论文标题
一种准确有效的方案，用于平滑域上的功能扩展
An accurate and efficient scheme for function extensions on smooth domains
论文作者
论文摘要
提出了一种新的方案，以构建在d维度中平滑域D上定义的N时间可分化函数的N时间可区分函数扩展。扩展方案依赖于D的明确公式，该公式由D中N+1函数值的线性组合组合，该组合将函数沿正常的方向扩展到边界。与边界的平滑度是自动的。通过将函数扩展作为数值求解器中的步骤来说明该方案的性能，以在具有两个和三个维度的复杂几何形状的倍数连接域上的不均匀泊松方程。我们表明，进行功能扩展所需的适度额外工作导致了部分微分方程的更准确的解决方案。
A new scheme is proposed to construct an n-times differentiable function extension of an n-times differentiable function defined on a smooth domain D in d-dimensions. The extension scheme relies on an explicit formula consisting of a linear combination of n+1 function values in D, which extends the function along directions normal to the boundary. Smoothness tangent to the boundary is automatic. The performance of the scheme is illustrated by using function extension as a step in a numerical solver for the inhomogeneous Poisson equation on multiply connected domains with complex geometry in two and three dimensions. We show that the modest additional work needed to do function extension leads to considerably more accurate solutions of the partial differential equation.
