Generating optimal topologies in structural design using a homogenization method
Computer Methods in Applied Mechanics and Engineering
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
Crystal growth and dendritic solidification
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
A fast level set based algorithm for topology-independent shape modeling
Journal of Mathematical Imaging and Vision - Special issue on topology and geometry in computer vision
A variational level set approach to multiphase motion
Journal of Computational Physics
The fast construction of extension velocities in level set methods
Journal of Computational Physics
A PDE-based fast local level set method
Journal of Computational Physics
Structural boundary design via level set and immersed interface methods
Journal of Computational Physics
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Level set methods: an overview and some recent results
Journal of Computational Physics
Journal of Computational Physics
A Self-Referencing Level-Set Method for Image Reconstruction from Sparse Fourier Samples
International Journal of Computer Vision
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
Fast Surface Reconstruction Using the Level Set Method
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
Geometric Level Set Methods in Imaging,Vision,and Graphics
Geometric Level Set Methods in Imaging,Vision,and Graphics
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Incorporating topological derivatives into level set methods
Journal of Computational Physics
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
A multilevel, level-set method for optimizing eigenvalues in shape design problems
Journal of Computational Physics
Level Set Evolution without Re-Initialization: A New Variational Formulation
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
On level set regularization for highly ill-posed distributed parameter estimation problems
Journal of Computational Physics
Principles of Optimal Design
A gradient descent procedure for variational dynamic surface problems with constraints
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
IEEE Transactions on Image Processing
Shape and topology optimization of compliant mechanisms using a parameterization level set method
Journal of Computational Physics
Adjoint-based optimization of PDEs in moving domains
Journal of Computational Physics
A semi-implicit level set method for structural shape and topology optimization
Journal of Computational Physics
A variational level set method for the topology optimization of steady-state Navier-Stokes flow
Journal of Computational Physics
Design of piezoelectric actuators using a multiphase level set method of piecewise constants
Journal of Computational Physics
A Moving Grid Framework for Geometric Deformable Models
International Journal of Computer Vision
Variational piecewise constant level set methods for shape optimization of a two-density drum
Journal of Computational Physics
Level-set based topology optimization for electromagnetic dipole antenna design
Journal of Computational Physics
Radial basis function based level set interpolation and evolution for deformable modelling
Image and Vision Computing
Applied Numerical Mathematics
Finite Elements in Analysis and Design
An isoparametric approach to level set topology optimization using a body-fitted finite-element mesh
Computers and Structures
Parametric Level Set Methods for Inverse Problems
SIAM Journal on Imaging Sciences
Stress-based topology optimization using an isoparametric level set method
Finite Elements in Analysis and Design
Structural and Multidisciplinary Optimization
Level-set methods for structural topology optimization: a review
Structural and Multidisciplinary Optimization
A survey of structural and multidisciplinary continuum topology optimization: post 2000
Structural and Multidisciplinary Optimization
Hi-index | 31.48 |
In this paper, the conventional level set methods are extended as an effective approach for shape and topology optimization by the introduction of the radial basis functions (RBFs). The RBF multiquadric splines are used to construct the implicit level set function with a high level of accuracy and smoothness and to discretize the original initial value problem into an interpolation problem. The motion of the dynamic interfaces is thus governed by a system of coupled ordinary differential equations (ODEs) and a relatively smooth evolution can be maintained without reinitialization. A practical implementation of this method is further developed for solving a class of energy-based optimization problems, in which approximate solution to the original Hamilton-Jacobi equation may be justified and nucleation of new holes inside the material domain is allowed for. Furthermore, the severe constraints on the temporal and spatial discretizations can be relaxed, leading to a rapid convergence to the final design insensitive to initial guesses. The normal velocities are chosen to perform steepest gradient-based optimization by using shape sensitivity analysis and a bi-sectioning algorithm. A physically meaningful and efficient extension velocity method is also presented. The proposed method is implemented in the framework of minimum compliance design and its efficiency over the existing methods is highlighted. Numerical examples show its accuracy, convergence speed and insensitivity to initial designs in shape and topology optimization of two-dimensional (2D) problems that have been extensively investigated in the literature.