Level Set Method
The power of modern computer science
The Level Set method is a powerful tool in computational modeling, utilizing binarized design variables to implicitly represent shapes. Originally developed for the study of multiphase flow, the method has since been adapted for use in a variety of fields, including computer vision, stress minimization, and structural strain energy optimization. With the advancement of computational power, the Level Set method has become increasingly accessible for solving complex and computationally demanding problems.However, the method is not without its challenges. The evolution of boundaries can be sensitive to the local solution within the optimization loop, leading to the potential for local minima. To address these issues, various methodologies have been developed, such as the use of topological derivative terms, parametrized level sets, and regularized Heaviside functions to prevent numerical instabilities.