  We revisit open string mirror symmetry for the elliptic curve, using matrix
factorizations for describing D-branes on the B-model side. We show how flat
coordinates can be intrinsically defined in the Landau-Ginzburg model, and
derive the A-model partition function counting disk instantons that stretch
between three D-branes. In mathematical terms, this amounts to computing the
simplest Fukaya product m_2 from the LG mirror theory. In physics terms, this
gives a systematic method for determining non-perturbative Yukawa couplings for
intersecting brane configurations.
