Computation of Electromagnetic Fields for a Humidity Sensor

We simulate an electromagnetic humidity sensor in order to determine its eigenfrequencies. The underlying model is given by Maxwell’s field equations, they are transformed into two decoupled two-dimensional problems by eliminating the magnetic field and changing to cylinder coordinates.A time-harmonic approach leads to two generalized eigenproblems that are discretized using appropriate finite elements. The usual multigrid solvers are modified in order to cope with the anisotropic structure of the resulting matrices. These modifications can be used in order to build robust eigenproblem solvers of optimal asymptotic complexity.Numerical experiments show that the resulting method is able to capture those effects that are relevant for the sensor under investigation.