Preconditioning for hyperelasticity-based mesh optimisation
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Date
2017-06
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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.
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Keywords
mesh optimisation, hyperelasticity, nonconvex optimisation, preconditioning, finite elements