Preconditioning for hyperelasticity-based mesh optimisation

Abstract

A robust mesh optimisation method is presented that directly enforces the resulting deformation to be orientation preserving. Motivated by aspects from mathematical elasticity, the energy functional of the mesh deformation can be related to a stored energy functional of a hyperelastic material. Formulating the functional in the principal invariants of the deformation gradient allows fine grained control over the resulting deformation. Solution techniques for the arising nonconvex and highly nonlinear system are presented. As existing preconditioners are not sufficient, a PDE-based preconditioner is developed.