This paper describes the development and evaluation of a new nonhydrostatic dynamical framework for global and regional atmospheric modeling, with an emphasis on the numerical performance of dry dynamics. The model is formulated in a layer‐averaged manner using a generalized hybrid sigma‐mass vertical coordinate and an unstructured mesh. The mass‐based equations allow a flexible and effective switch between the hydrostatic and nonhydrostatic solvers. The unstructured mesh treats the conventional icosahedral grid and the more general Voronoi polygon in a consistent manner, allowing a flexible switch between quasi‐uniform and variable‐resolution modeling. The horizontal discretization and vertical discretization are formulated in an explicit Eulerian approach, while those terms describing the vertically propagating fast waves are solved implicitly. The model is equipped with physically based Smagorinsky diffusion as a tuning tool. A suite of multiscale test cases from hydrostatic to nonhydrostatic regimes is used to assess the model performance. The general strategies for evaluation focus on two aspects: (i) the nonhydrostatic solver should behave similarly to its hydrostatic counterpart under the hydrostatic regime and (ii) the nonhydrostatic solver should produce unique nonhydrostatic responses under the nonhydrostatic regime. In the context of model evaluation, model sensitivity to numerical configurations is further explored to understand the impact of isolated components, helping to identify appropriate configurations for realistic modeling applications. The present framework is a prototype toward a Global‐Regional Integrated forecast SysTem (GRIST).
Models of fermions interacting with classical degrees of freedom are applied to a large variety of systems in condensed matter physics. For this class of models, Weiße [Phys. Rev. Lett. 102, 150604 (2009)] has recently proposed a very efficient numerical method, called O(N ) Green-Function-Based Monte Carlo (GFMC) method, where a kernel polynomial expansion technique is used to avoid the full numerical diagonalization of the fermion Hamiltonian matrix of size N , which usually costs O(N 3 ) computational complexity. Motivated by this background, in this paper we apply the GFMC method to the double exchange model in three spatial dimensions. We mainly focus on the implementation of GFMC method using both MPI on a CPU-based cluster and Nvidia's Compute Unified Device Architecture (CUDA) programming techniques on a GPU-based (Graphics Processing Unit based) cluster. The time complexity of the algorithm and the parallel implementation details on the clusters are discussed. We also show the performance scaling for increasing Hamiltonian matrix size and increasing number of nodes, respectively. The performance evaluation indicates that for a 32 3 Hamiltonian a single GPU shows higher performance equivalent to more than 30 CPU cores parallelized using MPI.
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