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This paper discusses the generation of icosahedral hexagonal-pentagonal grids, optimization of the grids, how optimization affects the accuracy of finite-difference Laplacian, Jacobian, and divergence operators, and a parallel multigrid solver that can be used to solve Poisson equations on the grids. Three different grid optimization methods are compared through an error convergence analysis. The optimization process increases the accuracy of the operators. Optimized grids up to 1-km griddoi:10.1175/mwr-d-12-00236.1 fatcat:6em3bljfindoxlrsdbwicyo2tu