Pub Date : 2023-06-01DOI: 10.4208/nmtma.oa-2023-0044
Ruisong Gao, Yufeng Wang, Min Yang and Chuanjun Chen
{"title":"PI-VEGAN: Physics Informed Variational Embedding Generative Adversarial Networks for Stochastic Differential Equations","authors":"Ruisong Gao, Yufeng Wang, Min Yang and Chuanjun Chen","doi":"10.4208/nmtma.oa-2023-0044","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2023-0044","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135095882","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 : 2023-06-01DOI: 10.4208/jcm.2301-m2022-0208
Chunxiong Zheng, Xianwei Wen, Jinyu Zhang and Zhenya Zhou
Asymptotic theory for the circuit envelope analysis is developed in this paper. A typical feature of circuit envelope analysis is the existence of two significantly distinct timescales: one is the fast timescale of carrier wave, and the other is the slow timescale of modulation signal. We first perform pro forma asymptotic analysis for both the driven and autonomous systems. Then resorting to the Floquet theory of periodic operators, we make a rigorous justification for first-order asymptotic approximations. It turns out that these asymptotic results are valid at least on the slow timescale. To speed up the computation of asymptotic approximations, we propose a periodization technique, which renders the possibility of utilizing the NUFFT algorithm. Numerical experiments are presented, and the results validate the theoretical findings.
{"title":"Asymptotic Theory for the Circuit Envelope Analysis","authors":"Chunxiong Zheng, Xianwei Wen, Jinyu Zhang and Zhenya Zhou","doi":"10.4208/jcm.2301-m2022-0208","DOIUrl":"https://doi.org/10.4208/jcm.2301-m2022-0208","url":null,"abstract":"Asymptotic theory for the circuit envelope analysis is developed in this paper. A typical feature of circuit envelope analysis is the existence of two significantly distinct timescales: one is the fast timescale of carrier wave, and the other is the slow timescale of modulation signal. We first perform pro forma asymptotic analysis for both the driven and autonomous systems. Then resorting to the Floquet theory of periodic operators, we make a rigorous justification for first-order asymptotic approximations. It turns out that these asymptotic results are valid at least on the slow timescale. To speed up the computation of asymptotic approximations, we propose a periodization technique, which renders the possibility of utilizing the NUFFT algorithm. Numerical experiments are presented, and the results validate the theoretical findings.","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47375271","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 : 2023-06-01DOI: 10.4208/nmtma.oa-2023-0039
Teng-Teng Yao, Xiao-Qing Jin and Zhi Zhao
{"title":"A Riemannian Inertial Mann Algorithm for Nonexpansive Mappings on Hadamard Manifolds","authors":"Teng-Teng Yao, Xiao-Qing Jin and Zhi Zhao","doi":"10.4208/nmtma.oa-2023-0039","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2023-0039","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135144242","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 : 2023-06-01DOI: 10.4208/nmtma.oa-2022-0190
Yuchao Tang, Shirong Deng and Tieyong Zeng
{"title":"Low Rank and Total Variation Based Two-Phase Method for Image Deblurring with Salt-and-Pepper Impulse Noise","authors":"Yuchao Tang, Shirong Deng and Tieyong Zeng","doi":"10.4208/nmtma.oa-2022-0190","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0190","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"32 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135145124","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 : 2023-06-01DOI: 10.4208/jcm.2207-m2022-0020
Hong-lin Liao, Tao Tang null, Tao Zhou
{"title":"Discrete Energy Analysis of the Third-Order Variable-Step BDF Time-Stepping for Diffusion Equations","authors":"Hong-lin Liao, Tao Tang null, Tao Zhou","doi":"10.4208/jcm.2207-m2022-0020","DOIUrl":"https://doi.org/10.4208/jcm.2207-m2022-0020","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136177614","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 : 2023-06-01DOI: 10.4208/nmtma.oa-2023-0082
Alessia Del Grosso, Manuel J. Castro Díaz, Christophe Chalons and Tomás Morales de Luna
{"title":"On Lagrange-Projection Schemes for Shallow Water Flows Over Movable Bottom with Suspended and Bedload Transport","authors":"Alessia Del Grosso, Manuel J. Castro Díaz, Christophe Chalons and Tomás Morales de Luna","doi":"10.4208/nmtma.oa-2023-0082","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2023-0082","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135194185","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 : 2023-06-01DOI: 10.4208/jcm.2211-m2021-0255
Y. Qian, Fei Wang and Wenjing Yan
In this paper, we introduce and analyze an augmented mixed discontinuous Galerkin (MDG) method for a class of quasi-Newtonian Stokes flows. In the mixed formulation, the unknowns are strain rate, stress and velocity, which are approximated by a discontinuous piecewise polynomial triplet P S k +1 - P S k +1 - P k for k ≥ 0. Here, the discontinuous piecewise polynomial function spaces for the field of strain rate and the stress field are designed to be symmetric. In addition, the pressure is easily recovered through simple postprocessing. For the benefit of the analysis, we enrich the MDG scheme with the constitutive equation relating the stress and the strain rate, so that the well-posedness of the augmented formulation is obtained by a nonlinear functional analysis. For k ≥ 0, we get the optimal convergence order for the stress in broken H ( div )-norm and velocity in L 2 -norm. Furthermore, the error estimates of the strain rate and the stress in L 2 -norm, and the pressure in L 2 -norm are optimal under certain conditions. Finally, several numerical examples are given to show the performance of the augmented MDG method and verify the theoretical results. Numerical evidence is provided to show that the orders of convergence are sharp
{"title":"Mixed Discontinuous Galerkin Method for Quasi-Newtonian Stokes Flows","authors":"Y. Qian, Fei Wang and Wenjing Yan","doi":"10.4208/jcm.2211-m2021-0255","DOIUrl":"https://doi.org/10.4208/jcm.2211-m2021-0255","url":null,"abstract":"In this paper, we introduce and analyze an augmented mixed discontinuous Galerkin (MDG) method for a class of quasi-Newtonian Stokes flows. In the mixed formulation, the unknowns are strain rate, stress and velocity, which are approximated by a discontinuous piecewise polynomial triplet P S k +1 - P S k +1 - P k for k ≥ 0. Here, the discontinuous piecewise polynomial function spaces for the field of strain rate and the stress field are designed to be symmetric. In addition, the pressure is easily recovered through simple postprocessing. For the benefit of the analysis, we enrich the MDG scheme with the constitutive equation relating the stress and the strain rate, so that the well-posedness of the augmented formulation is obtained by a nonlinear functional analysis. For k ≥ 0, we get the optimal convergence order for the stress in broken H ( div )-norm and velocity in L 2 -norm. Furthermore, the error estimates of the strain rate and the stress in L 2 -norm, and the pressure in L 2 -norm are optimal under certain conditions. Finally, several numerical examples are given to show the performance of the augmented MDG method and verify the theoretical results. Numerical evidence is provided to show that the orders of convergence are sharp","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44270859","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 : 2023-06-01DOI: 10.4208/jcm.2301-m2021-0313
Debora Cores and Johanna Figueroa
{"title":"A Low-Cost Optimization Approach for Solving Minimum Norm Linear Systems and Linear Least-Squares Problems","authors":"Debora Cores and Johanna Figueroa","doi":"10.4208/jcm.2301-m2021-0313","DOIUrl":"https://doi.org/10.4208/jcm.2301-m2021-0313","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43089056","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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