4 papers · 1 filter
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…
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
Ãlvaro 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…
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…