CMG Collaborative Research: Fast and Efficient Radial Basis Function Algorithms for Geophysical Modeling on Arbitrary Geometries

CMG 协作研究：任意几何形状地球物理建模的快速高效径向基函数算法

• 批准号: 0934330
• 负责人: Louise Kellogg
• 金额: $ 20万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0934330&HistoricalAwards=false
• 关键词: CMG; Collaborative; Research; Fast; Efficient

Numerical method innovations in the geosciences have not paralleled theexplosion in computer hardware development over the last decades. Yet, forscientific computing to advance, it is crucial that novel numericalapproaches are developed that improve the simplicity, flexibility, andaccuracy of algorithms while taking advantage of this revolution in hardwaretechnology. The current project is aimed at exactly that objective: todevelop fast, efficient and parallelizable radial basis function (RBF)methodologies, enhanced by novel graphics processing unit (GPU) technology,for applications in computational geosciences. A collaborative team ofcomputational mathematicians and geophysicists has been established for thispurpose. The RBF approach is very attractive in that it achieves high-orderaccuracy for arbitrary geometries in n-dimensional space, naturally permitslocal refinement, is mesh-free (no grids), algorithmic complexity does notincrease with dimension and, generally offers higher accuracy with longertime steps than traditional spectral methods for a given number of nodes.However, RBFs are still in an early developmental stage; key issues to beaddressed are: 1) development of localized high-order RBF-finite difference(RBF-FD) stencils on irregular node layouts in n-dimensional space forarbitrary geometries with stable time-stepping, 2) adaptive local noderefinement schemes for RBF-FD, 3) development of hybrid spectral RBF and FDschemes to maximize advantages of RBFs and while minimizing theircomputational cost, and 4) implementation of the method on hardwareaccelerators, such as GPUs. Scientific targets for application include 3Dmantle convection with varying properties, models of the geodynamo in anelliptic geometry, and tsunami modeling with irregular coastline topography.By advancing the frontier of computational mathematics that will takeadvantage of today?s booming technology industry, society can be offered amore in depth understanding of geophysical processes related to mantleconvection, the geodynamo, and tsunamis. These phenomena play a key role incontinental movement, polarity reversal of the earth?s magnetic field,earthquakes, and coastal flooding. The proposed innovative mathematicalcomputational approach may hold the key to unlocking long-standing questions of fundamental importance in such geophysics areas. An interdisciplinary collaborative team of computational mathematicians and geophysicists has been assembled from a national lab and four universities (NCAR-Colorado, Boise State Univ.-Idaho, Univ. of Minnesota, Florida State Univ., and the Univ. of California?Davis) to develop new methods in computational mathematics for addressing these critical geophysical problems. The project supports collaborative participation among researchers at different stages in their careers as well as Ph.D, Masters, and undergraduate students in 4 states and in a myriad of scientific and mathematical disciplines. These students will have the opportunity to participate as members of an interdisciplinary team composed of senior personnel with a demonstrated commitment to education and research. NCAR will serve not only as an integrating hub for scientific endeavors but provide a medium for students from across the country to work together on multiple facets of the proposal. Through the SciPARCS 10 week internship program at NCAR, students will have the opportunity to engage in joint collaborative research, preparing them for a career in computational geosciences for the 21st century.

在过去的几十年里，地球科学中数值方法的创新并没有取代计算机硬件的爆炸式发展。然而，对于科学计算的进步，至关重要的是，新的数值方法的发展，提高简单性，灵活性和准确性的算法，同时利用这一革命的硬件技术。目前的项目正是针对这一目标：开发快速，高效和可并行的径向基函数（RBF）方法，增强了新的图形处理单元（GPU）技术，在计算地球科学的应用。一个由计算数学家和计算机科学家组成的协作小组已经为此目的建立起来。径向基函数方法是非常有吸引力的，因为它实现了n维空间中任意几何形状的高阶精度，自然无需局部加密，是无网格的（无网格），算法复杂度不随维数增加而增加，并且对于给定的节点数，通常比传统的谱方法提供更高的精度和更长的时间步长。然而，径向基函数仍处于早期发展阶段;需要解决的关键问题是：1）在n维空间不规则节点布局上发展具有稳定时间步长的局部高阶RBF有限差分（RBF-FD）格式，2）RBF-FD的自适应局部节点细化方案，3）发展混合谱RBF和FD方案，以最大化RBF的优势，同时最小化其计算成本，4）在硬件加速器（如GPU）上实现该方法。应用的科学目标包括具有不同属性的3D地幔对流，椭圆几何中的地球发电机模型，以及具有不规则海岸线地形的海啸建模。随着科技产业的蓬勃发展，社会可以更深入地了解与地幔对流、地球发电机和海啸有关的地球物理过程。这些现象在大陆运动、地球极性反转中起着关键作用。的磁场，地震和沿海洪水。所提出的创新的计算方法可能是解开这些物理学领域长期存在的具有根本重要性的问题的关键。一个由计算数学家和数学家组成的跨学科合作小组已经从一个国家实验室和四所大学（NCAR科罗拉多大学，博伊西州立大学-爱达荷州，明尼苏达大学，佛罗里达州立大学，和加州大学呢？戴维斯）开发新的计算数学方法来解决这些关键的地球物理问题。该项目支持研究人员在职业生涯的不同阶段以及博士，硕士和本科生在4个州和无数的科学和数学学科的协作参与。这些学生将有机会作为一个跨学科团队的成员参加，该团队由对教育和研究有明确承诺的高级人员组成。NCAR不仅将成为科学工作的综合中心，还将为来自全国各地的学生提供一个在提案的多个方面共同合作的媒介。通过SciPARCS在NCAR为期10周的实习计划，学生将有机会参与联合合作研究，为他们在21世纪世纪的计算地球科学职业生涯做好准备。