  Following the proposals of Donaldson-Thomas, Haydys and Gaiotto-Moore-Witten,
we give a construction of Fukaya-Seidel categories for a suitable class of
Morse Landau-Ginzburg models using the complex gradient flow equation, which
has the potential for generalization to some infinite dimensional examples.
  In the course of this construction, we give an alternative proof to Seidel's
spectral sequence for Lagrangian Floer cohomology, which can be viewed as a
finite dimensional model for a potential bordered monopole Floer theory. The
key observation is that under a neck-stretching limit, this complex gradient
flow equation produces a natural geometric filtration on the Floer cochain
complex. The resulting spectral sequence is then identified with Seidel's
original one.
