基于PHT-样条加强等几何分析配置方法

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.