Specific-purpose globalizations for Newton’s method: anisotropic optimization of curved meshes

Abstract

We derive an optimization method to adapt straight-edged and curved piece-wise polynomial meshes to the stretching and alignment of a target metric. Two globalization strategies for the optimization method are proposed: backtracking line search and restricted trust region. To compare both globalization approaches, we derive a specific-purpose implementation of Newton’s method for each globalization. To propose these two new implementations, we present different emulation methods to interchange between both approaches their nonshared globalization features. Once the number of non-linear iterations is comparable, we have been able to improve the inexact Newton implementation, with both globalization methods, to reduce one order of magnitude the total number of sparse matrix-vector products. I.