Combining High-Order Metric Interpolation and Geometry Implicitization for Curved <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e687" altimg="si4.svg"><mml:mi>r</mml:mi></mml:math>-Adaption

We detail how to use Newton's method for distortion-based curved $r$-adaption a discrete high-order metric field while matching target geometry. Specifically, we combine two terms: distortion measuring the deviation from metric; and penalty term boundary. For this combination, consider four ingredients. First, represent field, log-Euclidean interpolation on (straight-edged) mesh. Second, interpolation, first second derivatives in physical coordinates. Third, domain boundaries, propose an implicit representation 2D 3D NURBS models. Fourth, representation, obtain derivatives. The of allow minimizing objective function with method. second-order minimization, resulting meshes simultaneously match features Matching geometry using optimization is unprecedented capability $r$-adaption. This will be critical global cavity-based mesh adaption.