Semi-Lagrange Level Set Methods

Level Set Methods are numerical algorithms which can simulate the evolution of dynamic implicit interfaces.These interfaces can freely break apart and merge together, which allows natural treatment of topological changes. These techniques have quite a wide range of applications, including structural topology optimization & design, fluid and combustion simulation, computer graphics, image processing, and computer vision.

But numerical stability condition in the explicit upwind scheme for discrete level-set equation severely restricts the time step, requiring a large number of time steps for a numerical solution. In order to improve the numerical efficiency, we propose to employ a semi-Lagrange scheme to solve level set equation. Therefore, a much larger time step can be obtained and a much smaller number of time steps are required.

1. Topology control in topology optimization;
2. Geometric feature control in level set evolution;
3. Using topology derivation in level set methods;
4. Level set methods for kinematics design and analysis for mechanisms and robots;
5. Level set methods for wave-guide design in photonics, electromagnetics, and RF;
6. Semi-Lagrange time stepping in Level set base structural optimization methods.

• HKSAR Research Grants Council (RGC) Competitive Earmarked Research Grant (CERG)

• The Natural Science Foundation of China (NFSC)