  With the developed "extended Monte Calro" (EMC) algorithm, we have studied
the depinning transition in Ising-type lattice models by extensive numerical
simulations, taking the random-field Ising model with a driving field and the
driven bond-diluted Ising model as examples. In comparison with the usual Monte
Carlo method, the EMC algorithm exhibits greater efficiency of the simulations.
Based on the short-time dynamic scaling form, both the transition field and
critical exponents of the depinning transition are determined accurately via
the large-scale simulations with the lattice size up to L = 8 912,
significantly refining the results in earlier literature. In the
strong-disorder regime, a new universality class of the Ising-type lattice
model is unveiled with the exponents {\beta} = 0.304(5), {\nu} = 1.32(3), z =
1.12(1), and {\zeta} = 0.90(1), quite different from that of the quenched
Edwards-Wilkinson equation.
