Parallel multilevel solvers for virtual element discretizations of saddle point problems


The Virtual Element Method (VEM) is a recent numerical technique for solving partial differential equations on computational grids constituted by polygonal or polyhedral elements of very general shape. This work aims to develop effective linear solvers for general order VEM approximations of three-dimensional scalar elliptic equations in mixed form and Stokes equations. To this end, we consider block algebraic multigrid preconditioners and balancing domain decomposition by constraints (BDDC) preconditioners. The latter allows us to use conjugate gradient iterations, albeit the algebraic linear systems arising from the discretization of the differential problems are indefinite, ill-conditioned, and of saddle point nature.

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