Pub Date : 2022-09-01DOI: 10.4208/jcm.2201-m2021-0183
Jian Lu, Y. Ye, Yiqiu Dong, Xiaoxia Liu and Yuru Zou
{"title":"Impulse Noise Removal by L1 Weighted Nuclear Norm Minimization","authors":"Jian Lu, Y. Ye, Yiqiu Dong, Xiaoxia Liu and Yuru Zou","doi":"10.4208/jcm.2201-m2021-0183","DOIUrl":"https://doi.org/10.4208/jcm.2201-m2021-0183","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42796919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-01DOI: 10.4208/jcm.2111-m2020-0177
Yayun Fu, Wenjun Wang
{"title":"A Linearly-Implicit Energy-Preserving Algorithm for the Two-Dimensional Space-Fractional Nonlinear Schrödinger Equation Based on the SAV Approach","authors":"Yayun Fu, Wenjun Wang","doi":"10.4208/jcm.2111-m2020-0177","DOIUrl":"https://doi.org/10.4208/jcm.2111-m2020-0177","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47061843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-01DOI: 10.4208/jcm.2202-m2021-0324
Matthieu Aussal and Marc Bakry
{"title":"A Fast Free Memory Method for an Efficient Computation of Convolution Kernels","authors":"Matthieu Aussal and Marc Bakry","doi":"10.4208/jcm.2202-m2021-0324","DOIUrl":"https://doi.org/10.4208/jcm.2202-m2021-0324","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44612824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-01DOI: 10.4208/jcm.2203-m2020-0303
Siru Gong and Yangfeng Su
{"title":"Implicit Determinant Method for Solving an Hermitian Eigenvalue Optimization Problem","authors":"Siru Gong and Yangfeng Su","doi":"10.4208/jcm.2203-m2020-0303","DOIUrl":"https://doi.org/10.4208/jcm.2203-m2020-0303","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47649043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-01DOI: 10.4208/jcm.2103-m2020-0107
Baiying Dong, Xiu-juan Feng, Zhilin Li
{"title":"An $L^{infty}$ Second Order Cartesian Method for 3D Anisotropic Interface Problems","authors":"Baiying Dong, Xiu-juan Feng, Zhilin Li","doi":"10.4208/jcm.2103-m2020-0107","DOIUrl":"https://doi.org/10.4208/jcm.2103-m2020-0107","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42476733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-01DOI: 10.4208/jcm.2102-m2020-0211
Huan Liu, Xiangcheng Zheng null, Hongfei Fu
{"title":"Analysis of a Multi-Term Variable-Order Time-Fractional Diffusion Equation and Its Galerkin Finite Element Approximation","authors":"Huan Liu, Xiangcheng Zheng null, Hongfei Fu","doi":"10.4208/jcm.2102-m2020-0211","DOIUrl":"https://doi.org/10.4208/jcm.2102-m2020-0211","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41606503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-01DOI: 10.4208/jcm.2008-m2020-0077
Jiang Qian, Xiquan Shi, Jinming Wu null, Dianxuan Gong
In this paper, matrix representations of the best spline quasi-interpolating operator over triangular sub-domains in S1 2(∆ (2) mn), and coefficients of splines in terms of B-net are reviewed firstly. Moreover, by means of coefficients in terms of B-net, computation of bivariate numerical cubature over triangular sub-domains with respect to variables x and y is transferred into summation of coefficients of splines in terms of B-net. Thus concise bivariate cubature formulas are constructed over rectangular sub-domain. Furthermore, by means of module of continuity and max-norms, error estimates for cubature formulas are derived over both sub-domains and the domain. MSC:
{"title":"Construction of Cubature Formulas Via Bivariate Quadratic Spline Spaces over Non-Uniform Type-2 Triangulation","authors":"Jiang Qian, Xiquan Shi, Jinming Wu null, Dianxuan Gong","doi":"10.4208/jcm.2008-m2020-0077","DOIUrl":"https://doi.org/10.4208/jcm.2008-m2020-0077","url":null,"abstract":"In this paper, matrix representations of the best spline quasi-interpolating operator over triangular sub-domains in S1 2(∆ (2) mn), and coefficients of splines in terms of B-net are reviewed firstly. Moreover, by means of coefficients in terms of B-net, computation of bivariate numerical cubature over triangular sub-domains with respect to variables x and y is transferred into summation of coefficients of splines in terms of B-net. Thus concise bivariate cubature formulas are constructed over rectangular sub-domain. Furthermore, by means of module of continuity and max-norms, error estimates for cubature formulas are derived over both sub-domains and the domain. MSC:","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47839002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we develop a two-grid method (TGM) based on the FEM for 2D nonlinear time fractional two-term mixed sub-diffusion and diffusion wave equations. A two-grid algorithm is proposed for solving the nonlinear system, which consists of two steps: a nonlinear FE system is solved on a coarse grid, then the linearized FE system is solved on the fine grid by Newton iteration based on the coarse solution. The fully discrete numerical approximation is analyzed, where the Galerkin finite element method for the space derivatives and the finite difference scheme for the time Caputo derivative with order α ∈ (1 , 2) and α 1 ∈ (0 , 1). Numerical stability and optimal error estimate O ( h r +1 + H 2 r +2 + τ min { 3 − α, 2 − α 1 } ) in L 2 -norm are presented for two-grid scheme, where t, H and h are the time step size, coarse grid mesh size and fine grid mesh size, respectively. Finally, numerical experiments are provided to confirm our theoretical results and effectiveness of the proposed algorithm.
{"title":"A Two-Grid Finite Element Approximation for Nonlinear Time Fractional Two-Term Mixed Sub-Diffusion and Diffusion Wave Equations","authors":"Yanping Chen, Qiling Gu, Qingfeng Li, Yunqing Huang","doi":"10.4208/jcm.2104-m2021-0332","DOIUrl":"https://doi.org/10.4208/jcm.2104-m2021-0332","url":null,"abstract":"In this paper, we develop a two-grid method (TGM) based on the FEM for 2D nonlinear time fractional two-term mixed sub-diffusion and diffusion wave equations. A two-grid algorithm is proposed for solving the nonlinear system, which consists of two steps: a nonlinear FE system is solved on a coarse grid, then the linearized FE system is solved on the fine grid by Newton iteration based on the coarse solution. The fully discrete numerical approximation is analyzed, where the Galerkin finite element method for the space derivatives and the finite difference scheme for the time Caputo derivative with order α ∈ (1 , 2) and α 1 ∈ (0 , 1). Numerical stability and optimal error estimate O ( h r +1 + H 2 r +2 + τ min { 3 − α, 2 − α 1 } ) in L 2 -norm are presented for two-grid scheme, where t, H and h are the time step size, coarse grid mesh size and fine grid mesh size, respectively. Finally, numerical experiments are provided to confirm our theoretical results and effectiveness of the proposed algorithm.","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48707189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-01DOI: 10.4208/jcm.2101-m2020-0075
Kai Wang null, Na-Na Wang
{"title":"Analysis of a Fully Discrete Finite Element Method for Parabolic Interface Problems with Nonsmooth Initial Data","authors":"Kai Wang null, Na-Na Wang","doi":"10.4208/jcm.2101-m2020-0075","DOIUrl":"https://doi.org/10.4208/jcm.2101-m2020-0075","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47993647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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