2018/08/15 by Daniel Fortunato, Chris H. Rycroft, Fortunato, Daniel +3 · 1 citation
Computer Science · Engineering · #65F08 #65N30 #65N55 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Lattice Boltzmann Simulation Studies #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1808.05320
openalex publication_date 2018/08/15 · openalex created_date 2023/03/19 · openalex updated_date 2026/07/30
An efficient hp-multigrid scheme is presented for local discontinuous\nGalerkin (LDG) discretizations of elliptic problems, formulated around the idea\nof separately coarsening the underlying discrete gradient and divergence\noperators. We show that traditional multigrid coarsening of the primal\nformulation leads to poor and suboptimal multigrid performance, whereas\ncoarsening of the flux formulation leads to optimal convergence and is\nequivalent to a purely geometric multigrid method. The resulting\noperator-coarsening schemes do not require the entire mesh hierarchy to be\nexplicitly built, thereby obviating the need to compute quadrature rules,\nlifting operators, and other mesh-related quantities on coarse meshes. We show\nthat good multigrid convergence rates are achieved in a variety of numerical\ntests on 2D and 3D uniform and adaptive Cartesian grids, as well as for curved\ndomains using implicitly defined meshes and for multi-phase elliptic interface\nproblems with complex geometry. Extension to non-LDG discretizations is briefly\ndiscussed.\n