Parallel, Adaptive Cartesian Grid Algorithms for Natural Hazards Modeling

用于自然灾害建模的并行自适应笛卡尔网格算法

• 批准号: 1819257
• 负责人: Donna Calhoun
• 金额: $ 31.56万
• 依托单位: Boise State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-07-01 至 2023-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1819257&HistoricalAwards=false
• 关键词: Parallel; Adaptive; Cartesian; Grid; Algorithms

Geophysical hazards such as flooding, tsunamis, debris flows, landslides, storm surges and potential dam failures threaten communities across the United States and globally. This project develops computational tools that can efficiently simulate these hazards, enabling a diverse group of researchers and emergency planners to develop hazard maps of areas most likely to be impacted by these disasters. For efficiency, the computational framework uses adaptive, "depth-averaged" mathematical models that only require two dimensional planar grids, rather than fully three dimensional meshes. A primary goal of the project is to correct our depth-averaged model to capture localized waves that may spill over flood barriers or overtop harbor breakwaters. These correction terms will give current users of the computational framework critical additional capabilities for modeling shallow geophysical hazards and allow them to create more robust hazard maps. The computational tools can also take full advantage of emerging hardware trends available on desktop workstations, moderate sized compute clusters, as well as massively parallel computing facilities available at NSF funded supercomputing sites. The project also provides users with tools for visualizing results using open source software such as the Google Earth browser. Ultimately, computational modeling can aid responders in predicting how to distribute emergency resources in the event of unavoidable hazards and serve to inform developers, legislative representatives, and citizenry of potential risks in their communities.The research will focus on the implementation of a direct solver for variable coefficient elliptic problems on adaptively refined quad-tree meshes. The targeted solver is the Hierarchical Poincare Steklov (HPS) solver, developed by A. Gillman and P. Martinsson. Satisfying four crucial properties, this solver (1) has the ease of use of matrix-free methods, (2) can solve nearby systems quickly, (3) has optimal O(N) efficiency, and (4) provides parameters that can be tuned to reduce computational cost in proportion to accuracy requirements. Furthermore, the method uses low rank approximations to compress dense matrices and accelerate matrix computations. In the proposed work, the PI will modify the original HPS solver for use with second order, finite volume schemes and implement the solver in ForestClaw, the parallel, patch-based Cartesian adaptive quad-tree code. The PI will also report on the scalability and parallel efficiency of the implementation of the HPS method. Two technical challenges that will arise are to develop effective procedures for merging Dirichlet-to-Neumann maps across processor boundaries and incrementally updating the solver factorization for dynamically evolving meshes. The targeted application is the solution to the Serre-Green Naghdi equations for modeling dispersive corrections to the shallow water wave equations. These corrections will be included in the GeoClaw extension of ForestClaw. GeoClaw (D. George, R. J. LeVeque, M. J. Berger) is a widely used software package for solving depth-averaged flow equations. The addition of these correction terms to the GeoClaw extension will provide GeoClaw users with critical capabilities for modeling tsunamis, flooding, debris flows, storm surges and other shallow geophysical flows. Ultimately, the proposed solver can be used within the ForestClaw framework as a general purpose elliptic solver for a variety of physical flow phenomena.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

洪水、海啸、泥石流、山体滑坡、风暴潮和潜在的水坝溃决等地球物理灾害威胁着美国和全球的社区。 该项目开发的计算工具可以有效地模拟这些灾害，使不同的研究人员和应急规划人员能够开发最有可能受到这些灾害影响的地区的灾害地图。 为了提高效率，计算框架使用自适应的“深度平均”数学模型，仅需要二维平面网格，而不是完全三维的网格。 该项目的主要目标是纠正我们的深度平均模型，以捕获可能溢出防洪堤或港口防波堤的局部波浪。 这些修正项将为计算框架的当前用户提供模拟浅层地球物理灾害的关键附加功能，并允许他们创建更强大的灾害图。 这些计算工具还可以充分利用桌面工作站、中等规模计算集群以及 NSF 资助的超级计算站点上可用的大规模并行计算设施上的新兴硬件趋势。 The project also provides users with tools for visualizing results using open source software such as the Google Earth browser. 最终，计算模型可以帮助响应者预测在发生不可避免的危险时如何分配应急资源，并告知开发商、立法代表和公民其社区中的潜在风险。该研究将重点关注在自适应细化四树网格上实现变系数椭圆问题的直接求解器。 The targeted solver is the Hierarchical Poincare Steklov (HPS) solver, developed by A. Gillman and P. Martinsson. 该求解器满足四个关键属性，(1) 易于使用无矩阵方法，(2) 可以快速求解附近的系统，(3) 具有最佳的 O(N) 效率，(4) 提供可调整的参数，以根据精度要求按比例降低计算成本。 Furthermore, the method uses low rank approximations to compress dense matrices and accelerate matrix computations. 在拟议的工作中，PI 将修改原始 HPS 求解器以与二阶有限体积方案一起使用，并在 ForestClaw（并行的、基于补丁的笛卡尔自适应四叉树代码）中实现该求解器。 The PI will also report on the scalability and parallel efficiency of the implementation of the HPS method.将出现的两个技术挑战是开发有效的程序来跨处理器边界合并狄利克雷到诺伊曼图，并逐步更新求解器因式分解以动态演化网格。 目标应用是解决 Serre-Green Naghdi 方程，用于对浅水波浪方程的色散校正进行建模。 These corrections will be included in the GeoClaw extension of ForestClaw. GeoClaw (D. George, R. J. LeVeque, M. J. Berger) is a widely used software package for solving depth-averaged flow equations.在 GeoClaw 扩展中添加这些修正项将为 GeoClaw 用户提供模拟海啸、洪水、泥石流、风暴潮和其他浅层地球物理流的关键功能。 最终，所提出的求解器可以在 ForestClaw 框架内用作各种物理流现象的通用椭圆求解器。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优点和更广泛的影响审查标准进行评估，被认为值得支持。