论文标题
智能云搭配：直接来自CAD的几何感知适应性
Smart cloud collocation: geometry-aware adaptivity directly from CAD
论文作者
论文摘要
计算机辅助设计（CAD）广泛用于创建和优化各种工业系统和流程。将CAD几何形状转换为用于解决PDE的计算离散化，需要护理并深入了解所选的计算方法。在本文中，我们提出了一种基于智能云的新颖集成搭配方案。它使我们能够以最小的努力将CAD几何形状转换为完整的点搭配模型，以意识到基础几何形状。对于此过程，仅以步进文件的形式和边界条件的形式仅以域的几何形状。我们还使用\ textIt {a posteriori}错误指示引入了生成的智能云的自适应改进过程。该方案可以应用于任何2D或3D几何形状，可应用于任何PDE，可以应用于大多数点搭配方法。我们用应用于稳定的线性弹性问题的无网格通用有限差（GFD）方法来说明这一点。我们进一步表明，从初始离散化到改进策略的每个步骤都连接并受到上一步中选择的方法的影响，因此需要一个集成方案，其中应立即考虑整个解决方案过程。
Computer Aided Design (CAD) is widely used in the creation and optimization of various industrial systems and processes. Transforming a CAD geometry into a computational discretization that be used to solve PDEs requires care and a deep knowledge of the selected computational method. In this article, we present a novel integrated collocation scheme based on smart clouds. It allows us to transform a CAD geometry into a complete point collocation model, aware of the base geometry, with minimum effort. For this process, only the geometry of the domain, in the form of a STEP file, and the boundary conditions are needed. We also introduce an adaptive refinement process for the resultant smart cloud using an \textit{a posteriori} error indication. The scheme can be applied to any 2D or 3D geometry, to any PDE and can be applied to most point collocation approaches. We illustrate this with the meshfree Generalized Finite Difference (GFD) method applied to steady linear elasticity problems. We further show that each step of this process, from the initial discretization to the refinement strategy, is connected and is affected by the approach selected in the previous step, thus requiring an integrated scheme where the whole solution process should be considered at once.
