  The finite element method is widely used in simulations of various fields.
However, when considering domains whose extent differs strongly in different
spatial directions a finite element simulation becomes computationally very
expensive due to the large number of degrees of freedom. An example of such a
domain are the cables inside of the magnets of particle accelerators. For
translationally invariant domains, this work proposes a quasi-3-D method.
Thereby, a 2-D finite element method with a nodal basis in the cross-section is
combined with a spectral method with a wavelet basis in the longitudinal
direction. Furthermore, a spectral method with a wavelet basis and an adaptive
and time-dependent resolution is presented. All methods are verified. As an
example the hot-spot propagation due to a quench in Rutherford cables is
simulated successfully.
