128 citations · 513 across the 59 of their papers we have counts for
64 papers
A variational model of nonlinear poroelasticity
James H. Adler, Xiaozhe Hu, Arkadz Kirshtein
We derive a thermodynamically-consistent model of fluid flow through a poroelastic medium. Starting from elastic and fluid free-energy densities, an energy-dissipation rate, and a…
A Counterexample to a Problem of Pommerenke on Convex Functions in the Class
Yuankai Guo, Xiaozhe Hu
Let denote the class of functions that are analytic and univalent in the exterior unit disk . In 19…
Quantum-inspired methods for finite-element discretizations of the high-dimensional Poisson equation
Xue Wang, James H. Adler, Xiaozhe Hu
In recent years, quantum linear system algorithms have been applied to partial differential equations (PDEs), particularly in high-dimensional settings, demonstrating an exponentia…
Parameter-robust Preconditioners for the Stokes-Darcy Coupled Problem without Fractional Operators
Wietse M. Boon, Xiaozhe Hu, Xue Wang
We consider the Stokes-Darcy coupled problem, which models the interaction between free-flow and porous medium flow. By enforcing the normal flux continuity interface condition dir…
Oscillation-free numerical schemes for Biot's model and their iterative coupling solution
Álvaro Pé de la Riva, Francisco J. Gaspar, Xiaozhe Hu +3
In this work, we present a new stabilization method aimed at removing spurious oscillations in the pressure approximation of Biot's model for poroelasticity with low permeabilities…
Physics-informed nonlinear vector autoregressive models for the prediction of dynamical systems
James H. Adler, Samuel Hocking, Xiaozhe Hu +1
Machine learning techniques have recently been of great interest for solving differential equations. Training these models is classically a data-fitting task, but knowledge of the…
Improving Greedy Algorithms for Rational Approximation
James H. Adler, Xiaozhe Hu, Xue Wang +1
When developing robust preconditioners for multiphysics problems, fractional functions of the Laplace operator often arise and need to be inverted. Rational approximation in the un…
A Local Fourier Analysis for Additive Schwarz Smoothers
Álvaro Pé de la Riva, Carmen Rodrigo, Francisco J. Gaspar +3
In this work, a local Fourier analysis is presented to study the convergence of multigrid methods based on additive Schwarz smoothers. This analysis is presented as a general frame…
Algebraic multigrid methods for metric-perturbed coupled problems
Ana Budisa, Xiaozhe Hu, Miroslav Kuchta +2
We develop multilevel methods for interface-driven multiphysics problems that can be coupled across dimensions and where complexity and strength of the interface coupling deteriora…
Parameter-free preconditioning for nearly-incompressible linear elasticity
James H Adler, Xiaozhe Hu, Yuwen Li +1
It is well known that via the augmented Lagrangian method, one can solve Stokes' system by solving the nearly incompressible linear elasticity equation. In this paper, we show that…
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…
Structure-Preserving Discretization of Fractional Vector Calculus using Discrete Exterior Calculus
Alon Jacobson, Xiaozhe Hu
Fractional vector calculus is the building block of the fractional partial differential equations that model non-local or long-range phenomena, e.g., anomalous diffusion, fractiona…
Rational approximation preconditioners for multiphysics problems
Ana Budisa, Xiaozhe Hu, Miroslav Kuchta +2
We consider a class of mathematical models describing multiphysics phenomena interacting through interfaces. On such interfaces, the traces of the fields lie (approximately) in the…
Solving Graph Laplacians via Multilevel Sparsifiers
Xiaozhe Hu, Junyuan Lin
We consider effective preconditioners for solving Laplacians of general weighted graphs. Theoretically, spectral sparsifiers (SSs) provide preconditioners of optimal computational…
Pressure-robust enriched Galerkin methods for the Stokes equations
Xiaozhe Hu, Seulip Lee, Lin Mu +1
In this paper, we present a pressure-robust enriched Galerkin (EG) scheme for solving the Stokes equations, which is an enhanced version of the EG scheme for the Stokes problem pro…
A Stable Mimetic Finite-Difference Method for Convection-Dominated Diffusion Equations
James H. Adler, Casey Cavanaugh, Xiaozhe Hu +2
Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated reg…
A Deep Neural Network/Meshfree Method for Solving Dynamic Two-phase Interface Problems
Xingwen Zhu, Xiaozhe Hu, Pengtao Sun
In this paper, a meshfree method using the deep neural network (DNN) approach is developed for solving two kinds of dynamic two-phase interface problems governed by different dynam…
Effective Preconditioners for Mixed-Dimensional Scalar Elliptic Problems
Xiaozhe Hu, Eirik Keilegavlen, Jan M. Nordbotten
Discretization of flow in fractured porous media commonly lead to large systems of linear equations that require dedicated solvers. In this work, we develop an efficient linear sol…
A Multigrid Preconditioner for Spatially Adaptive High-order Meshless Method on Fluid-solid Interaction Problems
Zisheng Ye, Xiaozhe Hu, Wenxiao Pan
We present a monolithic geometric multigrid preconditioner for solving fluid-solid interaction problems in Stokes limit. The problems are discretized by a spatially adaptive high-o…
An Enriched Galerkin Method for the Stokes Equations
Son-Young Yi, Xiaozhe Hu, Sanghyun Lee +1
We present a new enriched Galerkin (EG) scheme for the Stokes equations based on piecewise linear elements for the velocity unknowns and piecewise constant elements for the pressur…
An Efficient High-order Numerical Solver for Diffusion Equations with Strong Anisotropy
David Green, Xiaozhe Hu, Jeremy Lore +2
In this paper, we present an interior penalty discontinuous Galerkin finite element scheme for solving diffusion problems with strong anisotropy arising in magnetized plasmas for f…
Monolithic multigrid for a reduced-quadrature discretization of poroelasticity
James H. Adler, Yunhui He, Xiaozhe Hu +2
Advanced finite-element discretizations and preconditioners for models of poroelasticity have attracted significant attention in recent years. The equations of poroelasticity offer…
Ladder Polynomial Neural Networks
Li-Ping Liu, Ruiyuan Gu, Xiaozhe Hu
Polynomial functions have plenty of useful analytical properties, but they are rarely used as learning models because their function class is considered to be restricted. This work…
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…