Convergence results for 3D sparse grid approaches (Q2713562)

The paper concerns numerical tests of a multigrid approach using a sparse family of grids. This is formed by taking a subset of a partially ordered set of semi-refined grids created from an original coarse grid by successive semi-refinements in only one but not necessarily fixed coordinate direction. NEWLINENEWLINENEWLINEAfter presenting a brief review of principal approximation results from \textit{P. W. Hemker} and \textit{C. Pflaum} [Appl. Numer. Math. 25, 55-87 (1997; Zbl 0882.65005)], the authors pay attention to model anisotropic Poisson equations defined on the unit cube in 3D and solved by various two-level multigrid methods. NEWLINENEWLINENEWLINEFirst, successive semi-coarsening in each spatial direction is tested. Though showing good convergence, the method is not considered efficient due to excessive number of arithmetic operations. That is why three other algorithms based on semi-coarsening are proposed, numerically tested, and discussed. Numerous convergence history graphs are plotted. The reader, however, might lack a table comparing the execution time of the proposed algorithms.