| Residential College | false |
| Status | 已發表Published |
| Stagnation-shortening inexact Newton method based on unsupervised learning for highly nonlinear hyperelasticity problems on three-dimensional unstructured meshes, 18th Copper Mountain Conference On Iterative Methods, Colorado, USA, April 14-19, 2024. | |
Yujie Gong; Li Luo  ; Xiao-Chuan Cai
| |
| 2024-04 | |
| Conference Name | 18th Copper Mountain Conference On Iterative Methods |
| Conference Date | April 14-19, 2024 |
| Conference Place | Colorado, USA |
| Country | USA |
| Contribution Rank | 2 |
| Abstract | Inexact Newton-type method is widely used in many scientific and engineering applications, but in many situations it converges slowly or even fail to converge, for reasons that are difficult to quantify. In this paper, we propose a novel nonlinearly preconditioned inexact Newton algorithm with learning capability to improve the convergence and robustness of the method. The proposed method searches through the nonlinear residual and stagnated solution spaces generated during the Newton iterations and identify the ``bad subspaces'' using an unsupervised learning technique, namely principal component analysis. In the nonlinear preconditioner, a learned small-scale projected problem corresponding to the slow subspace of the nonlinear residuals is constructed and solved to provide a much better initial guess for the global inexact Newton method to converge nearly quadratically. As an application, we consider the modeling of the human artery with stenosis using the hyperelasticity equation with multiple material parameters. Due to the significant difference in the material coefficients between the plaques and the healthy parts of the blood vessels, the problem is nonlinearly very difficult. Numerical experiments demonstrate that proposed nonlinearly preconditioned inexact Newton offers significantly reduced number of nonlinear iterations and robustness for this rather tough hyperelasticity problem. |
| Subject Area | 数学 ; 计算数学 ; 偏微分方程数值解 |
| URL | View the original |
| Funding Project | Highly parallel preconditioned inexact Newton methods for nonlinear system of equations ; Parallel Algorithms for Two-phase Flows ; Preconditioning techniques for nonlinear systems |
| Document Type | Conference paper |
| Collection | DEPARTMENT OF MATHEMATICS Faculty of Science and Technology |
| Corresponding Author | Li Luo; Xiao-Chuan Cai |
| Affiliation | Department of Mathematics, University of Macau |
| First Author Affilication | University of Macau |
| Corresponding Author Affilication | University of Macau |
| Recommended Citation GB/T 7714 | Yujie Gong,Li Luo,Xiao-Chuan Cai. Stagnation-shortening inexact Newton method based on unsupervised learning for highly nonlinear hyperelasticity problems on three-dimensional unstructured meshes, 18th Copper Mountain Conference On Iterative Methods, Colorado, USA, April 14-19, 2024.[C], 2024. |
| APA | Yujie Gong., Li Luo., & Xiao-Chuan Cai (2024). Stagnation-shortening inexact Newton method based on unsupervised learning for highly nonlinear hyperelasticity problems on three-dimensional unstructured meshes, 18th Copper Mountain Conference On Iterative Methods, Colorado, USA, April 14-19, 2024.. . |
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| CopperMountain2024.p（112KB） | 会议论文 | 开放获取 | CC BY-NC-SA | View Download | ||
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