3 papers
math.NA2026
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…
math.NA2026
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…
math.AP2025
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…