Computational Methods for Electric Machines

Many time-dependent problems can be modeled by non-linear instationary PDEs or systems of such PDEs, e.g. problems in electromagnetics such as eddy current problems describing the transient behavior of electrical machines. Some challenges include the presence of strong nonlinearities in space and time, degenerate operators, time-periodicity, complicated or moving geometries, and multi-physics problems at vastly different time-scales. The reliable discretization and the fast solution of the arising systems of non-linear algebraic equations are crucial for an efficient numerical simulation of such kind of problems. There are many different discretization techniques ranging from classical approaches like time-stepping in combination with standard space discretization methods like FEM or IGA to fully unstructured adaptive space-time discretizations. Efficient solvers and their parallelization in space and time are the key ingredients to the efficient numerical solution of non-linear instationary PDE problems.
Fast solution methods are especially important if many problems have to be solved, e.g. in the context of optimization algorithms or uncertainty quantification.