Convolution hierarchical deep-learning neural network tensor decomposition (C-HiDeNN-TD) for high-resolution topology optimization

H Li, S Knapik, Y Li, C Park, J Guo, S Mojumder… - Computational …, 2023 - Springer
High-resolution structural topology optimization is extremely challenging due to a large
number of degrees of freedom (DoFs). In this work, a Convolution-Hierarchical Deep …

Convolution Hierarchical Deep-learning Neural Networks (C-HiDeNN): finite elements, isogeometric analysis, tensor decomposition, and beyond

Y Lu, H Li, L Zhang, C Park, S Mojumder… - Computational …, 2023 - Springer
This paper presents a general Convolution Hierarchical Deep-learning Neural Networks (C-
HiDeNN) computational framework for solving partial differential equations. This is the first …

RKPM2D: an open-source implementation of nodally integrated reproducing kernel particle method for solving partial differential equations

TH Huang, H Wei, JS Chen, MC Hillman - Computational particle …, 2020 - Springer
We present an open-source software RKPM2D for solving PDEs under the reproducing
kernel particle method (RKPM)-based meshfree computational framework. Compared to …

Peridynamic analysis of dynamic fracture: influence of peridynamic horizon, dimensionality and specimen size

SN Butt, G Meschke - Computational Mechanics, 2021 - Springer
In peridynamic models for fracture, the dissipated fracture energy is regularized over a non-
local region denoted as the peridynamic horizon. This paper investigates the influence of …

Convolution finite element based digital image correlation for displacement and strain measurements

Y Lu, W Zhu - Computer Methods in Applied Mechanics and …, 2024 - Elsevier
This work presents a novel global digital image correlation (DIC) method, based on a newly
developed convolution finite element (C-FE) approximation. The convolution approximation …

[PDF][PDF] Nonlocal Operator Method for Solving Partial Differential Equations: State-of-the-Art Review and Future Perspectives.

Y Zhang, H Ren, T Rabczuk - J. Adv. Eng. Comput., 2022 - pdfs.semanticscholar.org
The nonlocal operator method (NOM) is based on nonlocal theory and employs nonlocal
operators of integral form to replace the local partial differential operators. NOM naturally …

A variational multiscale immersed meshfree method for heterogeneous materials

TH Huang, JS Chen, MR Tupek, FN Beckwith… - Computational …, 2021 - Springer
We introduce an immersed meshfree formulation for modeling heterogeneous materials with
flexible non-body-fitted discretizations, approximations, and quadrature rules. The interfacial …

Convolution tensor decomposition for efficient high-resolution solutions to the Allen–Cahn equation

Y Lu, C Yuan, H Guo - Computer Methods in Applied Mechanics and …, 2025 - Elsevier
This paper presents a convolution tensor decomposition based model reduction method for
solving the Allen–Cahn equation. The Allen–Cahn equation is usually used to characterize …

[HTML][HTML] Data-driven modeling of an unsaturated bentonite buffer model test under high temperatures using an enhanced axisymmetric reproducing kernel particle …

J Baek, Y Wang, X He, Y Lu, JS McCartney… - Computers and …, 2024 - Elsevier
In deep geological repositories for high level nuclear waste with close canister spacings,
bentonite buffers can experience temperatures higher than 100° C. In this range of extreme …

A stabilized quasi and bending consistent meshfree Galerkin formulation for Reissner–Mindlin plates

TH Huang, YL Wei - Computational Mechanics, 2022 - Springer
The state-of-the-art locking-free meshfree Galerkin formulation for modeling the Reissner–
Mindlin plate problems is plagued by the following issues:(1) the requirement of a large …