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A gluing method for non-matching meshes. (English) Zbl 1390.65041
Summary: This paper presents a gluing method for composite meshes. Different meshes are generated independently and are glued together using some new elements to connect them, referred to as extension elements. The resulting global mesh is non-conforming and consists of connected overlapping meshes. The method is inherently implicit, parallel and versatile, in the sense that it is PDE independent. The most cited gluing method is probably the Chimera method, used for overset grids, where patch meshes are superimposed onto a background mesh. The method employed here was originally devised for such situations and is now applied to disjoint or overlapping meshes. One of the advantages of the method is that the meshes do not have to coincide and can present a gap between them. The method is illustrated through some simple examples to demonstrate the mesh convergence. Finally, we consider the solution of the airflow in the complete respiratory system, by joining independent meshes for the large and small airways, and the simulation of the flow passing through a bypass in a stenosed artery.

65F50 Computational methods for sparse matrices
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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