Applied Math Seminar | David Del Rey Fernandez, Mathematically rigorous discretizations for high-performance computing

MS Teams

Speaker

David Del Rey Fernandez |  NASA Langley Research Center/National Institute of Aerospace

Title

Mathematically rigorous discretizations for high-performance computing

Abstract

In science and engineering, there has been, for decades, an increasing reliance on numerical simulations to inform scientific discovery and engineering practice. Next-generation high-performance computing (HPC) promises unprecedented compute power that could enable scientific computing to mature into a fully predictive science. However, two fundamental obstacles impede this maturation. First, the unprecedented power of next-generation HPC comes via unprecedented complexity. Second, in order to become predictive, scientific computing requires algorithms that are provably predictive (i.e., provably convergent and endowed with error estimation and uncertainty quantification). In this talk, I will cover past and ongoing research aimed at developing predictive and useful (e.g., efficient) algorithms for HPC. In the first part, I will discuss my contributions to extending the summation-by-parts (SBP) framework, which is a discretization agnostic approach, for the analysis and development of discretizations with provable properties (e.g., stability and conservation). Starting from its finite-difference origins, I will walk through various generalizations of the SBP framework ending with algorithms that are nonlinearly stable (entropy stable) and that are amenable to h/p adaptation, moving mesh problems, and unstructured meshes. In the second half of the talk, I will discuss ongoing and future research directions aimed at developing provably predictive numerical frameworks and associated technologies for efficient deployment on HPC resources. The focus is on frameworks and technologies for broad classes of time-dependent partial differential equations and applications including diffusion-reaction and convection-diffusion-reaction equations (e.g., epidemic modeling), wave equations (e.g., non-destructive testing and ultrasound for medical imaging and intervention), machine learning (e.g., error estimation and mesh adaptation), and the compressible Euler and Navier-Stokes equations (e.g., external aerodynamics).