A Structural-Based Mortar Method using the Arlequin Framework for Non-Matching Meshes

  • Portillo, David (ETSII, Universidad Politécnica de Madrid)

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The coupling of non-matching meshes is a fundamental problem in computational mechanics, traditionally addressed by mortar methods that enforce interface constraints via Lagrange multipliers. However, these methods often require complex and computationally expensive projections between master and slave surfaces. In this work, we propose a novel structural-based mortar approach that leverages the Arlequin framework recently advanced by Portillo and Romero. Instead of a direct surface-to-surface constraint, we interpret the coupling as the embedding of an intermediate structural model that acts as a localized ”mortar” layer between independent 3D domains. This formulation transforms the interface problem into a volumetric overlap where the structural degrees of freedom mediate the transfer of fields. By utilizing the H1 inner products characteristic of the Arlequin method, our approach ensures a consistent and stable transmission of displacements across the non-matching boundaries. This structural mortar effectively regularizes the interface, making it particularly robust for coupling meshes with high refinement disparitiy or complex topological transitions. Numerical results demonstrate that this method maintains the optimal convergence rates while significantly reducing the geometrical complexity of the mesh-tying process.