Numerical Techniques

• Represent boundary by zero level set of signed distance function phi
• Propagate boundary by Hamilton-Jacobi equation (the Level Set Method)
• Compute curvature from phi
• Find Lagrange multiplier for volume conservation by Newton's Method
• Update phi by the Fast Marching Method to maintain distance function
• Discretize Linear Elasticity problem using the Finite Element Method on structured grid
• Set Young's Modulus E=small number outside domain
• Solve linear system of equations using multigrid solver