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

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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.