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; 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.

在过去几十年中，地球科学中的数值方法创新与计算机硬件开发中的示例没有平行。然而，有效的计算要推进，至关重要的是，开发出新的数值透镜，从而提高了算法的简单性，灵活性和准确性，同时利用这场革命的硬性技术。当前的项目旨在确切的目标：快速，高效且可行的径向基函数（RBF）方法，通过新型图形处理单元（GPU）技术增强了计算地球科学的应用。为此，已经建立了一个合作的计算机数学家和地球物理学家的团队。 RBF方法非常有吸引力，因为它可以在n维空间中实现高阶准确度，自然允许无定位的细化（无网格）（无网格），算法的复杂性无需限制，并且通常会与传统的光谱方法相比，与传统的频谱方法相比，具有更高的准确性。 阶段; 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 RBF并最大程度地减少其计算成本，以及4）在HardwareAccelerator（例如GPU）上实施该方法。应用的科学目标包括具有不同属性的3DMantle对流，Anelliptic几何形状中的地球魔术模型以及具有不规则海岸线形态的海啸建模。通过推进计算机数学的边界，这些界限将在今天的繁荣技术行业中提高与地球的繁荣相关的过程，并将其与Geody omore in emearys Insection and geoyys and geoly and geolysions提供。海啸。这些现象起着关键的作用，寡地运动，地球磁场的极性逆转，地震和沿海洪水。拟议的创新数学计算方法可能是解锁此类地球物理领域基本重要性的长期问题的关键。一个跨学科数学家和地球物理学家的跨学科合作团队已从国家实验室和四个大学（Ncar-Colorado，Boise State Univ.-Idaho，Univ。该项目支持研究人员在职业生涯中的不同阶段以及在四个州以及无数科学和数学学科的博士学位，硕士和本科生的合作参与。这些学生将有机会参加由高级人员组成的跨学科团队的成员，并表现出对教育和研究的承诺。 NCAR不仅将作为科学努力的集成枢纽，而且还为来自全国各地的学生提供媒介，以在提案的多个方面共同努力。通过在NCAR的10周实习计划的SCIPARCS，学生将有机会参与共同的合作研究，为他们为21世纪的计算地球科学事业做好准备。