Numerical Improvements, Mesh Adaptation and Parameter Identification for Parallel Finite Element Stokes Ice Sheet Modeling

并行有限元斯托克斯冰盖建模的数值改进、网格自适应和参数识别

• 批准号: 1215659
• 负责人: Lili Ju
• 金额: $ 15.76万
• 依托单位: University South Carolina Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-08-01 至 2015-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1215659&HistoricalAwards=false
• 关键词: Numerical; Improvements; Mesh; Adaptation; Parameter

The numerical modeling of land ice evolution has been a subject of growing interest because of the crucial role land ice plays in global sea level and other parts of the climate system. Nonlinear 3D Stokes flow is the gold standard among conceptual models for ice sheet dynamics. The current widely-used shallow-ice, shallow-shelf, L1L2, and higher-order approximations are all obtained as reduced forms of the 3D Stokes model by means of scaling analysis, but in many situations, with an attendant loss of fidelity. The PI has closely collaborated with a team of collaborators on the preliminary development of a parallel finite element nonlinear 3D Stokes dynamical core for ice sheet modeling. The goal of the proposed project is to advance the current finite element Stokes ice sheet model by further studying and enhancing its efficiency, accuracy, usability, and robustness. The PI will first investigate some issues related to the finite element Stokes ice sheet dynamics solver, including analysis and implementation of Newton-based fast iterative methods for treating both rheological and basal boundary condition nonlinearities and an adaptive hybrid discretization scheme for enhancing the local conservation properties in our numerical model. In the ice-sheet model we consider, the Stokes ice sheet dynamics equations are fully coupled to the equation for temperature evolution, thus stable and accurate finite element temperature solver with accuracy commensurate with that of the Stokes solver is desired and will also be developed. It is well-known that the adjoint equation approach allows one to directly obtain accurate solutions for the quantity of interests. The PI will also investigate and develop adjoint equation-based methods for adaptive mesh refinement and identification of basal boundary sliding parameter using goal-oriented optimization approaches.Although numerical ice sheet models have steadily improved in recent years, much work is needed to make them more reliable, efficient and usable at long time and whole ice sheet scales. The enhanced numerical Stokes ice sheet model will achieve high degrees of efficiency and accuracy through the use of high-order accurate adaptive finite element discretization schemes, highly scalable parallel linear and nonlinear system solvers, goal-oriented variable resolution meshing strategies, and effective inverse design for model parameters. The proposed investigation would offer new insights through numerical simulations to the understanding of land ice evolution. The PI will actively disseminate his research results and tested software not only toresearchers in the area but also to much broader communities with interests in numerical methods and computational geophysics through publications, attending meetings, maintaining an informative web-site. The potential impact of the project is very substantial. Direct and transformative innovations resulting from the proposed project will greatly improve computational ice sheet model capabilities in the climate system modeling. In addition, this project will also offer a unique educational opportunity for graduate students with interests in computational and applied mathematics by having them participate in an interdisciplinary research program that combines mathematics, computer science and geological sciences.

由于陆地冰在全球海平面和气候系统其他部分中发挥着至关重要的作用，陆地冰演化的数值模拟已成为人们日益关注的主题。非线性 3D 斯托克斯流是冰盖动力学概念模型的黄金标准。目前广泛使用的浅冰、浅陆架、L1L2和高阶近似都是通过标度分析作为3D Stokes模型的简化形式获得的，但在许多情况下，伴随着保真度的损失。 PI 与合作者团队密切合作，初步开发了用于冰盖建模的并行有限元非线性 3D Stokes 动力核心。该项目的目标是通过进一步研究和提高当前的有限元斯托克斯冰盖模型的效率、准确性、可用性和鲁棒性来推进当前的有限元斯托克斯冰盖模型。 PI将首先研究与有限元斯托克斯冰盖动力学求解器相关的一些问题，包括分析和实现用于处理流变和基础边界条件非线性的基于牛顿的快速迭代方法，以及用于增强数值模型中的局部守恒特性的自适应混合离散方案。在我们考虑的冰盖模型中，斯托克斯冰盖动力学方程与温度演化方程完全耦合，因此需要并且也将开发稳定且精确的有限元温度求解器，其精度与斯托克斯求解器相当。众所周知，伴随方程方法可以直接获得感兴趣数量的精确解。 PI还将研究和开发基于伴随方程的方法，使用面向目标的优化方法进行自适应网格细化和识别基底边界滑动参数。尽管数值冰盖模型近年来稳步改进，但仍需要做大量工作才能使其在长时间和整个冰盖尺度上更加可靠、高效和可用。增强型斯托克斯冰盖数值模型将通过使用高阶精确自适应有限元离散化方案、高度可扩展的并行线性和非线性系统求解器、面向目标的可变分辨率网格划分策略以及模型参数的有效逆设计来实现高效率和高精度。拟议的调查将通过数值模拟为理解陆地冰的演化提供新的见解。 PI 将通过出版物、参加会议、维护信息丰富的网站，积极向该领域的研究人员以及对数值方法和计算地球物理学感兴趣的更广泛的社区传播他的研究成果和测试的软件。该项目的潜在影响非常巨大。拟议项目产生的直接和变革性创新将极大地提高气候系统建模中的计算冰盖模型能力。此外，该项目还将为对计算和应用数学感兴趣的研究生提供独特的教育机会，让他们参与结合数学、计算机科学和地质科学的跨学科研究项目。