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Orientation preserving mesh optimisation and preconditioning
Author(s) -
Paul Jordi
Publication year - 2018
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5764
Subject(s) - hyperelastic material , preconditioner , partial differential equation , nonlinear system , deformation (meteorology) , elasticity (physics) , mathematics , computer science , orientation (vector space) , energy functional , mathematical optimization , mathematical analysis , geometry , materials science , physics , iterative method , quantum mechanics , composite material
Summary 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 partial differential equation–based preconditioner is developed.