Abstract: Volume parameterization is the key step in three-dimensional isogeometric
analysis. In this paper, we propose discrete Coons method for B-spline parametric volume
generation from given boundary surfaces. The parametric formula of Coons volume interpolating
the boundary surfaces is firstly presented. From the discrete version of this formula, for B-spline
volume generation, the inner control points can be obtained by the linear combination of the
boundary control points. Furthermore, the discrete coons mask is generalized into a unified form
in the mask, which provides various choices for the generation of inner control points. The volume
parameterization obtained from different mask and their influences on the result of isogeometric
analysis are also compared by an example for heat conduction problems.

Key words: isogeometric analysis, computational domain, Coons parametric volume, mask