Optimal analysis-aware parameterization of computational domain in 3D isogeometric analysis

In the isogeometric analysis framework, a computational domain is exactly described using the same representation as the one employed in the CAD process. For a CAD object, various computational domains can be constructed with the same shape but with different parameterizations; however one basic requirement is that the resulting parameterization should have no self-intersections. Moreover we will show, with an example of a 3D thermal conduction problem, that different parameterizations of a computational domain have different impacts on the simulation results and efficiency in isogeometric analysis. In this paper, a linear and easy-to-check sufficient condition for the injectivity of a trivariate B-spline parameterization is proposed. For problems with exact solutions, we will describe a shape optimization method to obtain an optimal parameterization of a computational domain. The proposed injective condition is used to check the injectivity of the initial trivariate B-spline parameterization constructed by discrete Coons volume method, which is a generalization of the discrete Coons patch method. Several examples and comparisons are presented to show the effectiveness of the proposed method. During the refinement step, the optimal parameterization can achieve the same accuracy as the initial parameterization but with less degrees of freedom. ► Different parameterizations of a computational domain have different impacts on the simulation results and efficiency in 3D isogeometric analysis. ► A linear and easy-to-check sufficient condition for injectivity of a trivariate B-spline parameterization is proposed. ► A shape optimization method to obtain an optimal parameterization of a computational domain. ► Discrete Coons volume method to construct initial trivariate B-spline parameterization.