Adaptive and Multiscale Discretization

The modeling of fusion energy systems, ice sheets, and particle accelerators must resolve physics over orders of magnitude in both space and time.  The Adaptive and Multiscale Discretization team develops and deploys technologies capable of providing accurate solutions to multiscale problems using architecture-aware methods that effectively execute on systems from CPU-only laptops to GPU-accelerated supercomputers.

• Adaptive discretization methods are key to ensuring accurate and efficient predictions of quantities of interest from simulations.  Our research activities include:

  • Developing high-order discontinuous Petrov Galerkin methods to produce well-conditioned systems allowing application of efficient iterative solvers for applications currently requiring the use of direct solvers. 

  • Enhancing embedded boundary cut cell and staggered mesh methods to improve the ability of efficient structured mesh methods to address problems over complex domains.

  • Advancing AI-based, physics informed, equation preconditioners to speed adaptive solution using iterative methods.

  • Applying Bayesian UQ tools to enable applications to define problem-specific error norms that can drive selection of time integrators within adaptive spatial and temporal adaptive workflows.

  • Developing GPU based dynamic load balancing technologies to control load balance during adaptive simulations.

• Multiscale discretization develops models and algorithms that greatly enhance the ability of our software to effectively perform multiscale simulations.  Our research activities include:

  • Developing multi-level-aware time integration methods to enable time-stepping strategies that leverage multi-resolution hierarchies.

  • Extending multi-rate integration approaches to enable higher order methods. Investigate neural ODEs to approximate fast dynamics for surrogate-accelerated multi-rate integration.

  • Developing implicit-explicit and multi-rate integration MRI methods that ensure first-principles accuracy and predictive ability and that leverage scientific AI data-driven techniques.

  • Developing efficiently multiscale couple methodologies that ensure the accuracy of the coupled simulation workflow while supporting the coupling of existing physics simulation codes acting at different scales and using different discretization methods.

Our solvers capabilities are delivered to SciDAC Partnerships via our packages available through the FASTMath Software Catalog.