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

偏微分方程是对许多物理现象进行精确数学描述的理想方法。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冒险。该项目旨在开发新的计算方法来解决时变偏微分方程。这项研究将在奥克兰大学进行，由著名的时间整合方案专家John Butcher博士指导。这些新方法将推动计算科学的发展，允许使用更少资源的更精确的物理模型。一般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、多阶段的方法。当采用自适应阶跃和阶序变化策略时，一般线性方法始终优于竞争的龙格-库塔和线性多步方案。这项拨款将资助研究开发一种新的高阶时间积分器的自适应时间步进代码，这种代码可以用一般线性方法表示。这些新方案旨在利用现有的并行计算机体系结构，并将纳入新的自适应步骤和顺序变化策略。该奖项由美国国家科学基金会和新西兰皇家学会共同资助，隶属于东亚和太平洋暑期研究所项目，支持一名美国研究生进行暑期研究。

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.