  Recently a variational integrator for ideal magnetohydrodynamics in
Lagrangian labeling has been developed. Its built-in frozen-in equation makes
it optimal for studying current sheet formation. We use this scheme to study
the Hahm-Kulsrud-Taylor problem, which considers the response of a 2D plasma
magnetized by a sheared field under sinusoidal boundary forcing. We obtain an
equilibrium solution that preserves the magnetic topology of the initial field
exactly, with a fluid mapping that is non-differentiable. Unlike previous
studies that examine the current density output, we identify a singular current
sheet from the fluid mapping. These results are benchmarked with a constrained
Grad-Shafranov solver. The same signature of current singularity can be found
in other cases with more complex magnetic topologies.
