A Trust‐Region Method for <i>p</i>‐Harmonic Shape Optimization

ABSTRACT The appropriate scaling of deformation fields has a significant impact on the performance of shape optimization algorithms. We introduce a pointwise gradient constraint to an efficient algorithm for ‐Laplace problems, while the complexity of the algorithm remains polynomial. Using this algorithm, we compute descent directions for shape optimization using ‐harmonic approach that fulfill a trust‐region type constraint. Numerical experiments show the advantages of deformations computed with this approach when compared to deformations that are scaled after computation. This considers, in particular, the approximation of the limit setting and the preservation of mesh quality during an optimization with a fixed step size.