FETI-DP preconditioners for the Virtual Element Method on general 2D meshes
For computational scientists solving large elliptic problems with complex meshes, this work extends FETI-DP domain decomposition to Virtual Element Methods, but is incremental as it applies an existing method to a new discretization.
The paper analyzes FETI-DP preconditioners for Virtual Element Method discretizations of elliptic problems on general 2D meshes, demonstrating numerical scalability and robustness with respect to heterogeneous coefficients and mesh shapes.
We analyze the performance of a state-of-the-art domain decomposition approach, the Finite Element Tearing and Interconnecting Dual Primal (FETI-DP) method, for the efficient solution of very large linear systems arising from elliptic problems discretized by the Virtual Element Method. We provide numerical experiments on a model linear elliptic problem with highly heterogeneous diffusion coefficients on arbitrary Voronoi meshes, which we modify by adding nodes and edges deriving from the intersection with an unrelated coarse decomposition. The experiments confirm also in this case that the FETI-DP method is numerically scalable with respect to both the problem size and number of subdomains, and its performance is robust with respect to jumps in the diffusion coefficients and shape of the mesh elements.