V-cycle multigrid algorithms for discontinuous Galerkin methods on non-nested polytopic meshes
Provides theoretical convergence guarantees for multigrid solvers on non-nested polytopic meshes, addressing a known bottleneck in high-order DG methods.
The paper proves uniform convergence of V-cycle multigrid algorithms for discontinuous Galerkin discretizations on polytopic meshes, with convergence independent of mesh size and polynomial degree p when smoothing steps are sufficiently large.
In this paper we analyse the convergence properties of V-cycle multigrid algorithms for the numerical solution of the linear system of equations arising from discontinuous Galerkin discretization of second-order elliptic partial differential equations on polytopal meshes. Here, the sequence of spaces that stands at the basis of the multigrid scheme is possibly non nested and is obtained based on employing agglomeration with possible edge/face coarsening. We prove that the method converges uniformly with respect to the granularity of the grid and the polynomial approximation degree p, provided that the number of smoothing steps, which depends on p, is chosen sufficiently large.