Generating optimal topologies in structural design using a homogenization method
Computer Methods in Applied Mechanics and Engineering
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Journal of Computational Physics
Fast reaction, slow diffusion, and curve shortening
SIAM Journal on Applied Mathematics
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SIAM Journal on Applied Mathematics
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Journal of Computational Physics
A Variational Model for Image Classification and Restoration
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Level Set Model for Image Classification
International Journal of Computer Vision
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 phase field approach in the numerical study of the elastic bending energy for vesicle membranes
Journal of Computational Physics
Image Segmentation Using Some Piecewise Constant Level Set Methods with MBO Type of Projection
International Journal of Computer Vision
A semi-implicit level set method for structural shape and topology optimization
Journal of Computational Physics
Design of piezoelectric actuators using a multiphase level set method of piecewise constants
Journal of Computational Physics
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
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In this paper, we combine a Piecewise Constant Level Set (PCLS) method with a MBO scheme to solve a structural shape and topology optimization problem. The geometrical boundary of structure is represented implicitly by the discontinuities of PCLS functions. Compared with the classical level set method (LSM) for solving Hamilton---Jacobi partial differential equation (H-J PDE) we don't need to solve H-J PDE, thus it is free of the CFL condition and the reinitialization scheme. For solving optimization problem under some constraints, Additive Operator Splitting (AOS) and Multiplicative Operator Splitting (MOS) schemes will be used. To increase the convergency speed and the efficiency of PCLS method we combine this approach with MBO scheme. Advantages and disadvantages are discussed by solving some examples of 2D structural topology optimization problems.