Efficient parallel optimization for approximating CAD curves featuring super-convergence

Abstract

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.