  Motivated by the absence of dark matter signals in direct detection
experiments and the discovery of gravitational waves (GWs) at aLIGO, we discuss
the possibility to explore a generic classes of scalar dark matter models using
the complementary searches via phase transition gravitational waves and the
future lepton collider signatures. We focus on the inert scalar multiplet dark
matter models and the mixed inert scalar dark matter models, which could
undergo a strong first-order phase transitions during the evolution of the
early universe, and might produce detectable phase transition GW signals at
future GW experiments, such as eLISA, DECIGO and BBO. We find that the future
GW signature, together with circular electron-positron collider, could further
explore the model's blind spot parameter region, at which the dark matter-Higgs
coupling is identically zero, thus avoiding the dark matter spin-independent
direct detection constraints.
