Efficient parallel optimization for approximating CAD curves featuring super-convergence

TL;DR

This paper introduces a parallel constrained optimization method for CAD curve approximation that achieves super-convergent rates, utilizing a Julia interface and tested on aircraft models to demonstrate efficiency and accuracy.

Contribution

The paper presents a novel parallel optimization technique with super-convergence guarantees for CAD curve approximation, including a Julia interface and application to complex models.

Findings

Achieves super-convergence rates for 2D and 3D CAD curves.

Demonstrates efficiency of the parallel solver on aircraft models.

Maintains curve quality with constrained disparity functional.

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.