Efficient Parallel Optimization for Approximating CAD Curves Featuring Super-convergence. (July 2023) - Docampo Sánchez, Julia
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 when the solver attains a minimum, the constrained disparity preserves the original super-convergence: 2 p order for planar curves and ⌊ 3 2 ( p − 1 ) ⌋ + 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-parametrization. Moreover, we introduce a 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. Graphical abstract: Highlights: Constrained optimization accelerates the convergence of the Newton method. Nonmonotonic line searches reduce the number of non-linear iterations. Super-convergence in the disparity measure results in higher point-wise error reduction. A parallel algorithm for element optimization has limited performance in a cluster. A parallel algorithm for curve optimization using 48 cores reduces the CPU times by a factor of 8.