论文标题
使用NURBS设计和PHT-Splines的自适应形状优化，用于溶液近似时间
Adaptive shape optimization with NURBS designs and PHT-splines for solution approximation in time-harmonic acoustics
论文作者
论文摘要
提出了几何独立场近似（礼物）作为等几何分析（IGA）的概括，其中使用了不同类型的花键用于计算域的参数化和未知解决方案的近似。用于溶液近似的几何形状和PHT-Spline的不均理性B-Splines（NUBR）的礼物成功地应用于时间谐波声学问题上，在某些情况下，在某些情况下，在某些情况下，适应性PHT-Spline网格在某些情况下以比均匀细化的方法较低的计算成本获得了高度准确的解决方案。因此，研究礼物的表现优化问题是很有趣的，其中NURB用于对边界进行建模，其控制点是设计变量和PHT-spline用于在优化过程中适应解决方案的溶液与边界变化的近似值。 在这项工作中，我们证明了礼物在2D声学优化问题中的应用，并使用三个基准示例，我们表明该方法在自由度和计算时间的程度上产生了具有大量计算节省的准确解决方案。
Geometry Independent Field approximaTion (GIFT) was proposed as a generalization of Isogeometric analysis (IGA), where different types of splines are used for the parameterization of the computational domain and approximation of the unknown solution. GIFT with Non-Uniform Rational B-Splines (NUBRS) for the geometry and PHT-splines for the solution approximation were successfully applied to problems of time-harmonic acoustics, where it was shown that in some cases, adaptive PHT-spline mesh yields highly accurate solutions at lower computational cost than methods with uniform refinement. Therefore, it is of interest to investigate performance of GIFT for shape optimization problems, where NURBS are used to model the boundary with their control points being the design variables and PHT-splines are used to approximate the solution adaptively to the boundary changes during the optimization process. In this work we demonstrate the application of GIFT for 2D acoustic shape optimization problems and, using three benchmark examples, we show that the method yields accurate solutions with significant computational savings in terms of the number of degrees of freedom and computational time.
