  Newcomb's Lagrangian for ideal magnetohydrodynamics (MHD) in Lagrangian
labeling is discretized using discrete exterior calculus. Variational
integrators for ideal MHD are derived thereafter. Besides being symplectic and
momentum-preserving, the schemes inherit built-in advection equations from
Newcomb's formulation, and therefore avoid solving them and the accompanying
error and dissipation. We implement the method in 2D and show that numerical
reconnection does not take place when singular current sheets are present. We
then apply it to studying the dynamics of the ideal coalescence instability
with multiple islands. The relaxed equilibrium state with embedded current
sheets is obtained numerically.
