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An augmented Lagrangian formulation to impose boundary conditions for distortion based mesh moving and curving

Ruiz-Girones, Eloi, Abel Gargallo-Peiro, Josep Sarrate, Xevi Roca

Proceedings, 26th International Meshing Roundtable, Elsevier, Science Direct, September 18-21 2017

INTERNATIONAL
MESHING
ROUNTABLE

26th International Meshing Roundtable
Barcelona, Spain
September 18-21, 2017

Eloi Ruiz-Girones, Barcelona Supercomputing Center, ES, eloi.ruizgirones@bsc.es
Abel Gargallo-Peiro, Barcelona Supercomputing Center, ES, abel.gargallo@bsc.es
Josep Sarrate, Universitat Politecnica de Catalunya, ES, jose.sarrate@upc.edu
Xevi Roca, Barcelona Supercomputing Center, ES, xevi.roca@bsc.es

Abstract
We formulate a mesh morphing technique as mesh distortion minimization problem constrained to satisfy the imposed displacement of the boundary nodes. The method avoids inverted elements during the optimization process and therefore, it does not need to feature untangling capabilities to obtain a valid mesh. To solve the constrained minimization problem, we apply the augmented Lagrangian technique to incorporate the constraint in the objective function using the Lagrangian multipliers and a penalty parameter. We have applied the proposed formulation to mesh moving and mesh curving problems. The results show that the method has the ability to deal with large displacements for 2D and 3D meshes with non-uniform sizing, and mesh curving of highly stretched 2D high-order meshes.

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