Multirate Time Integration Algorithms for Adaptive Simulations of PDEs

用于偏微分方程自适应模拟的多速率时间积分算法

• 批准号: 0515170
• 负责人: Adrian Sandu
• 金额: $ 18万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-08-15 至 2009-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0515170&HistoricalAwards=false
• 关键词: Multirate; Time; Integration; Algorithms; Adaptive

ABSTRACT0515170 Adrian SanduVirginia Polytechnic Institute and State UniversityMULTIRATE TIME INTEGRATION ALGORITHMS FOR ADAPTIVE SIMULATIONS OF PDESLarge scale simulations of time-dependent partial differential equations (PDEs) often involve grids of multiple resolutions covering different subdomains. When explicit temporal integration is employed, stability requirements restrict the global simulation time step. The time step bound is driven by the finest mesh patch or by the highest wave velocity, and is typically (much) smaller than necessary for other variables in the computational domain. Improvements in the efficiency and overall simulation capabilities require the development of new, adaptive, multirate time integration methods. The development of multirateintegration is challenging due to the conservation and stability constraints which time stepping schemes need to satisfy.The overall goal of the proposed project is to develop efficient time stepping methods for parallel simulation of large-scale time-dependent PDEs. Multirate algorithms will be constructed such that: (1) differenttime steps can be used in different subdomains to achieve efficiency; (2) the methods can be constructed with high order of temporal accuracy; (3) linear and nonlinear stability impose only local restrictions of the stepsize (e.g., local Courant numbers); (4) the methods are conservative; and (5) different methods can be applied to different processes in multi-physics simulations. The research approach is to employ theframework of multirate integration for both Runge-Kutta and linear multistep methods. The multirate integration techniques will inherit the strong stability properties of the corresponding single rate integrators.Moreover, implicit-explicit multirate methods will be constructed, which are appropriate for multiphysics multiscale simulations. The methods will be illustrated in real-life, multi-scale, multi-physics simulationsarising in the prediction of atmospheric pollution.

Adrian Sandu弗吉尼亚理工学院和州立大学偏微分方程自适应模拟的多速率时间积分算法大规模时变偏微分方程（PDE）的模拟通常涉及覆盖不同子域的多分辨率网格。当采用显式时间积分时，稳定性要求限制了全局模拟时间步长。时间步长边界由最精细的网格片或最高的波速驱动，并且通常（远）小于计算域中其他变量所需的时间步长。在效率和整体仿真能力的提高，需要新的，自适应的，多速率时间积分方法的发展。多速率积分的发展是具有挑战性的，由于守恒和稳定性的限制，时间推进计划需要满足。拟议项目的总体目标是发展高效的时间推进方法的并行模拟的大规模时间依赖偏微分方程。 多速率算法将被构造为使得：（1）不同的时间步长可以被用于不同的子域中以实现效率;（2）该方法可以以高阶的时间精度被构造;（3）线性和非线性稳定性仅施加步长的局部限制（例如，本地Courant编号）;（4）方法是保守的;（5）在多物理场模拟中，不同的方法可以应用于不同的过程。 研究方法是采用多速率积分的框架下的Runge-Kutta和线性多步方法。多速率积分技术将继承相应单速率积分器的强稳定性，并构造出适合于多物理场多尺度模拟的隐-显多速率方法。这些方法将在大气污染预测中出现的现实生活中，多尺度，多物理模拟中得到说明。