Parallel solvers for virtual element discretizations of elliptic equations in mixed form

Abstract The aim of this paper is twofold. On the one hand, we numerically test the performance of mixed virtual elements in three dimensions to solve the mixed formulation of three-dimensional elliptic equations on polyhedral meshes. On the other hand, we focus on the parallel solution of the linear system arising from such discretization, considering both direct and iterative parallel solvers. In the latter case, we develop two block preconditioners, one based on the approximate Schur complement and one on a regularization technique. Both these topics are numerically validated by several parallel tests performed on a Linux cluster. More specifically, we show that the proposed virtual element discretization recovers the expected theoretical convergence rates and we analyze the performance of the direct and iterative parallel solvers taken into account.