  Flexible boundary condition methods couple an isolated defect to a
harmonically responding medium through the bulk lattice Green's function; in
the case of an interface, interfacial lattice Green's functions. We present a
method to compute the lattice Green's function for a planar interface with
arbitrary atomic interactions suited for the study of line defect/interface
interactions. The interface is coupled to two different semi-infinite bulk
regions, and the Green's function for interface-interface, bulk-interface and
bulk-bulk interactions are computed individually. The elastic bicrystal Green's
function and the bulk lattice Green's function give the interaction between
bulk regions. We make use of partial Fourier transforms to treat in-plane
periodicity. Direct inversion of the force constant matrix in the partial
Fourier space provides the interface terms. The general method makes no
assumptions about the atomic interactions or crystal orientations. We simulate
a screw dislocation interacting with a $(10\bar{1}2)$ twin boundary in Ti using
flexible boundary conditions and compare with traditional fixed boundary
conditions results. Flexible boundary conditions give the correct core
structure with significantly less atoms required to relax by energy
minimization. This highlights the applicability of flexible boundary conditions
methods to modeling defect/interface interactions by \textit{ab initio}
methods.
