Volumetric spline parameterization and computational efficiency are two main challenges in isogeometric analysis (IGA). To tackle this problem, we propose a framework of computation reuse in IGA on a set of three-dimensional models with similar semantic features. Given a template domain, B-spline based consistent volumetric parameterization is first constructed for a set of models with similar semantic features. An efficient quadrature-free method is investigated in our framework to compute the entries of stiffness matrix by Bezier extraction and polynomial approximation. In our approach, evaluation on the stiffness matrix and imposition of the boundary conditions can be pre-computed and reused during IGA on a set of CAD models. Examples with complex geometry are presented to show the effectiveness of our methods, and efficiency similar to the computation in linear finite element analysis can be achieved for IGA taken on a set of models.

/pdf/isogeometric-computation-reuse-method-for-complex-objects-4xxfi5medt.pdf

Isogeometric computation reuse method for complex objects with topology-consistent volumetric parameterization

In this paper, we propose a method to obtain a constrained approximation of a rational Bezier curve by a polynomial Bezier curve. This problem is reformulated as an approximation problem between two polynomial Bezier curves based on weighted least-squares method, where weight functions $\rho(t)=\omega(t)$ and $\rho(t)=\omega(t)^{2}$ are studied respectively. The efficiency of the proposed method is tested using some examples.

Approximating rational Bezier curves by constrained Bezier curves of arbitrary degree

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Approximating rational Bezier curves by constrained Bezier curves of arbitrary degree