			Home About us Contact

Set Function (set + function)

Distribution by Scientific Domains

Engineering	57%
Information Science and Computing	28%

Kinds of Set Function

level set function

Selected Abstracts

Particle Level Set Advection for the Interactive Visualization of Unsteady 3D Flow

COMPUTER GRAPHICS FORUM, Issue 3 2008
Nicolas Cuntz
Abstract Typically, flow volumes are visualized by defining their boundary as iso-surface of a level set function. Grid-based level sets offer a good global representation but suffer from numerical diffusion of surface detail, whereas particle-based methods preserve details more accurately but introduce the problem of unequal global representation. The particle level set (PLS) method combines the advantages of both approaches by interchanging the information between the grid and the particles. Our work demonstrates that the PLS technique can be adapted to volumetric dye advection via streak volumes, and to the visualization by time surfaces and path volumes. We achieve this with a modified and extended PLS, including a model for dye injection. A new algorithmic interpretation of PLS is introduced to exploit the efficiency of the GPU, leading to interactive visualization. Finally, we demonstrate the high quality and usefulness of PLS flow visualization by providing quantitative results on volume preservation and by discussing typical applications of 3D flow visualization. [source]

A structural optimization method based on the level set method using a new geometry-based re-initialization scheme

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2010
Shintaro Yamasaki
Abstract Structural optimization methods based on the level set method are a new type of structural optimization method where the outlines of target structures can be implicitly represented using the level set function, and updated by solving the so-called Hamilton,Jacobi equation based on a Eulerian coordinate system. These new methods can allow topological alterations, such as the number of holes, during the optimization process whereas the boundaries of the target structure are clearly defined. However, the re-initialization scheme used when updating the level set function is a critical problem when seeking to obtain appropriately updated outlines of target structures. In this paper, we propose a new structural optimization method based on the level set method using a new geometry-based re-initialization scheme where both the numerical analysis used when solving the equilibrium equations and the updating process of the level set function are performed using the Finite Element Method. The stiffness maximization, eigenfrequency maximization, and eigenfrequency matching problems are considered as optimization problems. Several design examples are presented to confirm the usefulness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd. [source]

Piecewise constant level set method for structural topology optimization

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009
Peng Wei
Abstract In this paper, a piecewise constant level set (PCLS) method is implemented to solve a structural shape and topology optimization problem. In the classical level set method, the geometrical boundary of the structure under optimization is represented by the zero level set of a continuous level set function, e.g. the signed distance function. Instead, in the PCLS approach the boundary is described by discontinuities of PCLS functions. The PCLS method is related to the phase-field methods, and the topology optimization problem is defined as a minimization problem with piecewise constant constraints, without the need of solving the Hamilton,Jacobi equation. The result is not moving the boundaries during the iterative procedure. Thus, it offers some advantages in treating geometries, eliminating the reinitialization and naturally nucleating holes when needed. In the paper, the PCLS method is implemented with the additive operator splitting numerical scheme, and several numerical and procedural issues of the implementation are discussed. Examples of 2D structural topology optimization problem of minimum compliance design are presented, illustrating the effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd. [source]

An assumed-gradient finite element method for the level set equation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2005
Hashem M. Mourad
Abstract The level set equation is a non-linear advection equation, and standard finite-element and finite-difference strategies typically employ spatial stabilization techniques to suppress spurious oscillations in the numerical solution. We recast the level set equation in a simpler form by assuming that the level set function remains a signed distance to the front/interface being captured. As with the original level set equation, the use of an extensional velocity helps maintain this signed-distance function. For some interface-evolution problems, this approach reduces the original level set equation to an ordinary differential equation that is almost trivial to solve. Further, we find that sufficient accuracy is available through a standard Galerkin formulation without any stabilization or discontinuity-capturing terms. Several numerical experiments are conducted to assess the ability of the proposed assumed-gradient level set method to capture the correct solution, particularly in the presence of discontinuities in the extensional velocity or level-set gradient. We examine the convergence properties of the method and its performance in problems where the simplified level set equation takes the form of a Hamilton,Jacobi equation with convex/non-convex Hamiltonian. Importantly, discretizations based on structured and unstructured finite-element meshes of bilinear quadrilateral and linear triangular elements are shown to perform equally well. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Coupled ghost fluid/two-phase level set method for curvilinear body-fitted grids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2007
Juntao Huang
Abstract A coupled ghost fluid/two-phase level set method to simulate air/water turbulent flow for complex geometries using curvilinear body-fitted grids is presented. The proposed method is intended to treat ship hydrodynamics problems. The original level set method for moving interface flows was based on Heaviside functions to smooth all fluid properties across the interface. We call this the Heaviside function method (HFM). The HFM requires fine grids across the interface. The ghost fluid method (GFM) has been designed to explicitly enforce the interfacial jump conditions, but the implementation of the jump conditions in curvilinear grids is intricate. To overcome these difficulties a coupled GFM/HFM method was developed in which approximate jump conditions are derived for piezometric pressure and velocity and pressure gradients based on exact continuous velocity and stress and jump in momentum conditions with the jump in density maintained but continuity of the molecular and turbulent viscosities imposed. The implementation of the ghost points is such that no duplication of memory storage is necessary. The level set method is adopted to locate the air/water interface, and a fast marching method was implemented in curvilinear grids to reinitialize the level set function. Validations are performed for three tests: super- and sub-critical flow without wave breaking and an impulsive plunging wave breaking over 2D submerged bumps, and the flow around surface combatant model DTMB 5512. Comparisons are made against experimental data, HFM and single-phase level set computations. The proposed method performed very well and shows great potential to treat complicated turbulent flows related to ship flows. Copyright © 2007 John Wiley & Sons, Ltd. [source]

A semi-Lagrangian level set method for incompressible Navier,Stokes equations with free surface

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2005
Leo Miguel González Gutiérrez
Abstract In this paper, we formulate a level set method in the framework of finite elements-semi-Lagrangian methods to compute the solution of the incompressible Navier,Stokes equations with free surface. In our formulation, we use a quasi-monotone semi-Lagrangian scheme, which is both unconditionally stable and essentially non oscillatory, to compute the advective terms in the Navier,Stokes equations, the transport equation and the equation of the reinitialization stage for the level set function. The method we propose is quite robust and flexible with regard to the mesh and the geometry of the domain, as well as the magnitude of the Reynolds number. We illustrate the performance of the method in several examples, which range from a benchmark problem to test the volume conservation property of the method to the flow past a NACA0012 foil at high Reynolds number. Copyright © 2005 John Wiley & Sons, Ltd. [source]

A level set characteristic Galerkin finite element method for free surface flows

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2005
Ching-Long Lin
Abstract This paper presents a numerical method for free surface flows that couples the incompressible Navier,Stokes equations with the level set method in the finite element framework. The implicit characteristic-Galerkin approximation together with the fractional four-step algorithm is employed to discretize the governing equations. The schemes for solving the level set evolution and reinitialization equations are verified with several benchmark cases, including stationary circle, rotation of a slotted disk and stretching of a circular fluid element. The results are compared with those calculated from the level set finite volume method of Yue et al. (Int. J. Numer. Methods Fluids 2003; 42:853,884), which employed the third-order essentially non-oscillatory (ENO) schemes for advection of the level set function in a generalized curvilinear coordinate system. The comparison indicates that the characteristic Galerkin approximation of the level set equations yields more accurate solutions. The second-order accuracy of the Navier,Stokes solver is confirmed by simulation of decay vortex. The coupled system of the Navier,Stokes and level set equations then is validated by solitary wave and broken dam problems. The simulation results are in excellent agreement with experimental data. Copyright © 2005 John Wiley & Sons, Ltd. [source]

A projection scheme for incompressible multiphase flow using adaptive Eulerian grid

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2004
T. Chen
Abstract This paper presents a finite element method for incompressible multiphase flows with capillary interfaces based on a (formally) second-order projection scheme. The discretization is on a fixed Eulerian grid. The fluid phases are identified and advected using a level set function. The grid is temporarily adapted around the interfaces in order to maintain optimal interpolations accounting for the pressure jump and the discontinuity of the normal velocity derivatives. The least-squares method for computing the curvature is used, combined with piecewise linear approximation to the interface. The time integration is based on a formally second order splitting scheme. The convection substep is integrated over an Eulerian grid using an explicit scheme. The remaining generalized Stokes problem is solved by means of a formally second order pressure-stabilized projection scheme. The pressure boundary condition on the free interface is imposed in a strong form (pointwise) at the pressure-computation substep. This allows capturing significant pressure jumps across the interface without creating spurious instabilities. This method is simple and efficient, as demonstrated by the numerical experiments on a wide range of free-surface problems. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Discover dependency pattern among attributes by using a new type of nonlinear multiregression

INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 8 2001
Kebin Xu
Multiregression is one of the most common approaches used to discover dependency pattern among attributes in a database. Nonadditive set functions have been applied to deal with the interactive predictive attributes involved, and some nonlinear integrals with respect to nonadditive set functions are employed to establish a nonlinear multiregression model describing the relation between the objective attribute and predictive attributes. The values of the nonadditive set function play a role of unknown regression coefficients in the model and are determined by an adaptive genetic algorithm from the data of predictive and objective attributes. Furthermore, such a model is now improved by a new numericalization technique such that the model can accommodate both categorical and continuous numerical attributes. The traditional dummy binary method dealing with the mixed type data can be regarded as a very special case of our model when there is no interaction among the predictive attributes and the Choquet integral is used. When running the algorithm, to avoid a premature during the evolutionary procedure, a technique of maintaining diversity in the population is adopted. A test example shows that the algorithm and the relevant program have a good reversibility for the data. © 2001 John Wiley & Sons, Inc.16: 949,962 (2001) [source]

A Hybrid Approach to Multiple Fluid Simulation using Volume Fractions

COMPUTER GRAPHICS FORUM, Issue 2 2010
Nahyup Kang
Abstract This paper presents a hybrid approach to multiple fluid simulation that can handle miscible and immiscible fluids, simultaneously. We combine distance functions and volume fractions to capture not only the discontinuous interface between immiscible fluids but also the smooth transition between miscible fluids. Our approach consists of four steps: velocity field computation, volume fraction advection, miscible fluid diffusion, and visualization. By providing a combining scheme between volume fractions and level set functions, we are able to take advantages of both representation schemes of fluids. From the system point of view, our work is the first approach to Eulerian grid-based multiple fluid simulation including both miscible and immiscible fluids. From the technical point of view, our approach addresses the issues arising from variable density and viscosity together with material diffusion. We show that the effectiveness of our approach to handle multiple miscible and immiscible fluids through experiments. [source]

eXtended Stochastic Finite Element Method for the numerical simulation of heterogeneous materials with random material interfaces

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010
A. Nouy
Abstract An eXtended Stochastic Finite Element Method has been recently proposed for the numerical solution of partial differential equations defined on random domains. This method is based on a marriage between the eXtended Finite Element Method and spectral stochastic methods. In this article, we propose an extension of this method for the numerical simulation of random multi-phased materials. The random geometry of material interfaces is described implicitly by using random level set functions. A fixed deterministic finite element mesh, which is not conforming to the random interfaces, is then introduced in order to approximate the geometry and the solution. Classical spectral stochastic finite element approximation spaces are not able to capture the irregularities of the solution field with respect to spatial and stochastic variables, which leads to a deterioration of the accuracy and convergence properties of the approximate solution. In order to recover optimal convergence properties of the approximation, we propose an extension of the partition of unity method to the spectral stochastic framework. This technique allows the enrichment of approximation spaces with suitable functions based on an a priori knowledge of the irregularities in the solution. Numerical examples illustrate the efficiency of the proposed method and demonstrate the relevance of the enrichment procedure. Copyright © 2010 John Wiley & Sons, Ltd. [source]

Discover dependency pattern among attributes by using a new type of nonlinear multiregression

Study of electronic spectra of free-base porphin and Mg-porphin: Comprehensive comparison of variety of ab initio, DFT, and semiempirical methods

JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 3 2005
Josef
Abstract SAC (symmetry adapted cluster)/SAC-CI and CASPT2 (multiconfigurational second-order perturbation theory) electron excitation spectra of free-base porphin and magnesium-porphin were determined using basis set functions augmented by both the polarization and diffuse functions,6-31+G(d). Such basis is recommended for correct description of the spectra because diffuse functions play fundamental roles in the formation of Rydberg MOs. The obtained results indicated that already the lowest roots in Au, B1u, B2g, and B3g irreducible representations display Rydberg character. The calculated spectra are in a good agreement with both experimental and recently calculated electronic transitions. It is concluded that the SAC/SAC-CI level spectral lines are significantly affected by configuration selection when energy thresholds 5.0 × 10,6 and 5.0 × 10,7 a.u. are used for the determination of ground and excited state properties. © 2004 Wiley Periodicals, Inc. J Comput Chem 26: 294,303, 2005 [source]

Adaptive grid based on geometric conservation law level set method for time dependent PDE

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2009
Ali R. Soheili
Abstract A new method for mesh generation is formulated based on the level set functions, which are solutions of the standard level set evolution equation with the Cartesian coordinates as initial values (Liao et al. J Comput Phys 159 (2000), 103,122; Osher and Sethian J Comput Phys 79 (1988), 12; Sethian, Level set methods and fast marching methods, Cambridge University Press, 1999; Di et al. J Sci Comput 31 (2007), 75,98). The intersection of the level contours of the evolving functions form a new grid at each time. The velocity vector in the evolution equation is chosen according to the Geometric Conservation Law (GCL) method (Cao et al., SIAM J Sci Comput 24 (2002), 118,142.). This method has precise control over the Jacobian of transformation because of using the GCL method. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source]