Collaborative Research: CMG--Freedom from Coordinate Systems, and Spectral Accuracy with Local Refinement: Radial Basis Functions for Climate and Space-Weather Prediction

径向基函数（RBF）代表了在多维数据空间中进行插值和平滑的强大数学技术。它们在求解时变偏微分方程（PDEs）建模中的应用将由来自亚利桑那州立大学（首席研究员后来转到博伊西州立大学）、科罗拉多大学博尔德分校、密歇根大学和NCAR的数学家和地球科学家组成的多学科小组进行探索。这种新方法用于解决从气候科学到球面几何的浅水方程到日冕动力学等问题的吸引人的特性包括：1)在任意节点位置实现光谱精度和局部网格细化的能力，包括在陡坡事件中的分辨率；2)网格几何独立性允许应用于不规则几何；3)算法简单；4)比竞争光谱方法更高的精度。许多地球科学家感兴趣的是，rbf在球坐标系中的应用将被研究，最初应用于气候和太阳建模。教育拓展将以一个带有教学和应用模块的互动网站为特色。

Radial basis functions (RBF) represent powerful mathematical techniques for interpolation and smoothing in multidimensional data space. Their use in solving time-dependent partial differential equations (PDEs) for modeling is to be explored by a multidisciplinary group of mathematicians and geoscientists from Arizona State (principal investigator later transferred to Boise State University), University of Colorado Boulder, University of Michigan, and NCAR. Attractive attributes of this new methodology for use in problems ranging from climate science, to shallow water equations in spherical geometry to solar corona dynamics include: i) the ability to achieve spectral accuracy and local mesh refinement at arbitrary node locations including resolution in steep-gradient events, ii) grid geometry independence allowing application to irregular geometries, iii) algorithmic simplicity, and iv) higher accuracy than competing spectral methods. Of interest to many geoscientists, applications of RBFs in spherical coordinate systems will be investigated, with initial applications to climate and solar modeling. Educational outreach will feature an interactive web-site with instructional and applications modules.