To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical c...To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical computation of such models.This efficient solver employs algorithms based on discrete cosine transformations(DCT)or discrete sine transformations(DST)and is not restricted by any spatio-temporal schemes.Our proposed methodology is appropriate for a variety of phase-field models and is especially efficient when combined with flow field systems.Meanwhile,this study has conducted an extensive numerical comparison and found that employing DCT and DST techniques not only yields results comparable to those obtained via the Multigrid(MG)method,a conventional approach used in the resolution of the Poisson equations,but also enhances computational efficiency by over 90%.展开更多
低碳城市试点是我国实施绿色发展战略的重要抓手。为了检验低碳城市试点方案(Low Carbon City Pilot Scheme,LCCPS)对我国城市绿色技术创新水平的直接影响和间接影响,更全面地理解该政策的影响范围和效果,基于2003-2020年中国城市绿色...低碳城市试点是我国实施绿色发展战略的重要抓手。为了检验低碳城市试点方案(Low Carbon City Pilot Scheme,LCCPS)对我国城市绿色技术创新水平的直接影响和间接影响,更全面地理解该政策的影响范围和效果,基于2003-2020年中国城市绿色专利授权数据构建了空间双重差分模型(Spatial Difference-in-Difference,SDID)。结果表明:①低碳城市试点政策能够显著促进本地城市绿色技术创新,却对邻近城市绿色技术创新具有抑制作用。②相对于中部、西部、东北地区,低碳城市试点政策对我国东部地区的绿色技术创新水平的影响最大。③低碳城市试点政策对城市规模大的地区的绿色创新技术水平有更强的促进作用,同时城市规模大的城市对邻近地区绿色技术创新有着明显的促进作用。与资源型城市相比,非资源型城市通过实施低碳城市试点政策可以更好地推动绿色创新技术的研发,且资源型城市对其邻近地区绿色技术创新有显著的抑制作用。④机理分析表明,科技人才、绿色财政支持、绿色投资是低碳城市试点政策影响城市绿色技术创新的机制路径。展开更多
基金Supported by Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)+3 种基金National Natural Science Foundation of China(12301556)Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)Basic Research Plan of Shanxi Province(202203021211129)。
文摘To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical computation of such models.This efficient solver employs algorithms based on discrete cosine transformations(DCT)or discrete sine transformations(DST)and is not restricted by any spatio-temporal schemes.Our proposed methodology is appropriate for a variety of phase-field models and is especially efficient when combined with flow field systems.Meanwhile,this study has conducted an extensive numerical comparison and found that employing DCT and DST techniques not only yields results comparable to those obtained via the Multigrid(MG)method,a conventional approach used in the resolution of the Poisson equations,but also enhances computational efficiency by over 90%.
文摘低碳城市试点是我国实施绿色发展战略的重要抓手。为了检验低碳城市试点方案(Low Carbon City Pilot Scheme,LCCPS)对我国城市绿色技术创新水平的直接影响和间接影响,更全面地理解该政策的影响范围和效果,基于2003-2020年中国城市绿色专利授权数据构建了空间双重差分模型(Spatial Difference-in-Difference,SDID)。结果表明:①低碳城市试点政策能够显著促进本地城市绿色技术创新,却对邻近城市绿色技术创新具有抑制作用。②相对于中部、西部、东北地区,低碳城市试点政策对我国东部地区的绿色技术创新水平的影响最大。③低碳城市试点政策对城市规模大的地区的绿色创新技术水平有更强的促进作用,同时城市规模大的城市对邻近地区绿色技术创新有着明显的促进作用。与资源型城市相比,非资源型城市通过实施低碳城市试点政策可以更好地推动绿色创新技术的研发,且资源型城市对其邻近地区绿色技术创新有显著的抑制作用。④机理分析表明,科技人才、绿色财政支持、绿色投资是低碳城市试点政策影响城市绿色技术创新的机制路径。
