12 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 Unified Two-Grid Framework for Anderson Acceleration and Nonlinear GMRES
James Adler, Yunhui He, Xiaozhe Hu +1
In this work, we recast two widely used acceleration methods for fixed-point iterations, Anderson acceleration (AA) and the nonlinear generalized minimal residual method (NGMRES),…
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…
A unified spatiotemporal formulation with physics-preserving structure for time-dependent convection-diffusion problems
James H. Adler, Xiaozhe Hu, Seulip Lee
We propose a unified four-dimensional (4D) spatiotemporal formulation for time-dependent convection-diffusion problems that preserves underlying physical structures. By treating ti…
Error Estimates for the Arnoldi Approximation of a Matrix Square Root
James H. Adler, Xiaozhe Hu, Wenxiao Pan +1
The Arnoldi process provides an efficient framework for approximating functions of a matrix applied to a vector, i.e., of the form , by repeated matrix-vector multiplic…
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…
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…
Robust preconditioners for a new stabilized discretization of the poroelastic equations
James H. Adler, Francisco J. Gaspar, Xiaozhe Hu +3
In this paper, we present block preconditioners for a stabilized discretization of the poroelastic equations developed in [45]. The discretization is proved to be well-posed with r…
Robust Solvers for Maxwell's Equations with Dissipative Boundary Conditions
James H. Adler, Xiaozhe Hu, Ludmil T. Zikatanov
In this paper, we design robust and efficient linear solvers for the numerical approximation of solutions to Maxwell's equations with dissipative boundary conditions. We consider a…