  This work presents a new approach to efficiently model the cathode in the
moving boundary value problem of electrochemical machining. Until recently, the
process simulation with finite elements had the drawback of remeshing required
by the changing surface geometries. This disadvantage was overcome by a novel
model formulation for the anodic dissolution that utilizes effective material
parameters as well as the dissolution level as an internal variable and,
thereby, does not require remeshing. Now, we extend this concept to model
arbitrarily shaped and moving cathodes. Two methodologies are investigated to
describe the time varying position of the cathode. In the first approach, we
change the electric conductivity of elements within the cathode and, in a
second approach, we apply Dirichlet boundary conditions on the nodes of
corresponding elements. For both methods, elements on the cathode's surface are
treated with effective material parameters. This procedure allows for the
efficient simulation of industrially relevant, complex geometries without mesh
adaptation. The model's performance is validated by means of analytical,
numerical and experimental results from the literature. The short computation
times make the approach interesting for industrial applications.
