Agglomeration and refinement of polytopic meshes for DGFEM and VEM

• Date: 14. 4. 2022
• Time: 14:00 - 15:30
• Address:
  Sokolovská 83, Praha
• Room: K3
• Speaker: Scott Congreve

There has recently been significant work developing numerical methods to operate on meshes containing elements of arbitrary shape, so-called polytopic elements, such as polytopic discontinuous Galerkin finite element methods (DGFEM) and virtual element methods (VEM). One technique for constructing meshes of polytopic elements is to agglomerate existing meshes of standard elements. This technique is especially useful in the situations where multiple, hierarchical, meshes are required; e.g., for multiscale or multigrid methods. Existing methods for agglomeration either attempt to maintain element geometry, or are based on optimal graph splitting techniques of the dual graph for the mesh. However, meshes generated using these agglomeration techniques do not necessarily consider the a priori knowledge on the domain or method, and are not necessary guaranteed to meet the assumptions required by the numerical analysis of the methods being utilised. In this talk, we give a brief overview of some these problems, and the ideas we will explore as part of the forthcoming PRIMUS project to improve these agglomerations. Furthermore, we will briefly discuss ideas for adaptive mesh refinement of these agglomerated meshes.