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Energetic X-ray radiations emitted from various accretion systems are widelyconsidered to be produced by Comptonization in the hot corona. The corona andits interaction with the disc play an essential role in the evolution of thesystem and are potentially responsible for many observed features. However manyintrinsic properties of the corona are still poorly understood, especially forthe geometrical configurations. The traditional spectral fitting method is notpowerful enough to distinguish various configurations. In this paper we intentto investigate the possible configurations by modeling the polarizationproperties of X-ray radiations. The geometries of the corona include the slab,sphere and cylinder. The simulations are implemented through the publiclyavailable code, LEMON, which can deal with the polarized radiative transfer anddifferent electron distributions readily. The results demonstrate clearly thatthe observed polarizations are dependent on the geometry of the corona heavily.The slab-like corona produces the highest polarization degrees, the followingare the cylinder and sphere. One of the interesting things is that thepolarization degrees first increase gradually and then decrease with theincrease of photon energy. For slab geometry there exists a zero point wherethe polarization vanishes and the polarization angle rotates for $90^\circ$.These results may potentially be verified by the upcoming missions forpolarized X-ray observations, such as $IXPE$ and $eXTP$.

New simulations of the X-ray spectra and polarizations of accretion-disc corona systems with various geometrical configurations I. Model Description