论文标题
有效的平行优化，用于近似CAD曲线具有超级连接的曲线
Efficient parallel optimization for approximating CAD curves featuring super-convergence
论文作者
论文摘要
我们提出了一种有效的，平行的，受约束的优化技术，用于具有超稳态速率的近似CAD曲线。 优化函数是根据零件的多项式近似和曲线重新分配的差异度量。 受约束的问题解决了固定网格元素接口的差异功能。 我们有数值证据表明，受约束的差异保留了原始的超级符号：平面曲线的$ {2P} $订单和$ \ lfloor \ frac \ frac 32（p-1）\ rfloor + 2 $ 3D曲线，$ p $，是网状polynomial级别。 我们的优化方案由带有非单极线搜索的全球化牛顿方法组成，以及一个对数屏障函数，可防止曲线重新分配中元素反转。此外，我们将\ emph {Julia}接口引入了Egads几何内核和并行优化算法。我们使用多种飞机CAD型号在计算机群集上测试曲线网格生成工具的潜力。我们得出的结论是，该求解器非常适合并行计算，从而产生了对CAD曲线的超构造近似值。
We present an efficient, parallel, constrained optimization technique for approximating CAD curves with super-convergent rates. The optimization function is a disparity measure in terms of a piece-wise polynomial approximation and a curve re-parametrization. The constrained problem solves the disparity functional fixing the mesh element interfaces. We have numerical evidence that the constrained disparity preserves the original super-convergence: ${2p}$ order for planar curves and $\lfloor\frac 32(p-1)\rfloor + 2$ for 3D curves, $p$ being the mesh polynomial degree. Our optimization scheme consists of a globalized Newton method with a nonmonotone line search, and a log barrier function preventing element inversion in the curve re-parameterization. Moreover, we introduce a \emph{Julia} interface to the EGADS geometry kernel and a parallel optimization algorithm. We test the potential of our curve mesh generation tool on a computer cluster using several aircraft CAD models. We conclude that the solver is well-suited for parallel computing, producing super-convergent approximations to CAD curves.
