Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Feedback control via thermostats of multidimensional two-phase Stefan problems
Nonlinear Analysis: Theory, Methods & Applications
The adjoint method for the inverse design of solidification processes with convection
The adjoint method for the inverse design of solidification processes with convection
The fast construction of extension velocities in level set methods
Journal of Computational Physics
Shapes and geometries: analysis, differential calculus, and optimization
Shapes and geometries: analysis, differential calculus, and optimization
An Eulerian Formulation for Solving Partial Differential Equations Along a Moving Interface
Journal of Scientific Computing
Modelling dendritic solidification with melt convection using the extended finite element method
Journal of Computational Physics
Optimal control of the free boundary in a two-phase Stefan problem
Journal of Computational Physics
A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations
Journal of Computational Physics
Adjoint-based optimization of PDEs in moving domains
Journal of Computational Physics
An Eulerian approach to transport and diffusion on evolving implicit surfaces
Computing and Visualization in Science
A vertex-based hierarchical slope limiter for p-adaptive discontinuous Galerkin methods
Journal of Computational and Applied Mathematics
| Hi-index | 0.00 |
Optimal control (motion planning) of the free interface in classical two-phase Stefan problems is considered. The evolution of the free interface is modeled by a level set function. The first-order optimality system is derived on a formal basis. It provides gradient information based on the adjoint temperature and adjoint level set function. Suitable discretization schemes for the forward and adjoint systems are described. Numerical examples verify the correctness and flexibility of the proposed scheme.