Semi-implicit method for long time scale magnetohydrodynamic computations in three dimensions
Journal of Computational Physics
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
On the Topological Derivative in Shape Optimization
SIAM Journal on Control and Optimization
SIAM Journal on Scientific Computing
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
Level set methods: an overview and some recent results
Journal of Computational Physics
Journal of Computational Physics
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
Etude de Problème d'Optimal Design
Proceedings of the 7th IFIP Conference on Optimization Techniques: Modeling and Optimization in the Service of Man, Part 2
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
Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions
Journal of Computational Physics
A multilevel, level-set method for optimizing eigenvalues in shape design problems
Journal of Computational Physics
A Multilevel Method for Image Registration
SIAM Journal on Scientific Computing
Velocity Extension for the Level-set Method and Multiple Eigenvalues in Shape Optimization
SIAM Journal on Control and Optimization
A new algorithm for topology optimization using a level-set method
Journal of Computational Physics
On level set regularization for highly ill-posed distributed parameter estimation problems
Journal of Computational Physics
An extended level set method for shape and topology optimization
Journal of Computational Physics
Image Segmentation Using Some Piecewise Constant Level Set Methods with MBO Type of Projection
International Journal of Computer Vision
Incorporating topological derivatives into shape derivatives based level set methods
Journal of Computational Physics
Shape and topology optimization of compliant mechanisms using a parameterization level set method
Journal of Computational Physics
A fast and accurate semi-Lagrangian particle level set method
Computers and Structures
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
Design of piezoelectric actuators using a multiphase level set method of piecewise constants
Journal of Computational Physics
A level set method for structural shape and topology optimization using radial basis functions
Computers and Structures
Finite Elements in Analysis and Design
A hybrid topology optimization methodology combining simulated annealing and SIMP
Computers and Structures
Piecewise constant level set method for structural topology optimization with MBO type of projection
Structural and Multidisciplinary Optimization
A semi-Lagrangian level set method for structural optimization
Structural and Multidisciplinary Optimization
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 | 31.46 |
This paper proposes a new level set method for structural shape and topology optimization using a semi-implicit scheme. Structural boundary is represented implicitly as the zero level set of a higher-dimensional scalar function and an appropriate time-marching scheme is included to enable the discrete level set processing. In the present study, the Hamilton-Jacobi partial differential equation (PDE) is solved numerically using a semi-implicit additive operator splitting (AOS) scheme rather than explicit schemes in conventional level set methods. The main feature of the present method is it does not suffer from any time step size restriction, as all terms relevant to stability are discretized in an implicit manner. The semi-implicit scheme with additive operator splitting treats all coordinate axes equally in arbitrary dimensions with good rotational invariance. Hence, the present scheme for the level set equations is stable for any practical time steps and numerically easy to implement with high efficiency. Resultantly, it allows enhanced relaxation on the time step size originally limited by the Courant-Friedrichs-Lewy (CFL) condition of the explicit schemes. The stability and computational efficiency can therefore be greatly improved in advancing the level set evolvements. Furthermore, the present method avoids additional cost to globally reinitialize the level set function for regularization purpose. It is noted that the periodically applied reinitializations are time-consuming procedures. In particular, the proposed method is capable of creating new holes freely inside the design domain via boundary incorporating, splitting and merging processes, which makes the final design independent of initial guess, and helps reduce the probability of converging to a local minimum. The availability of the present method is demonstrated with two widely studied examples in the framework of the structural stiffness designs.