  The double-degenerate (DD) model, involving the merging of massive double
carbon-oxygen white dwarfs (CO WDs) driven by gravitational wave radiation, is
one of the classical pathways for the formation of type Ia supernovae (SNe Ia).
Recently, it has been proposed that the WD+He subgiant channel has a
significant contribution to the production of massive double WDs, in which the
primary WD accumulates mass by accreting He-rich matter from a He subgiant. We
evolved about 1800 CO WD+He star systems and obtained a large and dense grid
for producing SNe Ia through the DD model. We then performed a series of binary
population synthesis simulations for the DD model, in which the WD+He subgiant
channel is calculated by interpolations in this grid. According to our standard
model, the Galactic birthrate of SNe Ia is about 2.4*10^{-3} yr^{-1} for the
WD+He subgiant channel of the DD model; the total birthrate is about
3.7*10^{-3} yr^{-1} for all channels, reproducing that of observations.
Previous theoretical models still have deficit with the observed SNe Ia with
delay times <1 Gyr and >8 Gyr. After considering the WD+He subgiant channel, we
found that the delay time distributions is comparable with the observed
results. Additionally, some recent studies proposed that the violent WD mergers
are more likely to produce SNe Ia based on the DD model. We estimated that the
violent mergers through the DD model may only contribute to about 16% of all
SNe Ia.
