128 citations · 513 across the 59 of their papers we have counts for
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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…