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内插和平滑的强大数学技术。由来自亚利桑那州立大学、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将探索它们在求解与时间相关的偏微分方程(PDE)建模中的应用。这一新方法用于从气候科学到球面几何中的浅水方程再到太阳日冕动力学等问题，其吸引人的特点包括：i)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；ii)网格几何独立性，允许应用于不规则几何；iii)算法简单；以及iv)比竞争光谱方法更高的精度。许多地球科学家感兴趣的是，将研究RBF在球面坐标系中的应用，并初步应用于气候和太阳模拟。教育外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, 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.