209 citations · 549 across the 39 of their papers we have counts for
46 papers
A scalable domain decomposition method for FEM discretizations of nonlocal equations of integrable and fractional type
Manuel Klar, Giacomo Capodaglio, Marta D'Elia +3
Nonlocal models allow for the description of phenomena which cannot be captured by classical partial differential equations. The availability of efficient solvers is one of the mai…
A Multifidelity Monte Carlo Method for Realistic Computational Budgets
Anthony Gruber, Max Gunzburger, Lili Ju +1
A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of…
Energetically Consistent Model Reduction for Metriplectic Systems
Anthony Gruber, Max Gunzburger, Lili Ju +1
The metriplectic formalism is useful for describing complete dynamical systems which conserve energy and produce entropy. This creates challenges for model reduction, as the elimin…
An asymptotically compatible coupling formulation for nonlocal interface problems with jumps
Christian Glusa, Marta D'Elia, Giacomo Capodaglio +2
We introduce a mathematically rigorous formulation for a nonlocal interface problem with jumps and propose an asymptotically compatible finite element discretization for the weak f…
A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modeling
Anthony Gruber, Max Gunzburger, Lili Ju +1
The popularity of deep convolutional autoencoders (CAEs) has engendered new and effective reduced-order models (ROMs) for the simulation of large-scale dynamical systems. Despite t…
Parallel Exponential Time Differencing Methods for Geophysical Flow Simulations
Rihui Lan, Wei Leng, Zhu Wang +2
Two ocean models are considered for geophysical flow simulations: the multi-layer shallow water equations and the multi-layer primitive equations. For the former, we investigate th…