Theoretical modeling and numerical simulation have been performed at λ=2100 nm on silicon-on-insulator channel-waveguide directional couplers in which the outer two Si waveguides are passive and the central waveguide(s) are electro-optical (EO) "islands." The EO channel(s) utilize a 10 nm layer of Ge2Sb2Te5 phase-change-material sited at midlevel of a doped Si channel. A voltage-driven phase change produces a large change in the effective index of the TE(o) and TM(o) modes, thereby inducing crossbar 2×2 switching. A mode-matching method is employed to estimate EO switching performance in the limit of strong interguide coupling. Low-loss switching is predicted for cross-to-bar and bar-to-cross coupling lengths. These "self-holding" switches had active lengths of 500-1000 μm, which are shorter than those in couplers relying upon free-carrier injection. The four-waveguide devices had lower cross talk but higher loss than the three-waveguide devices. For the crystalline phase we sometimes used an active length that was smaller than that for the amorphous phase.