This paper presents a general formulation of an isogeometric collocation method (IGA-C) for the parameterization of computational domains for the isogeometric analysis (IGA) using non-uniform rational B-splines (NURBS). The boundary information of desired computational domains for IGA is imposed as a Dirichlet boundary condition on a simple and smooth initial parameterization of an initial computational domain, and the final parameterization is produced based on the numerical solution of a partial differential equation (PDE) that is solved using the IGA-C method. In addition, we apply intuitive derivative constraints while solving the PDE to achieve desired properties of smoothness and uniformity of the resulting parameterization. While one may use any general PDE with any constraint, the PDEs and additional constraints selected in our case are such that the resulting solution can be efficiently solved through a system of linear equations with or without additional linear constraints. This approach is different from typical existing parameterization methods in IGA that are often solved through an expensive nonlinear optimization process. The results show that the proposed method can efficiently produce satisfactory analysis-suitable parameterizations.

本文介绍了使用非均匀有理B样条（NURBS）对等几何分析（IGA）的计算域进行参数化的等几何配点方法（IGA-C）的一般公式。将IGA所需计算域的边界信息作为Dirichlet边界条件强加于初始计算域的简单且平滑的初始参数化上，并基于偏微分方程（PDE）的数值解生成最终参数化，即使用IGA-C方法解决。此外，我们在求解PDE时应用了直观的导数约束，以实现所需参数的平滑度和均匀性。尽管可以使用具有任何约束条件的任何通用PDE，在我们的情况下，选择的PDE和附加约束条件使得可以通过带有或不具有附加线性约束条件的线性方程组有效地求解所得的解。此方法与IGA中通常通过昂贵的非线性优化过程解决的典型现有参数化方法不同。结果表明，所提出的方法可以有效地产生令人满意的适合分析的参数化。