The domain interface method in non-conforming domain decomposition multifield problems

Abstract

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.

Comparison of Commercial and Open-Source FEM Software: A Case Study

“…Interface constraints in the mortar method are enforced over interacting nonconform domains in a variationally consistent way based on the Lagrange multiplier method. Additionally, the mortar method can preserve optimal convergence rates from the finite element methods, as long as appropriate mortar spaces are chosen [33]. However, for symmetrical bodies, conforming boundary conditions can be used.…”

Weighted Average Continuity Approach and Moment Correction: New Strategies for Non-consistent Mesh Projection in Structural Mechanics

“…A recent method was developed by Cafiero et al [15] on the base of the previous developments of Nitsche [57], Becker [5], Heintz [44] , Olivier [58] and Hartman [43]. This approach, inspired from the contact community avoids the expensive segment to segment projections needed for the mortar approach introducing a particular formulation in the gap between the non conforming meshes at the interface.The DIM approach [15] was also extended to the case of mixed fields as can be encoutered in multiphysics problems [51]. Another similar approach introduced virtual gap elements at the interface of the domains and imposes a zero strain condition to these elements [68].…”