From the 1 of 11 linked papers with an AI index.
11 papers
Regularity-informed data assimilation: A hierarchical Bayesian approach to ensemble Kalman filtering for hyperbolic conservation laws
Jan Glaubitz, Daniel Sharp, Mathieu le Provost +1
We propose a novel regularity-informed filtering framework for data assimilation in the context of hyperbolic conservation laws and other time-dependent partial differential equati…
Gaussian FSBP operators: Comparison and application to numerical methods for hyperbolic conservation laws
Jan Glaubitz, Henry Haase, Philipp Ãffner +1
The paper compares open and closed function-space summation-by-parts (FSBP) operators built with generalized Gaussian quadrature and introduces exact extrapolation operators for op…
Efficient sampling for sparse Bayesian learning using hierarchical prior normalization
Jan Glaubitz, Youssef Marzouk
We introduce an approach for efficient Markov chain Monte Carlo (MCMC) sampling for challenging high-dimensional distributions in sparse Bayesian learning (SBL). The core innovatio…
Preserving linear invariants in ensemble filtering methods
Mathieu Le Provost, Jan Glaubitz, Youssef Marzouk
Data assimilation combines dynamical models with observations to improve state estimates. Ensemble filters sequentially assimilate observations by updating a set of samples over ti…
Why summation by parts is not enough
Jan Glaubitz, Armin Iske, Joshua Lampert +1
We investigate the construction and performance of summation-by-parts (SBP) operators, which offer a powerful framework for the systematic development of structure-preserving numer…
Towards provable energy-stable overset grid methods using sub-cell summation-by-parts operators
Jan Glaubitz, Joshua Lampert, Andrew R. Winters +1
Overset grid methods handle complex geometries by overlapping simpler, geometry-fitted grids to cover the original, more complex domain. However, ensuring their stability -- partic…