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

Area of Science:

• Computational Mechanics
• Numerical Analysis
• Multiphysics Simulations

Background:

• Existing domain decomposition methods often struggle with non-conforming meshes and mixed-field problems.
• Ensuring solution continuity across interfaces with different discretizations poses a significant challenge in computational modeling.

Purpose of the Study:

• To extend the Domain Interface Method (DIM) for handling mixed fields in multiphysics simulations.
• To develop a non-conforming domain decomposition technique that efficiently connects non-matching meshes.
• To ensure solution field continuity across geometrically non-conforming interfaces.

Main Methods:

• Discretization of a fictitious zero-thickness interface.
• Incorporation of Lagrange multipliers to enforce solution continuity.
• Automatic Delaunay interface discretization for non-matching meshes.
• Consistent stabilization term based on a Nitsche method for constraint enforcement.

Main Results:

• The multifield DIM successfully accounts for connections between non-matching meshes without master/slave surface considerations.
• The method circumvents instabilities associated with the Ladyzhenskaya-Babuška-Brezzi (LBB) condition.
• Validation in large deformation settings for mixed displacement/pressure and thermomechanical problems shows continuity and objectivity comparable to monolithic solutions.

Conclusions:

• The enhanced multifield DIM provides a robust framework for multiphysics problems with non-conforming discretizations.
• The method demonstrates potential as a valuable tool for simulations requiring different spatial discretizations or field interpolations across domains.
• This approach offers a flexible and stable solution for complex computational challenges in engineering and physics.