81 citations · 106 across the 15 of their papers we have counts for
16 papers
Higher-order multiscale method and its convergence analysis for nonlinear thermo-electric coupling problems of composite structures
Hao Dong, Zongze Yang, Yufeng Nie
This paper proposes a higher-order multiscale computational method for nonlinear thermo-electric coupling problems of composite structures, which possess temperature-dependent mate…
Higher-order multi-scale method for high-accuracy nonlinear thermo-mechanical simulation of heterogeneous shells
Hao Dong, Xiaofei Guan, Yufeng Nie
In the present work, we consider multi-scale computation and convergence for nonlinear time-dependent thermo-mechanical equations of inhomogeneous shells possessing temperature-dep…
Self-optimization wavelet-learning method for predicting nonlinear thermal conductivity of highly heterogeneous materials with randomly hierarchical configurations
Jiale Linghu, Hao Dong, Weifeng Gao +1
In the present work, we propose a self-optimization wavelet-learning method (SO-W-LM) with high accuracy and efficiency to compute the equivalent nonlinear thermal conductivity of…
Higher-order multi-scale deep Ritz method for multi-scale problems of authentic composite materials
Jiale Linghu, Hao Dong, Junzhi Cui +1
The direct deep learning simulation for multi-scale problems remains a challenging issue. In this work, a novel higher-order multi-scale deep Ritz method (HOMS-DRM) is developed fo…
Convergence analysis of Jacobi spectral collocation methods for weakly singular nonlocal diffusion equations with volume constraints
Jiashu Lu, Mengna Yang, Yufeng Nie
This paper considers efficient spectral solutions for weakly singular nonlocal diffusion equations with Dirichlet-type volume constraints. The equation we consider contains an inte…
Provably size-guaranteed mesh generation with superconvergence
Xiangrong Li, Nan Qi, Yufeng Nie +1
The properties and applications of superconvergence on size-guaranteed Delaunay triangulation generated by bubble placement method (BPM), are studied in this paper. First, we deriv…
Finite Element Methods for Fractional PDEs in Three Dimensions
Zongze Yang, Zhanbin Yuan, Yufeng Nie +1
This paper is a generalization of the previous work (Yang et.al, J. Comput. Phys. 330 (2017), 863-883) to the 3-D irregular convex domains. The analytical calculation formula of fr…
Superconvergence of Numerical Gradient for Weak Galerkin Finite Element Methods on Nonuniform Cartesian Partitions in Three Dimensions
Dan Li, Yufeng Nie, Chunmei Wang
A superconvergence error estimate for the gradient approximation of the second order elliptic problem in three dimensions is analyzed by using weak Galerkin finite element scheme o…
Multiscale computational method for heat conduction problems of composite structures with diverse periodic configurations in different subdomains
Hao Dong, Junzhi Cui, Yufeng Nie +1
This study develops a novel multiscale computational method for heat conduction problems of composite structures with diverse periodic configurations in different subdomains. First…
Numerical algorithm for two-dimensional time-fractional wave equation of distributed-order with a nonlinear source term
Jiahui Hu, Jungang Wang, Zhanbin Yuan +2
In this paper, an alternating direction implicit (ADI) difference scheme for two-dimensional time-fractional wave equation of distributed-order with a nonlinear source term is pres…
Differential quadrature method for space-fractional diffusion equations on 2D irregular domains
X. G. Zhu, Z. B. Yuan, F. Liu +1
In mathematical physics, the space-fractional diffusion equations are of particular interest in the studies of physical phenomena modelled by Lévy processes, which are sometimes ca…
An efficient differential quadrature method for fractional advection-diffusion equation
X. G. Zhu, Y. F. Nie, W. W. Zhang
This article studies a direct numerical approach for fractional advection-diffusion equations (ADEs). Using a set of cubic trigonometric B-splines as test functions, a differential…
Maximum-norm error analysis of compact difference schemes for the backward fractional Feynman-Kac equation
Jiahui Hu, Jungang Wang, Zhanbin Yuan +2
The fractional Feynman-Kac equations describe the distribution of functionals of non-Brownian motion, or anomalous diffusion, including two types called the forward and backward fr…
Effective numerical treatment of sub-diffusion equation with non-smooth solution
Zongze Yang, Jungang Wang, Yan Li +1
In this paper we investigate a sub-diffusion equation for simulating the anomalous diffusion phenomenon in real physical environment. Based on an equivalent transformation of the o…
On a collocation method for the time-fractional convection-diffusion equation with variable coefficients
Xiaogang Zhu, Yufeng Nie
In this work, a new collocation approach using a combination of a wavelet operational matrix method and the exponential spline interpolation is proposed to solve the time-fractiona…
Finite element method for nonlinear Riesz space fractional diffusion equations on irregular domains
Z. Yang, Z. Yuan, Y. Nie +3
In this paper, we consider two-dimensional Riesz space fractional diffusion equations with nonlinear source term on convex domains. Applying Galerkin finite element method in space…