Time-Dependent Reaction Coefficient Identification Problems with a Free Boundary

Multiple time-dependent coefficient identification thermal problems with a free boundary

Adjoint-Based Optimal Control of Time-Dependent Free Boundary Problems

In this paper we show a simplified optimisation approach for free boundary problems in arbitrary space dimensions. This approach is mainly based on an extended operator splitting which allows a decoupling of the domain deformation and solving the remaining partial differential equation. First we give a short introduction to free boundary problems and the problems occurring in optimisation. Then...

Transparent Boundary Conditions for Time-Dependent Problems

A new approach to derive transparent boundary conditions (TBCs) for wave, Schrödinger, heat and drift-diffusion equations is presented. It relies on the pole condition and distinguishes between physical reasonable and unreasonable solutions by the location of the singularities of the spatial Laplace transform of the exterior solution. To obtain a numerical algorithm, a Möbius transform is appli...

Time-dependent problems with the boundary integral equation method

Time-dependent problems that are modeled by initial-boundary value problems for parabolic or hyperbolic partial differential equations can be treated with the boundary integral equation method. The ideal situation is when the right-hand side in the partial differential equation and the initial conditions vanish, the data are given only on the boundary of the domain, the equation has constant co...

Identification of the Density Dependent Coefficient in an Inverse Reaction-diffusion Problem from a Single Boundary Data

This study is devoted to the numerical solution of an inverse coefficient problem for a density dependent nonlinear reaction-diffusion equation. The method is based on approximating the unknown coefficient by polynomials. An optimal idea for solving the inverse problem is to minimize an error functional between the output data and the additional data. For this purpose, we find a polynomial of d...