Isogeometric collocation method based on residual parameterization of planar physical domain
Isogeometric collocation method based on residual parameterization of planar physical domain
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DOI：
10.1016/j.cam.2022.114889
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发表时间：
2022-10
期刊：
影响因子：
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通讯作者：
Pei-bai Zhou;Chungang Zhu
中科院分区：
文献类型：
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作者：
Pei-bai Zhou;Chungang Zhu
等几何分析是求解偏微分方程的有效工具。与等几何伽辽金法相比，等几何配点法具有更高的计算效率。在本文中，我们的目标是优化的区域参数化在IGC更好的数值精度求解偏微分方程。首先，我们提出了一种新的平面物理域的参数化方法，称为剩余参数化，这是通过最小化的目标函数组成的几何相关的泛函和分析相关的剩余范数的无约束优化问题。其次，由于计算剩余项的积分时计算量很大，因此将简化求积规则应用于剩余范数。最后，在残差参数化的基础上，利用带Greville点和超收敛点的IGC方法求解了二维物理区域的边值问题，验证了本文提出的残差参数化方法的有效性.数值算例表明，该方法的数值精度比标准IGC方法提高了近半个数量级。
Isogeometric analysis (IGA) becomes an effective tool for solving partial differential equations (PDEs). Compared with isogeometric Galerkin method, isogeometric collocation (IGC) method has higher computational efficiency. In this paper, we aim to optimize the domain parameterization in IGC for better numerical accuracy of solving PDEs. Firstly, we present a new parameterization method of planar physical domain, called residual parameterization, which is obtained by minimizing the objective functions consisting of geometry-related functionals and the analysis-related residual norms in an unconstrained optimization problem. Secondly, the reduced quadrature rules are applied to residual norms due to high computational cost in evaluating the integration of residual terms. Finally, based on the residual parameterization, we solve boundary value problems (BVPs) by IGC with Greville points and superconvergent points to verify the strength of our proposed residual parameterization of planar physical domain. Several numerical examples show that the numerical accuracy of the proposed method is improved nearly half order of magnitude compared with standard IGC method.