Adjoint-based optimization of two-dimensional Stefan problems

Optimization Method for One- and Two-dimensional Inverse Stefan Problems

In the paper, the oneand two-dimensional two-phase inverse Stefan problems are formulated and described by means of the optimizationmethod. These problems consist of the reconstruction of the function which describes the coe cient of convective heat-transfer, when the position of the moving interface of the phase change is well-known. In numerical calculations the NelderMead optimization method...

Towards Adjoint Based Constrained Optimization

Nonlinear Two-Phase Stefan Problem

In this paper we consider a nonlinear two-phase Stefan problem in one-dimensional space. The problem is mapped into a nonlinear Volterra integral equation for the free boundary.

Global Attractors for Two-phase Stefan Problems in One-dimensional Space

In this paper we consider one-dimensional two-phase Stefan problems for a class of parabolic equations with nonlinear heat source terms and with nonlinear flux conditions on the fixed boundary. Here, both timedependent and time-independent source terms and boundary conditions are treated. We investigate the large time behavior of solutions to our problems by using the theory for dynamical syste...

Geometry Optimization in Three-Dimensional Unsteady Flow Problems using the Discrete Adjoint

The unsteady discrete adjoint equations are utilized to construct objective function gradients for use in geometry optimization in large scale three-dimensional unsteady ow problems. An existing massively parallel unstructured Reynolds-averaged Navier-Stokes equations solver forms the basis for the framework used to solve both the primal and dual (adjoint) problems. The framework is also capabl...