EAPSI: A New Class of Parallel High-Order Time Integrators

EAPSI：一类新型并行高阶时间积分器

• 批准号: 1614232
• 负责人: Tommaso Buvoli
• 金额: $ 0.54万
• 依托单位: Buvoli Tommaso
• 依托单位国家: 美国
• 项目类别: Fellowship Award
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-06-01 至 2017-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1614232&HistoricalAwards=false
• 关键词: EAPSI; New; Class; Parallel; Order

Partial differential equations are ideal for developing accurate mathematical descriptions for many physical phenomena. In the last century, the study of partial differential equations has grown into an interdisciplinary venture spanning across the fields of mathematics, computation, physics, biology, economics and more. This project seeks to develop new computational methods for solving time-dependent partial differential equations. This research will be conducted at the University of Auckland under the mentorship of Dr. John Butcher, a noted expert on time-integration schemes. These new methods will advance the state of computational science, allowing for more accurate physical models that use fewer resources.General linear methods are powerful extensions of classical time-integration techniques as they allow for multistep, multistage methods. When implemented with adaptive step and order changing strategies, general linear methods consistently outperform competing Runge-Kutta and linear multistep schemes. This grant will fund research to develop an adaptive time-stepping code for a new class of high-order time-integrators which can expressed as general linear methods. These new schemes are designed to leverage existing parallel computer architectures, and will incorporate novel adaptive step and order changing strategies.This award under the East Asia and Pacific Summer Institutes program supports summer research by a U.S. graduate student and is jointly funded by NSF and the Royal Society of New Zealand.

偏微分方程是对许多物理现象进行精确数学描述的理想选择。在上个世纪，偏微分方程的研究已经发展成为跨越数学、计算、物理、生物学、经济学等领域的跨学科事业。该项目旨在开发新的计算方法来求解瞬态偏微分方程。这项研究将在奥克兰大学在著名时间积分方案专家 John Butcher 博士的指导下进行。这些新方法将推进计算科学的发展，允许使用更少的资源建立更准确的物理模型。通用线性方法是经典时间积分技术的强大扩展，因为它们允许多步骤、多阶段方法。当采用自适应步骤和顺序更改策略实施时，通用线性方法始终优于竞争的龙格-库塔和线性多步骤方案。这笔赠款将资助研究为新型高阶时间积分器开发自适应时间步进代码，该代码可以表示为通用线性方法。这些新方案旨在利用现有的并行计算机体系结构，并将纳入新颖的自适应步骤和顺序更改策略。该奖项属于东亚和太平洋夏季研究所计划，支持美国研究生的夏季研究，由 NSF 和新西兰皇家学会。