Some Aspects of Multigrid for Mixed Discretizations
A broad class of discretizations of the diffusion operator is based on its first order form, allowing the rigorous enforcement of many desirable physical properties of the continuous model. In this research we investigate the development of multilevel solvers for the local or hybrid forms of these discretizations on logically rectangular quadrilateral meshes. In this case, the local elimination of flux leads to a system that contains both cell- and edge-based scalar unknowns. Based on this natural partitioning of the system we develop approximate reduced systems that reside on a single logically rectangular grid. Each such approximate reduced system, formed as an approximate Schur complement or as a variational product, are used as the first coarse-grid in a multigrid hierarchy or as a preconditioner for Krylov based methods.
KeywordsVariational Product Multigrid Method Rectangular Grid Interpolation Operator Convergence Factor
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