  For D-brane system with three D-branes on compact Calabi-Yau threefolds, the
dual F-theory fourfolds for parallel/complete coincident/part coincident
D-brane system is constructed by the type II/F-theory duality. Complete
coincident means that the three D-branes coincide and part coincident
represents the coincident of two of the three D branes. The low energy
effective superpotentials are calculated by mirror symmetry, GKZ-system method
and the type II/F-theory duality on the B-model side, respectively. Using the
mirror symmetry, A-model superpotentials and the Ooguri-Vafa invariants are
obtained from the B-model side. These results indicate that the superpotential
contributed by one of three parallel D-branes is identical with the D-brane
system with only one D-brane, which is a signal of decoupling of the parallel
topological D-branes. However, the superpotential and Oogrui-Vafa invariants
are different among parallel, complete coincident and part coincident D-brane
system, which show the evidence of the phase transition due to the enhanced
gauge symmetry in the low energy theories and the geometrical singularity.
