Hosted here are a series of increasingly sophisticated hands-on lessons aimed at helping users of all experience levels learn to use a variety of scientific software packages for solving complex numerical problems. We begin with custom, hand-coded solutions to the homogeneous, one-dimensional heat equation to demonstrate basic numerical and performance issues such as accuracy, stability, time to solution, memory, and flops required, along with motivation for the use of numerical software packages to help achieve more robust, efficient, scalable, extensible, and portable software.
We slowly build upon these simple, early examples introducing additional complexities such as inhomogenieties, higher-order solutions, time-variabilities, nonlinearities, and complex geometries in higher dimensions. We demonstrate the use of a variety of numerical software packages to address these issues and the advantages they offer over hand-coded software.
Throughout the currently designed lesson plans, we use the MFEM (unstructured) and AMReX (structured, adaptive) packages as demonstration vehicles. Both of these packages include the basic functional pieces necessary to start from a continuous description of a physical problem to solve, through PDE specification, numerical analysis, discretization, algorithm development and then implementation. In addition, they include essential abstractions to support scalable, parallel expression of the algorithms and to orchestrate the application of various numerical packages in the solution.
In addition, we use PAPI (performance counters) to enable users to observe variations in performance (time and space) as algorithmic choices are varied and VisIt to visualize results.
These initial lessons are a starting point for a growing set of hands-on examples to demonstrate a broad range of numerical software packages.
The packages demonstrated here benefit from many person-years of software development aimed at addressing such issues as extreme scalability and multi-modal parallelism such as message-passing, many-threads and/or GPUs. Numerical results computed with the packages demonstrated here have been vetted over many years of use in a variety of application settings. Nonetheless, because the main focus of these lessons is in introducing how to use these packages, there are likely few specific hands-on lessons here in which there are opportunities to observe these important capabilities of numerical software packages.
See the Contributing Guide for instructions on contributing lessons.