A domain decomposition technique is proposed which is capable of properly connecting arbitrary non-conforming interfaces. The strategy essentially consists in considering a fictitious zero-width interface between the non-matching meshes which is discretized using a Delaunay triangulation. Continuity is satisfied across domains through normal and tangential stresses provided by the discretized interface and inserted in the formulation in the form of Lagrange multipliers. The final structure of the global system of equations resembles the dual assembly of substructures where the Lagrange multipliers are employed to nullify the gap between domains. A new approach to handle floating subdomains is outlined which can be implemented without significantly altering the structure of standard industrial finite element codes. The effectiveness of the developed algorithm is demonstrated through a patch test example and a number of tests that highlight the accuracy of the methodology and independence of the results with respect to the framework parameters. Considering its high degree of flexibility and non-intrusive character, the proposed domain decomposition framework is regarded as an attractive alternative to other established techniques such as the mortar approach.

The Domain Interface Method (DIM) is extended in this contribution for the case of mixed fields as encountered in multiphysics problems. The essence of the nonconforming domain decomposition technique consists in a discretization of a fictitious zero-thickness interface as in the original methodology and continuity of the solution fields across the domains is satisfied by incorporating the corresponding Lagrange Multipliers. The multifield DIM inherits the advantages of its irreducible version in the sense that the connections between non-matching meshes, with possible geometrically non-conforming interfaces, is accounted by the automatic Delaunay interface discretization without considering master and slave surfaces or intermediate surface projections as done in many established techniques, e.g. mortar methods. The multifield enhancement identifies the Lagrange multiplier field and incorporates its contribution in the weak variational form accounting for the corresponding consistent stabilization term based on a Nitsche method. This type of constraint enforcement circumvents the appearance of instabilities when the Ladyzhenskaya-Babuška-Brezzi (LBB) condition is not fulfilled by the chosen discretization. The domain decomposition framework is assessed in a large deformation setting for mixed displacement/pressure formulations and coupled thermomechanical problems. The continuity of the mixed field is studied in well selected benchmark problems for both mixed formulations and the objectivity of the response is compared to reference monolithic solutions. Results suggest that the presented strategy shows sufficient potential to be a valuable tool in situations where the evolving physics at particular domains require the use of different spatial discretizations or field interpolations.