Research
The NASC RTG's research explores the frontiers of numerical analysis and scientific computing across a range of applications. Examples of RTG research areas include the development of next-generation high-order numerical methods for physics-based simulations, structure-preserving and data-driven reduced order modeling, and large-scale optimization methods for problems governed by differential equations.
NASC researchers collaborate with domain experts from biology, computational neuroscience, and the geosciences in order to understand the specific mathematical and computational challenges arising from each application, and to ultimately provide mathematical and computational tools tailored towards application-specific challenges.
Publications
Chan, Shukla, Wu, Liu, Nalluri (2023). High order entropy stable schemes for the quasi-one-dimensional shallow water and compressible Euler equations
Lin, Chan (2023). High order entropy stable discontinuous Galerkin spectral element methods through subcell limiting
Masri, Shen, Riviere (2023). Discontinuous Galerkin approximations to elliptic and parabolic problems with a Dirac line source
Masri, Liu, Riviere (2023). Improved a priori error estimates for a discontinuous Galerkin pressure correction scheme for the Navier-Stokes equations
Kirk, Masri, Riviere (2023). Numerical analysis of a hybridized discontinuous Galerkin method for the Cahn-Hilliard problem
Grundvig, Heinkenschloss (2023). Line-Search Based Optimization using Function Approximations with Tunable Accuracy.
Diaz, Gosea, Heinkenschloss, Antoulas (2023). Interpolation-Based Model Reduction of Quadratic-Bilinear Dynamical Systems with Quadratic-Bilinear Outputs.
Diaz, Choi, Heinkenschloss (2024). A fast and accurate domain-decomposition nonlinear manifold reduced order model.
Cangelosi, Heinkenschloss, Needels, Alonso (2024). Simultaneous Design and Trajectory Optimization for Boosted Hypersonic Glide Vehicles.
Kritpracha, Riviere, Puelz (2024). Predicting the Effects of Surgically Determined Parameters on Exercise Tolerance in Fontan Patients.
Taylor, Wilcox, Chan (2024). An Energy Stable High-Order Cut Cell Discontinuous Galerkin Method with State Redistribution for Wave Propagation
Celaya, Kirk, Fuentes, Riviere (2024). Solutions to elliptic and parabolic problems via finite difference based unsupervised small linear convolutional neural network.
Kwan, Chan (2024). A robust first order meshless method for time-dependent nonlinear conservation laws