Algorithm Design and Analysis for High Order Numerical Methods

高阶数值方法的算法设计与分析

基本信息

  • 批准号:
    1112700
  • 负责人:
  • 金额:
    $ 35.43万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2011
  • 资助国家:
    美国
  • 起止时间:
    2011-08-01 至 2015-07-31
  • 项目状态:
    已结题

项目摘要

In this project, research in the algorithm design and analysis of high order numerical methods, including the finite difference and finite volume weighted essentially non-oscillatory (WENO) schemes and discontinuous Galerkin finite element methods, for solving hyperbolic and other convection dominated partial differential equations, will be carried out. While the emphasis of this project is on algorithm design and analysis, close attention will be paid to efficient parallel implementation and applications. The intellectual merit of the proposed activity lies in its comprehensive coverage of algorithm development, analysis, implementation and applications. Problems in applications motivate the design of new algorithms or new features in existing algorithms; mathematics tools are used to analyze these algorithms to give guidelines for their applicability and limitations; practical considerations including parallel implementation issues are addressed to make the algorithms competitive in large scale calculations; and collaborations with engineers and other applied scientists enable the efficient application of these new algorithms or new featuresin existing algorithms.The broader impacts resulting from the proposed activity will be a suite of powerful computational tools, suitable for various applications with involving convection dominated partial differential equations, in adaptive, multiscale and uncertain environments. These tools are expected to make positive contributions to computer simulations of the complicated solution structure in these applications. The application areas include (but are not limited to) computational fluid dynamics, traffic flow problems, semiconductor device simulations, and computational biology. Graduate students will be involved in this project, and will get training in performing mathematics research on problems closely related to applications. Special attention will be paid to the recruitment and training of Ph.D. students from under-represented groups including women.
本计划将研究高阶数值方法的演算法设计及分析,包括求解双曲型及其他对流占优偏微分方程的有限差分及有限体积加权基本无振荡(韦诺)格式及间断Galerkin有限元法。 虽然这个项目的重点是算法的设计和分析,密切关注将支付有效的并行实现和应用。拟议活动的智力价值在于其全面涵盖算法开发、分析、实施和应用。 应用中的问题激发了新算法或现有算法的新功能的设计;数学工具被用来分析这些算法,以给出它们的适用性和局限性的指导方针;包括并行实现问题在内的实际考虑被解决,以使算法在大规模计算中具有竞争力;以及与工程师和其他应用科学家的合作,使这些新算法或现有算法的新功能得到有效应用。活动将是一套强大的计算工具,适用于各种应用,涉及对流主导偏微分方程,在自适应,多尺度和不确定的环境。 这些工具预计将作出积极的贡献,在这些应用程序中的复杂的解决方案结构的计算机模拟。 应用领域包括(但不限于)计算流体动力学、交通流问题、半导体器件模拟和计算生物学。研究生将参与该项目,并将在与应用密切相关的问题上进行数学研究方面得到培训。 将特别注意博士的招聘和培训。包括妇女在内的代表性不足群体的学生。

项目成果

期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)

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Chi-Wang Shu其他文献

Improvement of convergence to steady state solutions of Euler equations with weighted compact nonlinear schemes
用加权紧致非线性格式改进欧拉方程稳态解的收敛性
  • DOI:
    10.1007/s10255-013-0230-6
  • 发表时间:
    2013-07
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Shuhai Zhang, Meiliang Mao;Chi-Wang Shu
  • 通讯作者:
    Chi-Wang Shu
Stability of high order finite difference schemes with implicit-explicit time-marching for convection-diffusion and convection-dispersion equations
对流扩散和对流色散方程隐式-显式时间推进高阶有限差分格式的稳定性
A high order positivity-preserving polynomial projection remapping method
一种高阶保正多项式投影重映射方法
  • DOI:
    10.1016/j.jcp.2022.111826
  • 发表时间:
    2023-02
  • 期刊:
  • 影响因子:
    4.1
  • 作者:
    Nuo Lei;Juan Cheng;Chi-Wang Shu
  • 通讯作者:
    Chi-Wang Shu
Optimal error estimates to smooth solutions of the central discontinuous Galerkin methods for nonlinear scalar conservation laws
Numerical experiments on the accuracy of ENO and modified ENO schemes

Chi-Wang Shu的其他文献

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{{ truncateString('Chi-Wang Shu', 18)}}的其他基金

High Order Schemes: Bound Preserving, Moving Boundary, Stochastic Effects and Efficient Time Discretization
高阶方案:保界、移动边界、随机效应和高效时间离散化
  • 批准号:
    2309249
  • 财政年份:
    2023
  • 资助金额:
    $ 35.43万
  • 项目类别:
    Standard Grant
High Order Schemes: Robustness, Efficiency, and Stochastic Effects
高阶方案:鲁棒性、效率和随机效应
  • 批准号:
    2010107
  • 财政年份:
    2020
  • 资助金额:
    $ 35.43万
  • 项目类别:
    Standard Grant
Algorithm Development, Analysis, and Application of High Order Schemes
高阶方案的算法开发、分析与应用
  • 批准号:
    1719410
  • 财政年份:
    2017
  • 资助金额:
    $ 35.43万
  • 项目类别:
    Standard Grant
High Order Schemes for Hyperbolic and Convection-dominated Problems
双曲和对流主导问题的高阶方案
  • 批准号:
    1418750
  • 财政年份:
    2014
  • 资助金额:
    $ 35.43万
  • 项目类别:
    Continuing Grant
SCREMS: High order numerical algorithms and their applications
SCEMS:高阶数值算法及其应用
  • 批准号:
    0922803
  • 财政年份:
    2009
  • 资助金额:
    $ 35.43万
  • 项目类别:
    Standard Grant
International Conference on Advances in Scientific Computing; December 2009; Providence, RI
国际科学计算进展会议;
  • 批准号:
    0940863
  • 财政年份:
    2009
  • 资助金额:
    $ 35.43万
  • 项目类别:
    Standard Grant
Efficient High Order Numerical Methods for Convection Dominated Partial Differential
对流主导偏微分的高效高阶数值方法
  • 批准号:
    0809086
  • 财政年份:
    2008
  • 资助金额:
    $ 35.43万
  • 项目类别:
    Continuing Grant
Collaborative Research: High Order Accurate Weighted Essentially Non-Oscillatory Algorithms with Applications to Cosmological Hydrodynamic Simulations
合作研究:高阶精确加权本质非振荡算法及其在宇宙流体动力学模拟中的应用
  • 批准号:
    0506734
  • 财政年份:
    2005
  • 资助金额:
    $ 35.43万
  • 项目类别:
    Standard Grant
High Order Numerical Methods for Wave Phenomena in Adaptive, Multiscale and Uncertain Environments
自适应、多尺度和不确定环境中波动现象的高阶数值方法
  • 批准号:
    0510345
  • 财政年份:
    2005
  • 资助金额:
    $ 35.43万
  • 项目类别:
    Standard Grant
High Order Methods for Linear and Nonlinear Waves
线性和非线性波的高阶方法
  • 批准号:
    0207451
  • 财政年份:
    2002
  • 资助金额:
    $ 35.43万
  • 项目类别:
    Standard Grant

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