6 papers
A Stabilized Numerical Framework for Necrotic Tumor Growth via Coupled Boundary Integral and Obstacle Solvers
Yu Feng, Shuo Ling, Wenjun Ying +1
We present a robust computational framework for Hele-Shaw tumor growth with necrotic cores, a problem identified as the incompressible limit of the Porous Media Equation. Simulatin…
Mean square error analysis of stochastic gradient and variance-reduced sampling algorithms
Jianfeng Lu, Xuda Ye, Zhennan Zhou
This paper considers mean square error (MSE) analysis for stochastic gradient sampling algorithms applied to underdamped Langevin dynamics under a global convexity assumption. A no…
Statistical Error of Numerical Integrators for Underdamped Langevin Dynamics with Deterministic And Stochastic Gradients
Xuda Ye, Zhennan Zhou
We propose a novel discrete Poisson equation approach to estimate the statistical error of a broad class of numerical integrators for the underdamped Langevin dynamics. The statist…
Efficient bound preserving and asymptotic preserving semi-implicit schemes for the fast reaction-diffusion system
Yu Zhao, Zhennan Zhou
We consider a special type of fast reaction-diffusion systems in which the coefficients of the reaction terms of the two substances are much larger than those of the diffusion term…
Uncertainty Quantification of Phase Transition Problems with an Injection Boundary
Zhenyi Zhang, Shengbo Ma, Zhennan Zhou
We develop an enthalpy-based modeling and computational framework to quantify uncertainty in Stefan problems with an injection boundary. Inspired by airfoil icing studies, we consi…
Optimal Convergence Rate of Lie-Trotter Approximation for Quantum Thermal Averages
Xuda Ye, Zhennan Zhou
The Lie--Trotter product formula is a foundational approximation for the quantum partition function, yet obtaining rigorous error bounds for the unbounded Hamiltonians common in ph…