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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2510.00516 |
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| _version_ | 1866908571675918336 |
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| author | Guan, Xinyi Hu, Jiayi Zhang, Lei Tang, Shaoqiang Liu, Wing Kam |
| author_facet | Guan, Xinyi Hu, Jiayi Zhang, Lei Tang, Shaoqiang Liu, Wing Kam |
| contents | In this paper, we propose a time-marching multi-level Variational Multiscale-Tensor Decomposition (VMS-TD) algorithm to solve the heat equation with a moving heat source model that arises from additive manufacturing. First, we take a second-order centered difference for time semi-discretization. The temperature field is decomposed according to multiple space resolution levels, each represented by the TD method. Then we adopt the VMS formulation [T.J.R. Hughes, G.R. Feijoo, L. Mazzei, J.B. Quincy. Comput. Methods Appl. Mech. Engrg. 166:3-24 (1998)] for the resulting elliptic problem to obtain a Galerkin weak form, and design VMS-TD algorithm to solve it. Furthermore, to comply with the TD solution scheme, special inter-scale data transfers are made at the scale interface and moving fine-scale subdomains. Numerical results demonstrate that the multi-level VMS-TD algorithm is much more efficient than the fully resolved TD algorithm, let alone traditional direct numerical simulation methods such as finite difference or finite element analysis. Compared with the well-known multi-grid methods or more recent GO-MELT framework [J.P. Leonor, G.J. Wagner. Comput. Methods Appl. Mech. Engrg, 426:116977 (2024)], the three-level VMS-TD uses much smaller degrees of freedom to reach accurate results. A multi-time-scale extension of VMS-TD algorithm is also proposed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00516 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time-marching multi-level variational multiscale tensor decomposition algorithm for heat conduction with moving heat source Guan, Xinyi Hu, Jiayi Zhang, Lei Tang, Shaoqiang Liu, Wing Kam Numerical Analysis 65M60, 80M10 In this paper, we propose a time-marching multi-level Variational Multiscale-Tensor Decomposition (VMS-TD) algorithm to solve the heat equation with a moving heat source model that arises from additive manufacturing. First, we take a second-order centered difference for time semi-discretization. The temperature field is decomposed according to multiple space resolution levels, each represented by the TD method. Then we adopt the VMS formulation [T.J.R. Hughes, G.R. Feijoo, L. Mazzei, J.B. Quincy. Comput. Methods Appl. Mech. Engrg. 166:3-24 (1998)] for the resulting elliptic problem to obtain a Galerkin weak form, and design VMS-TD algorithm to solve it. Furthermore, to comply with the TD solution scheme, special inter-scale data transfers are made at the scale interface and moving fine-scale subdomains. Numerical results demonstrate that the multi-level VMS-TD algorithm is much more efficient than the fully resolved TD algorithm, let alone traditional direct numerical simulation methods such as finite difference or finite element analysis. Compared with the well-known multi-grid methods or more recent GO-MELT framework [J.P. Leonor, G.J. Wagner. Comput. Methods Appl. Mech. Engrg, 426:116977 (2024)], the three-level VMS-TD uses much smaller degrees of freedom to reach accurate results. A multi-time-scale extension of VMS-TD algorithm is also proposed. |
| title | Time-marching multi-level variational multiscale tensor decomposition algorithm for heat conduction with moving heat source |
| topic | Numerical Analysis 65M60, 80M10 |
| url | https://arxiv.org/abs/2510.00516 |