Exploring the Role of Coarray Fortran for Highly Parallel Structured Adaptive Mesh Refinement Calculations

在结构化网格上进行并行自适应网格加密（AMR）计算在科学和工程的许多领域中起着非常重要的作用。软件和硬件基础设施以及它们所支持的计算能力是相辅相成的。软件基础设施的创新简化了曾经困难的计算问题。该提案的第一个目标是利用最近的一项创新（CoarrayFortran，以下简称CAF）来促进并行AMR的无缝实现。该项目还希望使基于CAF的AMR准备好在NSF上进行PetaScale计算？高端超级计算机。其第二个目标是开发一个高度并行的基于CAF的AMR框架，用于求解椭圆，抛物和双曲偏微分方程。这一探索性建议的结果将是一个小的，功能强大的和轻量级的框架PetaScale类AMR应用程序。首席PI正在编写一本关于“科学家和工程师的数值偏微分方程”的教科书，文本中的几个应用程序将在这个AMR框架中提供。沿着这本书，他还开发了一个网站，通过网站http://www.nd.edu/~dbalsara/Numerical-PDE-Course向任何人免费传播关于偏微分方程的精心制作的讲座。Co-PI正在与CAF的最初发明者合作编写一本关于“用Coarrays进行Fortran并行编程”的书。无论是编写教科书的努力，以及相关的网站开发，将大大提高教育资源提供给先进的本科生和研究生在STEM学科。

Parallel Adaptive Mesh Refinement (AMR) calculations carried out on structured meshes play an exceedingly important role in several areas of science and engineering. Software and hardware infrastructure, and the computational capabilities they enable, go hand in hand. Innovations in software infrastructure simplify once-difficult computational problems. The first goal of this proposal is to capitalize on one such recent innovation (Coarray Fortran, henceforth CAF) in facilitating seamless implementation of parallel AMR. The project further wishes to make CAF-based AMR ready for PetaScale computations on NSF?s high-end supercomputers. Its second goal is to develop a highly parallel CAF-based AMR framework for solving elliptic, parabolic and hyperbolic PDEs. The result of this exploratory proposal will be a small, capable and light-weight framework for PetaScale class AMR applications.The lead PI is writing a textbook on "Numerical PDEs for Scientists and Engineers" and several of the applications from the text will be made available in this AMR framework. Along with the text, he has developed a website that freely disseminates polished lectures on PDEs to anyone over the web -- http://www.nd.edu/~dbalsara/Numerical-PDE-Course . The Co-PI is working with the original inventor of CAF to write a book on "Parallel Programming in Fortran with Coarrays". Both the textbook-writing efforts, as well as the associated website development, will greatly enhance the educational resources available to advanced undergraduates and graduates in STEM disciplines.