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
Fast reaction, slow diffusion, and curve shortening
SIAM Journal on Applied Mathematics
Front propagation and phase field theory
SIAM Journal on Control and Optimization
Maximizing band gaps in two-dimensional photonic crystals
SIAM Journal on Applied Mathematics
Band structure optimization of two-dimensional photonic crystals in H-polarization
Journal of Computational Physics
Structural boundary design via level set and immersed interface methods
Journal of Computational Physics
Journal of Computational Physics
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
Phase-Field Relaxation of Topology Optimization with Local Stress Constraints
SIAM Journal on Control and Optimization
Shape and topology optimization of compliant mechanisms using a parameterization level set method
Journal of Computational Physics
A variational level set method for the topology optimization of steady-state Navier-Stokes flow
Journal of Computational Physics
Journal of Computational Physics
Photonic Crystals: Molding the Flow of Light
Photonic Crystals: Molding the Flow of Light
Photonic Crystals, Theory, Applications and Fabrication
Photonic Crystals, Theory, Applications and Fabrication
Shape and topology optimization based on the phase field method and sensitivity analysis
Journal of Computational Physics
Level-set based topology optimization for electromagnetic dipole antenna design
Journal of Computational Physics
Damage and fracture evolution in brittle materials by shape optimization methods
Journal of Computational Physics
Optimal topologies derived from a phase-field method
Structural and Multidisciplinary Optimization
| Hi-index | 31.45 |
We discuss a phase field method for shape optimization in the context of electromagnetic wave propagation. The proposed method has the same functional capabilities as the level set method for shape optimization. The first advantage of the method is the simplicity of computation, since extra operations such as re-initialization of functions are not required. The second is compatibility with the topology optimization method due to the similar domain representation and the sensitivity analysis. Structural shapes are represented by the phase field function defined in the design domain, and this function is optimized by solving a time-dependent reaction diffusion equation. The artificial double-well potential function used in the equation is derived from sensitivity analysis. We study four types of 2D or 2.5D (axisymmetric) optimization problems. Two are the classical problems of photonic crystal design based on the Bloch theory and photonic crystal wave guide design, and two are the recent topics of designing dielectric left-handed metamaterials and dielectric ring resonators.