  To deal with the multi-scale nature of the quench propagation problem in
superconducting magnets, this work presents a quasi-three-dimensional (Q3D)
approach combining a two-dimensional finite-element method (FEM) in the
transversal cross-section of the magnet for resolving the geometrical details,
with a one-dimensional spectral-element method based on orthogonal polynomials
in longitudinal direction for accurately and efficiently representing the
quench phenomena. The Q3D formulation is elaborated and the idea is illustrated
on a thermal benchmark problem. Finally, the method is validated against a
conventional 3D simulation carried out by a commercial software. In terms of
computational efficiency, it is shown that the proposed Q3D approach is
superior to the conventional 3D FEM.
