A Simple Level Set Method for Solving Stefan Problems

A Simple Level Set Method for Solving Stefan Problems

sented. This method can be applied to problems involving dendritic The process of crystal growth begins when one places a solidification. Our method consists of an implicit finite difference small seed of solid material into a surrounding bath of scheme for solving the heat equation and a level set approach undercooled liquid. Heat is released at the solid/liquid for capturing the front between...

A Level Set Method for Inverse Problems

A BINARY LEVEL SET METHOD FOR STRUCTURAL TOPOLOGY OPTIMIZATION

This paper proposes an effective algorithm based on the level set method (LSM) to solve shape and topology optimization problems. Since the conventional LSM has several limitations, a binary level set method (BLSM) is used instead. In the BLSM, the level set function can only take 1 and -1 values at convergence. Thus, it is related to phase-field methods. We don’t need to solve the Hamilton-Jac...

A New Method for Solving Constraint Satisfaction Problems

Many important problems in Artificial Intelligence can be defined as Constraint Satisfaction Problems (CSP). These types of problems are defined by a limited set of variables, each having a limited domain and a number of Constraints on the values of those variables (these problems are also called Consistent Labeling Problems (CLP), in which “Labeling" means assigning a value to a variable.) Sol...

A Level Set Method for Solving Free Boundary Problems Associated with Obstacles

A level set method is proposed for solving free boundary problems coming from contact with obstacles. Two different approaches are described and applied for solving an unilateral obstacle problem. The cost functionals coming from the new approach are nonsmooth. For solving the nonsmooth minimization problems, two methods are applied: firstly, a proximal bundle method, which is a method for solv...