33 citations · 47 across the 8 of their papers we have counts for
9 papers · 1 filter
HAZniCS -- Software Components for Multiphysics Problems
Ana Budisa, Xiaozhe Hu, Miroslav Kuchta +2
We introduce the software toolbox HAZniCS for solving interface-coupled multiphysics problems. HAZniCS is a suite of modules that combines the well-known FEniCS framework for finit…
Enforcing exact physics in scientific machine learning: a data-driven exterior calculus on graphs
Nathaniel Trask, Andy Huang, Xiaozhe Hu
As traditional machine learning tools are increasingly applied to science and engineering applications, physics-informed methods have emerged as effective tools for endowing infere…
A finite-element framework for a mimetic finite-difference discretization of Maxwell's equations
James H. Adler, Casey Cavanaugh, Xiaozhe Hu +1
Maxwell's equations are a system of partial differential equations that govern the laws of electromagnetic induction. We study a mimetic finite-difference (MFD) discretization of t…
Modeling, well-posedness and discretization for a class of models for mixed-dimensional problems with high dimensional gap
Erlend Hodneland, Xiaozhe Hu, Jan Martin Nordbotten
In this work, we illustrate the underlying mathematical structure of mixed-dimensional models arising from the composition of graphs and continuous domains. Such models are becomin…
Mixed-Dimensional Auxiliary Space Preconditioners
Ana Budisa, Wietse Boon, Xiaozhe Hu
This work introduces nodal auxiliary space preconditioners for discretizations of mixed-dimensional partial differential equations. We first consider the continuous setting and gen…
Modifying AMG coarse spaces with weak approximation property to exhibit approximation in energy norm
Xiaozhe Hu, Panayot S. Vassilevski
Algebraic multigrid (AMG) coarse spaces are commonly constructed so that they exhibit the so-called weak approximation (WAP) property which is necessary and sufficient condition fo…