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

偏微分方程式是发展许多物理现象的精确数学描述的理想选择。在上个世纪，偏微分方程式的研究已经成长为一项跨学科的冒险，横跨数学、计算、物理、生物、经济学等领域。这个项目寻求开发新的计算方法来求解依赖于时间的偏微分方程组。这项研究将在奥克兰大学的约翰·布彻博士的指导下进行，他是一位著名的时间整合计划专家。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、多阶段方法。当采用自适应步长和阶数改变策略时，一般线性方法的性能始终优于竞争的Runge-Kutta和线性多步方法。这笔拨款将用于研究开发一种适用于一类新的高阶时间积分器的自适应时间推进码，这种积分器可以表示为一般的线性方法。这些新计划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长和顺序改变策略。东亚和太平洋暑期学院计划下的这个奖项支持一名美国研究生的暑期研究，由NSF和新西兰皇家学会联合资助。

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.