# Gallery

#### The magnetic field induced by a coil

A stationary magnetic field generated by a given current density in a coil is computed. We used high order Nedelec elements (e.g. order 5), and iterative solvers with adjusted block smoothers.

#### Simulation of a transformer

NgSolve can simulate electromagnetic fields based on Maxwell equations. One typical application are power transformers. We can import the design of the transformer, generate fully automatic a finite element mesh, and run the simulation within 20 minutes on a desktop PC. Second order Nedelec elements have been used. The pictures show the magnetic fields on a slice through the highly permeable shields, the induced eddy currents in the casing, and Ohm's loss density:

Eddy currents in the busbars (the massive copper wires in a transformer). We have the eddy current model in the conductors, and can use magnetostatics in a big surrounding box:

#### Simulation of a machine frame

Netgen can import CAD files in IGES or Step format. A mesh of about 60k elements is generated within a minute. A static simulation is performed with 4th order elements, 1.5M unknowns, within about 10 minutes

#### Simulation of open resonances

The resonances in slat cavities are a major source of noise generated by an aircraft. We performed simulation of such open resonances [S. Hein, T. Hohage, W. Koch, and J. Schöberl: Acoustic Resonacnes in a High Lift Configuration Journal of Fluid Mechanics 582, pages 179-202, 2006]. The challenging part is the numerical treatment of the infinite domain. Here, we used the method of perfectly matched layers (PML). High order finite elements (with order up to 16), and Arnoldi eigenvalue solvers (with Krylov-spaces of dimension 500) were used. The first 3 cavity modes are plotted:

#### Some meshes generated by Netgen

A crank-shaft. The geometry was imported via STL:

The chest, data from X-ray examination: