FETI-DP Preconditioners for the Virtual Element Method on General 2D Meshes

Abstract

We analyze the performance of a state-of-the-art domain decomposition approach, the Finite Element Tearing and Interconnecting Dual Primal (FETI-DP) method (Toselli and Widlund, Domain decomposition methods—algorithms and theory. Springer series in computational mathematics, vol 34, 2005), for the efficient solution of very large linear systems arising from elliptic problems discretized by the Virtual Element Method (VEM) (Beirão da Veiga et al., Math Models Methods Appl Sci 24:1541–1573, 2014). 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.