Higher-order moving mesh methods for PDE-constrained shape optimization
This work provides a new discretization framework for shape optimization problems, benefiting researchers in computational design and PDE-constrained optimization by enabling higher-order accuracy.
The paper introduces a higher-order moving mesh method for PDE-constrained shape optimization that generalizes standard approaches to higher-order mesh deformations, enabling high-accuracy solutions. Numerical experiments demonstrate the method's ability to achieve high precision.
We present a new approach to discretizing shape optimization problems that generalizes standard moving mesh methods to higher-order mesh deformations and that is naturally compatible with higher-order finite element discretizations of PDE-constraints. This shape optimization method is based on discretized deformation diffeomorphisms and allows for arbitrarily high resolution of shapes with arbitrary smoothness. Numerical experiments show that it allows the solution of PDE-constrained shape optimization problems to high accuracy.