论文标题
在弯曲表面上应用于Helmholtz-Hodge分解的应用中的高阶协变量分化
High-order covariant differentiation in applications to Helmholtz-Hodge decomposition on curved surfaces
论文作者
论文摘要
提出了一种新型的高阶数值方案来计算任何弯曲表面上的协变量，尤其是用于发散和卷曲的衍生物。所提出的方案不需要构建弯曲的轴或度量张量，这将使协变量衍生物的准确性恶化并阻止其应用于复杂表面。作为一种应用，在Galerkin方法的上下文中，对Helmholtz-Hodge分解（HHD）进行了调整，用于在曲面上显示向量的无关，不可压缩和谐波成分。
A novel high-order numerical scheme is proposed to compute the covariant derivative, particularly for divergence and curl, on any curved surface. The proposed scheme does not require the construction of a curved axis or metric tensor, which would deteriorate the accuracy of the covariant derivative and prevent its application to complex surfaces. As an application, the Helmholtz-Hodge decomposition (HHD) is adapted in the context of the Galerkin method for displaying the irrotational, incompressible, and harmonic components of vectors on curved surfaces.
