  The conventional magnetic induction equation that governs hydromagnetic
dynamo action is transformed into an equivalent integral equation system. An
advantage of this approach is that the computational domain is restricted to
the region occupied by the electrically conducting fluid and to its boundary.
This integral equation approach is first employed to simulate kinematic dynamos
excited by Beltrami-like flows in a finite cylinder. The impact of externally
added layers around the cylinder on the onset of dynamo actions is
investigated. Then it is applied to simulate dynamo experiments within
cylindrical geometry including the von Karman sodium (VKS) experiment and the
Riga dynamo experiment. A modified version of this approach is utilized to
investigate magnetic induction effects under the influence of externally
applied magnetic fields which is also important to measure the proximity of a
given dynamo facility to the self-excitation threshold.
