6 papers
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…
An adaptive framework for first-order gradient methods
Xiaozhe Hu, Sara Pollock, Zhongqin Xue +1
Gradient methods are widely used in optimization problems. In practice, while the smoothness parameter can be estimated utilizing techniques such as backtracking, estimating the st…
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…
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…
Parameter-robust preconditioner for Stokes-Darcy coupled problem with Lagrange multiplier
Xiaozhe Hu, Miroslav Kuchta, Kent-Andre Mardal +1
In this paper, we propose a parameter-robust preconditioner for the coupled Stokes-Darcy problem equipped with various boundary conditions, enforcing the mass conservation at the i…