Generalized artificial-time PDE formulations and computational techniques for multi-rate systems

多速率系统的广义人工时间 PDE 公式和计算技术

• 批准号: 0515227
• 负责人: Jaijeet Roychowdhury
• 金额: $ 20万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0515227&HistoricalAwards=false
• 关键词: Generalized; artificial; time; PDE; formulations

A novel theoretical/computational approach, termed the Generalized Multitime Partial Differential Equation (GeMPDE), is being investigated. The chief advantage of the GeMPDE formulation is that it fundamentally enables, speeds up or greatly simplifies theoretical and computational analysis of physical and engineering systems, which feature slow/fast rates of dynamical change separated by many orders of magnitude.Differentiating features and intellectual merits that make the GeMPDE considerably more attractive than existing approaches include: its ability (demonstrated in preliminary results) to perform linearized .AC analysis of oscillatory systems with full generality and rigor (not possible previously); its use of multivariate phase and local frequency variables to yield theoretically and computationally robust system formulations; and its clean separation of disparate rates of variation using separated artificial time variables.Core theoretical and computational tasks being explored include: stochastic GeMPDE analysis, investigation of specialized GeMPDE forms targeting specific application domains, the development of robust GeMPDE-based solvers that adapt automatically to nonlinear systems containing both oscillatory and non-oscillatory components, large signal GeMPDE-based envelope analysis, and applications to periodically forced systems, systems of coupled oscillators and non-periodic autonomous systems.Broader impacts include a strongly linking educational and research components; direct application/validation on electronic circuits (PLLs, SD modulators), nano technological devices (arrays of Josephson junctions and single-electron tunneling devices), and biological systems (networks of firing neurons); and the use of open source methodologies for developing and disseminating prototype code resulting from this research.

正在研究一种新型的理论/计算方法，称为广义多时间偏微分方程（GEMPDE）。 GEMPDE配方的主要优点是，它从根本上实现，加快或极大地简化了对物理和工程系统的理论和计算分析，这些系统具有缓慢/快速的动态变化的速度缓慢/快速的动态变化速率，许多差异的特征和智力功能使Gempde具有相当有吸引力的系统（与现有的能力相比，都可以表现出来：在PRINIMIS中进行分析（包括Prelimimional incormiensiiss in Cornimissions）。具有完全的一般性和严格性（以前是不可能的）；它使用多元相和局部频率变量来产生理论和计算稳健的系统公式；及其使用分离的人造时间变量对变异速率进行清晰分离。探索的理论和计算任务包括：随机GEMPDE分析，针对特定应用领域的专业GEMPDE形式的调查，开发具有鲁棒性Gempde的基于鲁棒的基于GEMPDE的型号，这些基于强大的基于GEMPDE的旋转，这些旋转型均基于非线性的启发和非线性启发，并具有非线性的启发性启发和非线性启发，并具有非线性的非线性启发，并将其定向，以自动分析性启发性和非线性启用量，并且在定期强制系统，耦合振荡器和非周期性自治系统的系统中应用。Boader的影响包括与教育和研究组成部分密切相关的；直接应用/验证电子电路（PLL，SD调节器），纳米技术设备（Josephson连接和单电子隧道设备的阵列）和生物系统（射击神经元网络）；并使用开源方法来开发和传播这项研究产生的原型代码。