Zhu, Xi; Tang, Shaoqiang Clustering analysis for elastodynamic homogenization. (English) Zbl 1528.74092 Comput. Mech. 72, No. 4, 725-741 (2023). MSC: 74Q10 74S99 74E30 74J10 PDFBibTeX XMLCite \textit{X. Zhu} and \textit{S. Tang}, Comput. Mech. 72, No. 4, 725--741 (2023; Zbl 1528.74092) Full Text: DOI
Lu, Ye; Li, Hengyang; Zhang, Lei; Park, Chanwook; Mojumder, Satyajit; Knapik, Stefan; Sang, Zhongsheng; Tang, Shaoqiang; Apley, Daniel W.; Wagner, Gregory J.; Liu, Wing Kam Convolution hierarchical deep-learning neural networks (C-HiDeNN): finite elements, isogeometric analysis, tensor decomposition, and beyond. (English) Zbl 1527.74082 Comput. Mech. 72, No. 2, 333-362 (2023). MSC: 74S99 74S05 74S22 74F05 74P15 68T05 68T07 PDFBibTeX XMLCite \textit{Y. Lu} et al., Comput. Mech. 72, No. 2, 333--362 (2023; Zbl 1527.74082) Full Text: DOI
Yang, Yang; Liu, Tongrui; Aliabadi, M. H.; Tang, Shaoqiang Virtual clustering analysis for long fiber reinforced composites. (English) Zbl 1519.74080 Comput. Mech. 71, No. 6, 1139-1159 (2023). MSC: 74S99 74Q99 74E30 PDFBibTeX XMLCite \textit{Y. Yang} et al., Comput. Mech. 71, No. 6, 1139--1159 (2023; Zbl 1519.74080) Full Text: DOI
Guan, Xinyi; Zhang, Qian; Tang, Shaoqiang Numerical boundary treatment for shock propagation in the fractional KdV-Burgers equation. (English) Zbl 07492665 Comput. Mech. 69, No. 1, 201-212 (2022). MSC: 74-XX PDFBibTeX XMLCite \textit{X. Guan} et al., Comput. Mech. 69, No. 1, 201--212 (2022; Zbl 07492665) Full Text: DOI
Zhang, Lei; Cheng, Lin; Li, Hengyang; Gao, Jiaying; Yu, Cheng; Domel, Reno; Yang, Yang; Tang, Shaoqiang; Liu, Wing Kam Hierarchical deep-learning neural networks: finite elements and beyond. (English) Zbl 07360501 Comput. Mech. 67, No. 1, 207-230 (2021). MSC: 74-XX PDFBibTeX XMLCite \textit{L. Zhang} et al., Comput. Mech. 67, No. 1, 207--230 (2021; Zbl 07360501) Full Text: DOI
Zhang, Lei; Tang, Shaoqiang; Liu, Wing Kam Analytical expression of RKPM shape functions. (English) Zbl 1467.74094 Comput. Mech. 66, No. 6, 1343-1352 (2020). MSC: 74S22 65D17 PDFBibTeX XMLCite \textit{L. Zhang} et al., Comput. Mech. 66, No. 6, 1343--1352 (2020; Zbl 1467.74094) Full Text: DOI
Zhang, Lei; Tang, Shaoqiang; Yu, Cheng; Zhu, Xi; Liu, Wing Kam Fast calculation of interaction tensors in clustering-based homogenization. (English) Zbl 1467.74100 Comput. Mech. 64, No. 2, 351-364 (2019). MSC: 74S99 74Q05 PDFBibTeX XMLCite \textit{L. Zhang} et al., Comput. Mech. 64, No. 2, 351--364 (2019; Zbl 1467.74100) Full Text: DOI
Li, Hengyang; Kafka, Orion L.; Gao, Jiaying; Yu, Cheng; Nie, Yinghao; Zhang, Lei; Tajdari, Mahsa; Tang, Shan; Guo, Xu; Li, Gang; Tang, Shaoqiang; Cheng, Gengdong; Liu, Wing Kam Clustering discretization methods for generation of material performance databases in machine learning and design optimization. (English) Zbl 1470.74073 Comput. Mech. 64, No. 2, 281-305 (2019). MSC: 74S99 74A99 74P15 68T05 PDFBibTeX XMLCite \textit{H. Li} et al., Comput. Mech. 64, No. 2, 281--305 (2019; Zbl 1470.74073) Full Text: DOI
Liu, Wing Kam (ed.); Karniadakis, George (ed.); Tang, Shaoqiang (ed.); Yvonnet, Julien (ed.) A Computational Mechanics special issue on: Data-driven modeling and simulation – theory, methods, and applications. (English) Zbl 1476.00073 Comput. Mech. 64, No. 2, 275-277 (2019). MSC: 00B15 74-06 PDFBibTeX XMLCite \textit{W. K. Liu} (ed.) et al., Comput. Mech. 64, No. 2, 275--277 (2019; Zbl 1476.00073) Full Text: DOI
Tang, Shaoqiang; Zhang, Lei; Liu, Wing Kam From virtual clustering analysis to self-consistent clustering analysis: a mathematical study. (English) Zbl 1471.74079 Comput. Mech. 62, No. 6, 1443-1460 (2018). MSC: 74S99 74Q99 68T05 PDFBibTeX XMLCite \textit{S. Tang} et al., Comput. Mech. 62, No. 6, 1443--1460 (2018; Zbl 1471.74079) Full Text: DOI
Pang, Gang; Ji, Songsong; Yang, Yibo; Tang, Shaoqiang Eliminating corner effects in square lattice simulation. (English) Zbl 1470.74075 Comput. Mech. 62, No. 1, 111-122 (2018). MSC: 74S99 74A25 PDFBibTeX XMLCite \textit{G. Pang} et al., Comput. Mech. 62, No. 1, 111--122 (2018; Zbl 1470.74075) Full Text: DOI
Luan, Shengzhi; Lian, Yanping; Ying, Yuping; Tang, Shaoqiang; Wagner, Gregory J.; Liu, Wing Kam An enriched finite element method to fractional advection-diffusion equation. (English) Zbl 1429.65171 Comput. Mech. 60, No. 2, 181-201 (2017). MSC: 65L60 34A08 PDFBibTeX XMLCite \textit{S. Luan} et al., Comput. Mech. 60, No. 2, 181--201 (2017; Zbl 1429.65171) Full Text: DOI
Tang, Shaoqiang; Ying, Yuping; Lian, Yanping; Lin, Stephen; Yang, Yibo; Wagner, Gregory J.; Liu, Wing Kam Differential operator multiplication method for fractional differential equations. (English) Zbl 1400.34013 Comput. Mech. 58, No. 5, 879-888 (2016). MSC: 34A08 65L12 34A25 74N15 65L05 PDFBibTeX XMLCite \textit{S. Tang} et al., Comput. Mech. 58, No. 5, 879--888 (2016; Zbl 1400.34013) Full Text: DOI
Fang, Ming; Tang, Shaoqiang; Li, Zhihui; Wang, Xianming Artificial boundary conditions for atomic simulations of face-centered-cubic lattice. (English) Zbl 1312.74004 Comput. Mech. 50, No. 5, 645-655 (2012). MSC: 74A60 34A33 PDFBibTeX XMLCite \textit{M. Fang} et al., Comput. Mech. 50, No. 5, 645--655 (2012; Zbl 1312.74004) Full Text: DOI
Pang, Gang; Tang, Shaoqiang Time history kernel functions for square lattice. (English) Zbl 1334.70002 Comput. Mech. 48, No. 6, 699-711 (2011). MSC: 70-08 70F45 74A25 34A33 34A35 PDFBibTeX XMLCite \textit{G. Pang} and \textit{S. Tang}, Comput. Mech. 48, No. 6, 699--711 (2011; Zbl 1334.70002) Full Text: DOI
Wang, Xianming; Tang, Shaoqiang Matching boundary conditions for diatomic chains. (English) Zbl 1344.74048 Comput. Mech. 46, No. 6, 813-826 (2010). MSC: 74N99 74S99 82D25 PDFBibTeX XMLCite \textit{X. Wang} and \textit{S. Tang}, Comput. Mech. 46, No. 6, 813--826 (2010; Zbl 1344.74048) Full Text: DOI
Dreher, Michael; Tang, Shaoqiang Time history interfacial conditions in multiscale computations of lattice oscillations. (English) Zbl 1162.74334 Comput. Mech. 41, No. 5, 683-698 (2008). MSC: 74E15 82D25 PDFBibTeX XMLCite \textit{M. Dreher} and \textit{S. Tang}, Comput. Mech. 41, No. 5, 683--698 (2008; Zbl 1162.74334) Full Text: DOI
Liu, Wing Kam; Kim, Do Wan; Tang, Shaoqiang Mathematical foundations of the immersed finite element method. (English) Zbl 1178.74170 Comput. Mech. 39, No. 3, 211-222 (2007). MSC: 74S05 74F10 PDFBibTeX XMLCite \textit{W. K. Liu} et al., Comput. Mech. 39, No. 3, 211--222 (2007; Zbl 1178.74170) Full Text: DOI