{"title":"Three Indication Variables and Their Performance for the Troubled-Cell Indicator using K-Means Clustering","authors":"Zhihuan Wang, Zhen-Zhuo Gao, Hai-yun Wang, Qiang Zhang null, Hongqiang Zhu","doi":"10.4208/aamm.oa-2021-0234","DOIUrl":"https://doi.org/10.4208/aamm.oa-2021-0234","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70494645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4208/aamm.oa-2022-0048
Shan Zhang, Zihao Yang null, X. Guan
{"title":"Multi-Modes Multiscale Approach of Heat Transfer Problems in Heterogeneous Solids with Uncertain Thermal Conductivity","authors":"Shan Zhang, Zihao Yang null, X. Guan","doi":"10.4208/aamm.oa-2022-0048","DOIUrl":"https://doi.org/10.4208/aamm.oa-2022-0048","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70494793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4208/aamm.oa-2021-0282
H. Panahi-Kalus, Amin Moosaie null, M. Ahmadinejad
{"title":"A Two-Dimensional Thermoelastic Analysis of a Cylindrical Shell Made of FGM with Temperature-Dependent Physical Properties","authors":"H. Panahi-Kalus, Amin Moosaie null, M. Ahmadinejad","doi":"10.4208/aamm.oa-2021-0282","DOIUrl":"https://doi.org/10.4208/aamm.oa-2021-0282","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70494927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. This paper proposes a deep-learning-based Robin-Robin domain decomposition method (DeepDDM) for Helmholtz equations. We first present the plane wave activation-based neural network (PWNN), which is more efficient for solving Helmholtz equations with constant coefficients and wavenumber k than finite difference methods (FDM). On this basis, we use PWNN to discretize the subproblems divided by domain decomposition methods (DDM), which is the main idea of DeepDDM. This paper will investigate the number of iterations of using DeepDDM for continuous and discontinuous Helmholtz equations. The results demonstrate that: DeepDDM exhibits behaviors consistent with conventional robust FDM-based domain decomposition method (FDM-DDM) under the same Robin parameters, i.e., the number of iterations by DeepDDM is almost the same as that of FDM-DDM. By choosing suitable Robin parameters on different subdomains, the convergence rate is almost constant with the rise of wavenumber in both continuous and discontinuous cases. The performance of DeepDDM on Helmholtz equations may provide new insights for improving the PDE solver by deep learning.
{"title":"Deep Domain Decomposition Methods: Helmholtz Equation","authors":"Wuyang Li, Ziming Wang, Tao Cui, Yingxiang Xu null, Xueshuang Xiang","doi":"10.4208/aamm.oa-2021-0305","DOIUrl":"https://doi.org/10.4208/aamm.oa-2021-0305","url":null,"abstract":". This paper proposes a deep-learning-based Robin-Robin domain decomposition method (DeepDDM) for Helmholtz equations. We first present the plane wave activation-based neural network (PWNN), which is more efficient for solving Helmholtz equations with constant coefficients and wavenumber k than finite difference methods (FDM). On this basis, we use PWNN to discretize the subproblems divided by domain decomposition methods (DDM), which is the main idea of DeepDDM. This paper will investigate the number of iterations of using DeepDDM for continuous and discontinuous Helmholtz equations. The results demonstrate that: DeepDDM exhibits behaviors consistent with conventional robust FDM-based domain decomposition method (FDM-DDM) under the same Robin parameters, i.e., the number of iterations by DeepDDM is almost the same as that of FDM-DDM. By choosing suitable Robin parameters on different subdomains, the convergence rate is almost constant with the rise of wavenumber in both continuous and discontinuous cases. The performance of DeepDDM on Helmholtz equations may provide new insights for improving the PDE solver by deep learning.","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70494959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4208/aamm.oa-2021-0340
Zijin Zhu, Xiaoyan Hu null, Guoxi Ni
{"title":"Radially Symmetrical Problems for Compressible Fluids with a High-Resolution Boundary Condition","authors":"Zijin Zhu, Xiaoyan Hu null, Guoxi Ni","doi":"10.4208/aamm.oa-2021-0340","DOIUrl":"https://doi.org/10.4208/aamm.oa-2021-0340","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70495102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4208/aamm.oa-2021-0255
Jun Yang null, Nianyu Yi
{"title":"A Conservative SAV-RRK Finite Element Method for the Nonlinear Schrödinger Equation","authors":"Jun Yang null, Nianyu Yi","doi":"10.4208/aamm.oa-2021-0255","DOIUrl":"https://doi.org/10.4208/aamm.oa-2021-0255","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70494765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4208/aamm.oa-2021-0204
Danni Zhang null, Ruihan Guo
{"title":"Optimal Error Estimates of the Semi-Discrete Local Discontinuous Galerkin Method and Exponential Time Differencing Schemes for the Thin Film Epitaxy Problem Without Slope Selection","authors":"Danni Zhang null, Ruihan Guo","doi":"10.4208/aamm.oa-2021-0204","DOIUrl":"https://doi.org/10.4208/aamm.oa-2021-0204","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70494407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4208/aamm.oa-2021-0381
Guihua Zhao null, Hui Liang
. In this paper, the finite-time stability and instability are studied for nonlinear impulsive systems. There are mainly four concerns. 1) For the system with stabilizing impulses, a Lyapunov theorem on global finite-time stability is presented. 2) When the system without impulsive effects is globally finite-time stable (GFTS) and the settling time is continuous at the origin, it is proved that it is still GFTS over any class of impulse sequences, if the mixed impulsive jumps satisfy some mild conditions. 3) For systems with destabilizing impulses, it is shown that to be finite-time stable, the destabilizing impulses should not occur too frequently, otherwise, the origin of the impulsive system is finite-time instable, which are formulated by average dwell time (ADT) conditions respectively. 4) A theorem on finite-time instability is provided for system with stabilizing impulses. For each GFTS theorem of impulsive systems con-sidered in this paper, the upper boundedness of settling time is given, which depends on the initial value and impulsive effects. Some numerical examples are given to illus-trate the theoretical analysis.
{"title":"Finite-Time Stability and Instability of Nonlinear Impulsive Systems","authors":"Guihua Zhao null, Hui Liang","doi":"10.4208/aamm.oa-2021-0381","DOIUrl":"https://doi.org/10.4208/aamm.oa-2021-0381","url":null,"abstract":". In this paper, the finite-time stability and instability are studied for nonlinear impulsive systems. There are mainly four concerns. 1) For the system with stabilizing impulses, a Lyapunov theorem on global finite-time stability is presented. 2) When the system without impulsive effects is globally finite-time stable (GFTS) and the settling time is continuous at the origin, it is proved that it is still GFTS over any class of impulse sequences, if the mixed impulsive jumps satisfy some mild conditions. 3) For systems with destabilizing impulses, it is shown that to be finite-time stable, the destabilizing impulses should not occur too frequently, otherwise, the origin of the impulsive system is finite-time instable, which are formulated by average dwell time (ADT) conditions respectively. 4) A theorem on finite-time instability is provided for system with stabilizing impulses. For each GFTS theorem of impulsive systems con-sidered in this paper, the upper boundedness of settling time is given, which depends on the initial value and impulsive effects. Some numerical examples are given to illus-trate the theoretical analysis.","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70494747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4208/aamm.oa-2021-0263
Fangfang Cao, Yanmin Zhao, Fenling Wang, Yanhua Shi null, C. Yao
{"title":"Nonconforming Mixed FEM Analysis for Multi-Term Time-Fractional Mixed Sub-Diffusion and Diffusion-Wave Equation with Time-Space Coupled Derivative","authors":"Fangfang Cao, Yanmin Zhao, Fenling Wang, Yanhua Shi null, C. Yao","doi":"10.4208/aamm.oa-2021-0263","DOIUrl":"https://doi.org/10.4208/aamm.oa-2021-0263","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70494825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4208/aamm.oa-2021-0325
Xiaowei Chen, Xu Qian null, Songhe Song
. We propose a class of up to fourth-order maximum-principle-preserving and mass-conserving schemes for the conservative Allen-Cahn equation equipped with a non-local Lagrange multiplier. Based on the second-order finite-difference semi-discretization in the spatial direction, the integrating factor Runge-Kutta schemes are applied in the temporal direction. Theoretical analysis indicates that the proposed schemes conserve mass and preserve the maximum principle under reasonable time step-size restriction, which is independent of the space step size. Finally, the theoretical analysis is verified by several numerical examples.
{"title":"Fourth-Order Structure-Preserving Method for the Conservative Allen-Cahn Equation","authors":"Xiaowei Chen, Xu Qian null, Songhe Song","doi":"10.4208/aamm.oa-2021-0325","DOIUrl":"https://doi.org/10.4208/aamm.oa-2021-0325","url":null,"abstract":". We propose a class of up to fourth-order maximum-principle-preserving and mass-conserving schemes for the conservative Allen-Cahn equation equipped with a non-local Lagrange multiplier. Based on the second-order finite-difference semi-discretization in the spatial direction, the integrating factor Runge-Kutta schemes are applied in the temporal direction. Theoretical analysis indicates that the proposed schemes conserve mass and preserve the maximum principle under reasonable time step-size restriction, which is independent of the space step size. Finally, the theoretical analysis is verified by several numerical examples.","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70495022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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