V-cycle Multigrid Algorithms for Discontinuous Galerkin Methods on Non-nested Polytopic Meshes
Copyright policy )V-cycle Multigrid Algorithms for Discontinuous Galerkin Methods on Non-nested Polytopic Meshes
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.
26 pages, 23 figures, submitted to Journal of Scientific Computing
polygonal grids, Iterative numerical methods for linear systems, Discontinuous Galerkin · Polygonal grids · Multi-level methods · V -cycle ·Non-nested spaces, non-nested spaces, 65F10, 65M55, 65N22, Numerical Analysis (math.NA), Numerical solution of discretized equations for boundary value problems involving PDEs, Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs, multi-level methods, FOS: Mathematics, \(V\)-cycle, Mathematics - Numerical Analysis, discontinuous Galerkin
polygonal grids, Iterative numerical methods for linear systems, Discontinuous Galerkin · Polygonal grids · Multi-level methods · V -cycle ·Non-nested spaces, non-nested spaces, 65F10, 65M55, 65N22, Numerical Analysis (math.NA), Numerical solution of discretized equations for boundary value problems involving PDEs, Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs, multi-level methods, FOS: Mathematics, \(V\)-cycle, Mathematics - Numerical Analysis, discontinuous Galerkin
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