Strong imposition of Dirichlet boundary conditions for immersed finite element methods or immersed isogeometric methods remains a challenge. To address this issue, this paper presents a 3D conforming embedded isogeometric method for Boundary-Represented (B-Rep) solid CAD models by generalizing our bivariate B++ splines to trivariate B++ Splines. The proposed method can convert a B-Rep model into a trivariate B++ spline solid patch with body-fitted boundary representation while retaining key features of B-rep models, such as sharp points, sharp edges, and holes. The basis functions of the trivariate B++ spline solid patch satisfy the Kronecker delta property, which implies that we can strongly impose Dirichlet boundary conditions on B-Rep models without the necessity of Nitsche's method. The presented method can be viewed as a parameterization method that inherits the advantages of volumetric parameterization methods in that the basis functions of a reconstructed geometry satisfy the Galerkin method. In addition, compared with T-splines, the proposed method does not generate the extraordinary point and can achieve optimal convergence rate. Several numerical examples are used to demonstrate the reliability of the presented method.

中文翻译：

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使用三元 B++ 样条对具有强烈狄利克雷边界条件的 B-Rep CAD 模型进行嵌入式等几何分析


对于浸没有限元方法或浸没等几何方法，强施加狄利克雷边界条件仍然是一个挑战。为了解决这个问题，本文通过将二元 B++ 样条推广到三元 B++ 样条，提出了一种用于边界表示 （B-Rep） 实体 CAD 模型的 3D 一致性嵌入式等几何方法。所提出的方法可以将 B-Rep 模型转换为具有体拟合边界表示的三元 B++ 样条实体补丁，同时保留 B-rep 模型的关键特征，如尖点、尖边和孔。三元 B++ 样条实体补丁的基本函数满足 Kronecker delta 属性，这意味着我们可以在 B-Rep 模型上强施加狄利克雷边界条件，而无需 Nitsche 方法。所提出的方法可以看作是一种参数化方法，它继承了体积参数化方法的优点，即重建几何的基函数满足 Galerkin 方法。此外，与 T 样条相比，所提方法没有产生异常点，可以实现最优收敛速率。用几个数值算例来证明所提方法的可靠性。