Advances and Challenges in Computational Partial Differential Equations

This weeklong workshop, Advances and Challenges in Computational Partial Differential Equations, will bring together leading experts and emerging researchers to rethink and further advance the design, analysis, and implementation of modern partial differential equation solvers in regimes that remain challenging for existing methods. While many of the foundational numerical ideas are well established, their modern deployment in high-dimensional, data-rich, and multiphysics environments raises fundamentally new mathematical questions including maintaining nonlinear internal stability in under-resolved simulations, entropy convergence in long-time simulations, the coupling of adaptive meshes and reduced models, and computational scalability on next-generation architectures. The workshop will highlight both the theoretical advances and computational innovations addressing these challenges, and discuss emergent challenges in the field.

Topics: Partial Differential Equations