Adaptive domain decomposition techniques in electromagnetic field computation and electrothermomechanical coupling problems

Summary We consider efficient iterative solvers for the numerical solution of systems of PDEs arising in the computation of electromagnetic fields and in electrothermomechanical coupling problems. We focus on domain decomposition methods on nonmatching grids, also known as mortar element methods, and the solution of the resulting saddle point problems by multilevel preconditioned iterative schemes. The underlying hierarchy of triangulations is generated by adaptive grid refinement/coarsening on the basis of efficient and reliable residual type a posteriori error estimators. In particular, with regard to the electromagnetic field computations we rely on the use of edge element discretizations which require an appropriate treatment of the nontrivial kernel of the discrete curl operator by means of a distributed smoothing process. As applications, we address the numerical simulation of the operational behavior of integrated high voltage modules which is strongly determined by the coupling of electrical, thermal, and mechanical phenomena, and the structural optimization of high power electronic devices and systems featuring an all-in-one approach by primal-dual Newton interior-point methods.