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Optimized Icosahedral Grids: Performance of Finite-Difference Operators and Multigrid Solver

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  • 1 Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado
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Abstract

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 grid spacing over the earth have been created. The accuracy, performance, and scalability of the multigrid solver are demonstrated.

Corresponding author address: Dr. Ross Heikes, Department of Atmospheric Science, Colorado State University, Fort Collins, CO 80523-1371. E-mail: ross@atmos.colostate.edu

Abstract

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 grid spacing over the earth have been created. The accuracy, performance, and scalability of the multigrid solver are demonstrated.

Corresponding author address: Dr. Ross Heikes, Department of Atmospheric Science, Colorado State University, Fort Collins, CO 80523-1371. E-mail: ross@atmos.colostate.edu
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