Domain Decomposition With Non-Conforming Polyhedral Grids

Abstract

A novel mortar approach for the domain decomposition of field problems discretized in terms of nodal variables by the cell method is here proposed. This approach allows the use of both arbitrary polyhedral meshes and non–conforming discretizations, without limitations or complications due to the mesh type or the model geometry. Therefore, it provides a new domain decomposition method that can be practically used in engineering applications for coupling different parts of a model, which can be independently discretized and then reassembled together. More precisely: 1) Any part of the computational domain is first separately modeled in order to assess the mesh type and size that are best suited for ensuring an accurate local field reconstruction; 2) The different discretized parts can be combined together in order to obtain an accurate solution of a composite problem, while maintaining the local discretizations already determined. As a main advantage over existing mortar approaches, the algebraic structure of the final matrix system—derived by the cell method discretization—is not altered by the introduction of mortar interface conditions. As a result, the same preconditioning and iterative solver strategy can be extended as is to the proposed mortar method. This approach is validated by a convergence analysis on an analytical test case and its effectiveness for practical applications is assessed on a real–sized engineering problem.