2 results
Search Results
Now showing 1 - 2 of 2
- ItemShape optimization for a sharp interface model of distortion compensation(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Sturm, Kevin; Hintermüller, Michael; Hömberg, DietmarWe study a mechanical equilibrium problem for a material consisting of two components with different densities, which allows to change the outer shape by changing the interface between the subdomains. We formulate the shape design problem of compensating unwanted workpiece changes by controlling the interface, employ regularity results for transmission problems for a rigorous derivation of optimality conditions based on the speed method, and conclude with some numerical results based on a spline approximation of the interface.
- ItemAnalysis and simulation of multifrequency induction hardening(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Hömberg, Dietmar; Petzold, Thomas; Rocca, ElisabettaWe study a model for induction hardening of steel. The related differential system consists of a time domain vector potential formulation of the Maxwells equations coupled with an internal energy balance and an ODE for the volume fraction of austenite, the high temperature phase in steel. We first solve the initial boundary value problem associated by means of a Schauder fixed point argument coupled with suitable a-priori estimates and regularity results. Moreover, we prove a stability estimate entailing, in particular, uniqueness of solutions for our Cauchy problem. We conclude with some finite element simulations for the coupled system.