Block-structured adaptive mesh refinement (AMR) is a mature technology that provides the basis for the temporal and spatial discretization strategy for a large number of DOE applications. AMR reduces the computational cost and memory footprint compared to a uniform mesh while preserving the essential local descriptions of multiphysics algorithms that represent the different physical processes. Locally structured meshing, even with AMR and/or mapped multiblock, allows the researcher to focus on advanced temporal and spatial discretizations for complex multiphysics applications rather than on mesh creation. AMR also provides a natural framework for hierarchical parallelism.
A principal focus for the SciDAC-4 structured mesh work is the development and deployment of high-order accurate (fourth-order or greater) discretizations. High-order methods have the potential for providing higher accuracy per computational degree of freedom than the traditional second-order accurate methods used in most production versions of AMR. In addition, the amount of floating-point work performed per unit of data motion increases with the order of accuracy of the method, enabling more effective use of current and next-generation HPC computers. Higher-order accurate methods for structured meshes have been the target of a considerable research effort over the last decade.
Specific SciDAC-4 application projects that directly benefit from the FASTMath structured mesh work include the TEAMS (Towards Exascale Astrophysics of Mergers and Supernovae) project supported by the DOE Office of Nuclear Physics, the PRoSPect (Probabalistic Sea-Level Projections from Ice Sheet and Earth System Models) project supported by the DOE Office of Basic Energy
Research, and the ComPASS4 (Community Project for Accelerator Science and Simulation) supported by the DOE Office of High Energy Physics.