Asymptotic-preserving (AP) discretization strategies

To ensure that the numerical representation of the physical systems of interest is able to reproduce continuum singular-limit solutions automatically while avoiding the numerical resolution of small time and length scales associated with the small parameter. We envision a research program that tackles outstanding issues in AP discretizations for both thermal radiation transport and plasma models.

To ensure that the numerical representation of the physical systems of interest is able to reproduce continuum singular-limit solutions automatically while avoiding the numerical resolution of small time and length scales associated with the small parameter.

Structure-preserving (SP) methods

To develop discretizations and reduced order models (ROMs) that preserve physical properties of the continuum model, thereby restricting the numerical solution to physically realizable manifolds. Leveraging our extensive experience in developing SP Eulerian and Lagrangian discretizations, as well as SP ROMs and surrogates, we will expand and deploy these technologies in the products of this {\mmicc}s center, with the goal of enabling trustworthy hierarchies that include surrogates and ROMs that will play a role in accelerating scientific discovery and uncertainty quantification (UQ) assessment.