Efficient implementation of essentially non-oscillatory shock-capturing schemes
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
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
Real functions for representation of rigid solids
Computer Aided Geometric Design
Variational methods in image segmentation
Variational methods in image segmentation
A PDE-based fast local level set method
Journal of Computational Physics
A fast modular semi-Lagrangian method for moving interfaces
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
Geometric partial differential equations and image analysis
Geometric partial differential equations and image analysis
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Journal of Computational Physics
Level set surface editing operators
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
IEEE Transactions on Image Processing
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A level set based method is proposed for the simultaneous optimization of the material properties and the topology of functionally graded structures. The objective of the present study is to determine the optimal material properties (via the material volume fractions) and the structural topology to maximize the performance of the structure in a given application. In the proposed method, the volume fraction and the structural boundary are considered as the design variables, with the former being discretized as a scalar field and the latter being implicitly represented by the level set method. To perform simultaneous optimization, the two design variables are integrated into a common objective functional. Sensitivity analysis is conducted to obtain the descent directions. The optimization process is then expressed as the solution to a coupled Hamilton-Jacobi equation and diffusion partial differential equation. Numerical results are provided for the problem of mean compliance optimization in two dimensions.