Losasso, Ronald FedkiwAbstract:In this paper, we present an efficient semi-Lagrangian based particle Level Set Method for the accurate capturing of interfaces. This Method retains the robust topological properties of the Level Set Method with- out the adverse effects of numerical dissipation. Both the Level Set Method and the particle Level Set Method typically use high order accurate numerical discretizations in time and space, e.g. TVD Runge-Kutta and HJ-WENO schemes. We demonstrate that these computationally expensive schemes are not required. Instead, fast, low order accurate numerical schemes suffice. That is, the addition of particles to the Level Set Method not only removes the difficulties associated with numerical diffusion, but also alleviates the need for computationally expensive high order accurate schemes. We use an efficient, first order accurate semi-Lagrangian advection scheme coupled with a first order accurate fast marching Method to evolve the Level Set function. To accurately track the underlying flow characteristics, the particles are evolved with a second order accurate Method. Since we avoid complex high order accurate numerical Methods, extending the algorithm to arbitrary data structures becomes more feasible, and we show preliminary results obtained with an octree-based adaptive mesh.
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a hybrid particle Level Set Method for improved interface capturing
Journal of Computational Physics, 2002Co-Authors: Douglas Enright, Ronald Fedkiw, Joel H Ferziger, Ian M MitchellAbstract:In this paper, we propose a new numerical Method for improving the mass conservation properties of the Level Set Method when the interface is passively advected in a flow field. Our Method uses Lagrangian marker particles to rebuild the Level Set in regions which are underresolved. This is often the case for flows undergoing stretching and tearing. The overall Method maintains a smooth geometrical description of the interface and the implementation simplicity characteristic of the Level Set Method. Our Method compares favorably with volume of fluid Methods in the conservation of mass and purely Lagrangian schemes for interface resolution. The Method is presented in three spatial dimensions.
Hongkai Zhao - One of the best experts on this subject based on the ideXlab platform.
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a Level Set Method for interfacial flows with surfactant
Journal of Computational Physics, 2006Co-Authors: Jianjun Xu, Zhilin Li, John Lowengrub, Hongkai ZhaoAbstract:A Level-Set Method for the simulation of fluid interfaces with insoluble surfactant is presented in two-dimensions. The Method can be straightforwardly extended to three-dimensions and to soluble surfactants. The Method couples a semi-implicit discretization for solving the surfactant transport equation recently developed by Xu and Zhao [J. Xu, H. Zhao. An Eulerian formulation for solving partial differential equations along a moving interface, J. Sci. Comput. 19 (2003) 573-594] with the immersed interface Method originally developed by LeVeque and Li and [R. LeVeque, Z. Li. The immersed interface Method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal. 31 (1994) 1019-1044] for solving the fluid flow equations and the Laplace-Young boundary conditions across the interfaces. Novel techniques are developed to accurately conserve component mass and surfactant mass during the evolution. Convergence of the Method is demonstrated numerically. The Method is applied to study the effects of surfactant on single drops, drop-drop interactions and interactions among multiple drops in Stokes flow under a steady applied shear. Due to Marangoni forces and to non-uniform Capillary forces, the presence of surfactant results in larger drop deformations and more complex drop-drop interactions compared to the analogous cases for clean drops. The effects of surfactant are found to be most significant in flows with multiple drops. To our knowledge, this is the first time that the Level-Set Method has been used to simulate fluid interfaces with surfactant.
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fast surface reconstruction using the Level Set Method
Proceedings IEEE Workshop on Variational and Level Set Methods in Computer Vision, 2001Co-Authors: Hongkai Zhao, Stanley Osher, Ronald FedkiwAbstract:We describe new formulations and develop fast algorithms for implicit surface reconstruction based on variational and partial differential equation (PDE) Methods. In particular we use the Level Set Method and fast sweeping and tagging Methods to reconstruct surfaces from a scattered data Set. The data Set might consist of points, curves and/or surface patches. A weighted minimal surface-like model is constructed and its variational Level Set formulation is implemented with optimal efficiency. The reconstructed surface is smoother than piecewise linear and has a natural scaling in the regularization that allows varying flexibility according to the local sampling density. As is usual with the Level Set Method we can handle complicated topology and deformations, as well as noisy or highly nonuniform data Sets easily. The Method is based on a simple rectangular grid, although adaptive and triangular grids are also possible. Some consequences, such as hole filling capability, are demonstrated, as well as the viability and convergence of our new fast tagging algorithm.
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regular article a pde based fast local Level Set Method
Journal of Computational Physics, 1999Co-Authors: Danping Peng, Barry Merriman, Stanley Osher, Hongkai Zhao, Myungjoo KangAbstract:We develop a fast Method to localize the Level Set Method of Osher and Sethian (1988, J. Comput. Phys.79, 12) and address two important issues that are intrinsic to the Level Set Method: (a) how to extend a quantity that is given only on the interface to a neighborhood of the interface; (b) how to reSet the Level Set function to be a signed distance function to the interface efficiently without appreciably moving the interface. This fast local Level Set Method reduces the computational effort by one order of magnitude, works in as much generality as the original one, and is conceptually simple and easy to implement. Our approach differs from previous related works in that we extract all the information needed from the Level Set function (or functions in multiphase flow) and do not need to find explicitly the location of the interface in the space domain. The complexity of our Method to do tasks such as extension and distance reinitialization is O(N), where N is the number of points in space, not O(N log N) as in works by Sethian (1996, Proc. Nat. Acad. Sci. 93, 1591) and Helmsen and co-workers (1996, SPIE Microlithography IX, p. 253). This complexity estimation is also valid for quite general geometrically based front motion for our localized Method.
