高级检索

基于PHT-样条加强等几何分析配置方法

PHT-Spline-Based Enhanced Isogeometric Collocation Method

  • 摘要: 结合传统等几何分析配置法和传统等几何分析伽辽金法,提出一种基于PHT-样条函数的加强等几何分析配置方法.对于一个偏微分方程问题,基于具有局部细分特性的PHT-样条基础函数,应用传统等几何分析配置法在问题域内配置点定义线性方程组,并应用传统等几何分析伽辽金法施加边界条件,以保证多片结构连接的稳定;再将2组线性方程组及施加的边界条件合成一个整体系统.实例计算结果表明,该方法既具有配置法固有的计算效率高的优点,又改善了边界计算出现的不稳定问题,可有效地用于局部细分和多片结构的计算.

     

    Abstract: The current work presents an enhanced isogeometric analysis(IGA)collocation method by combining the traditional IGA collocation method and the Galerkin IGA method.The traditional IGA collocation method exhibits high computational efficiency when solving partial differential equations(PDEs)problems.But the method may produce unstable results along the domain and patch boundaries,influencing the quality of the solution.Compared to the traditional IGA collocation method,the Galerkin IGA method has higher accuracy and is more stable,at the cost of being much slower than the IGA collocation method.The proposed enhanced IGA collocation method combines the two traditional approaches.For a given PDEs problem,firstly,we apply the traditional IGA collocation method in the interior region of the domain by defining the collocation equations at the Greville abscissae points.Secondly,we use the Galerkin IGA method to impose the boundary conditions and ensure a stable multi-patch coupling.The discretization used in the method above is based on the PHT-spline basis functions.Finally,we combine the two types of constraints,together with the boundary conditions as a global linear system.In the end,we test the proposed method by solving 2D and 3D numerical examples with local refinement,showing good numerical performance and stability for multi-patch problems.

     

/

返回文章
返回