The ability to take advantage of computationally efficient high-order finite element methods to perform adaptive finite element analysis of complex engineering problems over general 3D domains requires the ability to adapt meshes with curved elements that maintain the level of geometric approximation of the domain boundary required. This paper presents a conforming curved mesh adaptation procedure aimed at effectively supporting automated adaptive analysis of problems for which the domain geometry is defined in a CAD system. The local mesh modification procedures interact with the CAD geometry to curve the mesh edges and faces representing those boundaries to the order of approximation of the high-order elements being used. The curved mesh edges and faces representing the domain boundaries are based on Bézier approximation geometry, which provides more accurate evaluations of surface-related quantities of interest than the commonly used interpolation methods. To attain computational efficiency during mesh adaptation, the interior mesh entities have their geometric order kept as low as possible while still maintaining control of element shapes. The order of curved mesh entities is limited to no higher than cubic, which allows the definition of an effective procedure to define the shape of the limited number of interior mesh entities that must be curved. The procedures, which are fully parallelized, are demonstrated on the adaptive radio-frequency analysis of a magnetically confined fusion system containing a fully represented radio-frequency antenna.

翻译：为实现复杂工程问题在一般三维区域上的自适应有限元分析，需充分利用计算高效的高阶有限元方法，这要求网格具备自适应能力，且其曲边单元能维持域边界所需的几何逼近精度。本文提出一种保形曲边网格自适应流程，旨在高效支持域几何由CAD系统定义的问题的自适应分析。局部网格修改过程与CAD几何交互，使表征边界的网格边/面弯曲至与所用高阶单元逼近阶次相匹配。基于贝塞尔逼近几何构建的域边界曲边/曲面，相比常用插值方法，能更精确地评估与曲面相关的关注量。为在网格自适应过程中实现计算效率，内部网格实体在保证单元形态可控的前提下，几何阶次尽可能保持低位。曲边网格实体阶次上限设为三次，由此可定义有效流程，以确定必须弯曲的有限数量内部网格实体的形态。该流程已实现完全并行化，并通过含完整射频天线的磁约束聚变系统的自适应射频分析予以验证。