1 citations · 4 across the 15 of their papers we have counts for
16 papers
Quantitative homogenization and large-scale regularity for nondivergence-form equations under a critical ellipticity moment
Jizu Huang, Yong Ma
We prove quantitative homogenization estimates for linear elliptic equations in nondivergence form with stationary, symmetric coefficients, finite range of dependence, and a determ…
A two-dimensional structural local-defect theory for scalar non-divergence advection-diffusion homogenization
Jizu Huang, Yong Ma
We develop a two-dimensional structural local-defect theory for scalar non-divergence advection--diffusion operators \(Lu=-a:D^2u+b\cdot\nabla u\), where \(a=a^{\mathrm{per}}+a^e\)…
PI-DOSnet: A Physics-Informed Deep Operator-Splitting Network for Evolution Partial Differential Equations
Jizu Huang, Yue Qian, Tao Zhou
Evolution partial differential equations (PDEs) describe time-dependent physical systems governed by differential laws and arise widely across science and engineering. In recent ye…
Low Stage and High Order Explicit Runge--Kutta Methods via - and -Conditions: Several Construction Details
Junyuan He, Jizu Huang
This note provides additional details on the construction of the /-space framework for sufficient order conditions of explicit Runge--Kutta (ERK) methods. Specifically, it pr…
Frequency-adaptive tensor neural networks for high-dimensional multi-scale problems
Jizu Huang, Yue Qiu, Rukang You
Tensor neural networks (TNNs) have demonstrated their superiority in solving high-dimensional problems. However, similar to conventional neural networks, TNNs are also influenced b…
Derivation of Runge--Kutta Order Conditions via Functional Tree Tensor Networks
Junyuan He, Zhonghao Sun, Jizu Huang
Tree tensor networks (TTNs) provide a compact and structured representation of high-dimensional data, making them valuable in various areas of computational mathematics and physics…
HaTT: Hadamard avoiding TT recompression
Zhonghao Sun, Jizu Huang, Chuanfu Xiao +1
The Hadamard product of tensor train (TT) tensors is a fundamental nonlinear operation in scientific computing and data analysis. However, due to its tendency to significantly incr…
APTT: An accuracy-preserved tensor-train method for the Boltzmann-BGK equation
Zhitao Zhu, Chuanfu Xiao, Kejun Tang +2
Solving the Boltzmann-BGK equation with traditional numerical methods suffers from high computational and memory costs due to the curse of dimensionality. In this paper, we propose…
CPAFT: A Consistent Parallel Advancing Front Technique for Unstructured Triangular/Tetrahedral Mesh Generation
Chengdi Ma, Jizu Huang, Hao Luo +1
Compared with the remarkable progress made in parallel numerical solvers of partial differential equations,the development of algorithms for generating unstructured triangular/tetr…
A robust two-level overlapping preconditioner for Darcy flow in high-contrast media
Changqing Ye, Shubin Fu, Eric T. Chung +1
In this article, a two-level overlapping domain decomposition preconditioner is developed for solving linear algebraic systems obtained from simulating Darcy flow in high-contrast…
An efficient multiscale multigrid preconditioner for Darcy flow in high-contrast media
Changqing Ye, Shubin Fu, Eric T. Chung +1
In this paper, we develop a multigrid preconditioner to solve Darcy flow in highly heterogeneous porous media. The key component of the preconditioner is to construct a sequence of…
Parallel energy stable phase field simulations of Ni-based alloys system
Jizu Huang, Chao Yang
In this paper, we investigate numerical methods for solving Nickel-based phase field system related to free energy, including the elastic energy and logarithmic type functionals. T…
Parallel energy-stable solver for a coupled Allen-Cahn and Cahn-Hilliard system
Jizu Huang, Chao Yang, Ying Wei
In this paper, we study numerical methods for solving the coupled Allen-Cahn/Cahn-Hilliard system associated with a free energy functional of logarithmic type. To tackle the challe…
High order fast algorithm for the Caputo fractional derivative
Kun Wang, Jizu Huang
In the paper, we present a high order fast algorithm with almost optimum memory for the Caputo fractional derivative, which can be expressed as a convolution of with the ke…
Mathematical and numerical analysis of the time-dependent Maxwell--Schrödinger Equations in the Coulomb gauge
Chupeng Ma, Liqun Cao, Jizu Huang +1
In this paper, we consider the initial-boundary value problem for the time-dependent Maxwell--Schrödinger equations in the Coulomb gauge. We first prove the global existence of wea…
Parallel energy-stable phase field crystal simulations based on domain decomposition methods
Ying Wei, Chao Yang, Jizu Huang
In this paper, we present a parallel numerical algorithm for solving the phase field crystal equation. In the algorithm, a semi-implicit finite difference scheme is derived based o…