Pub Date : 2024-07-01DOI: 10.4208/csiam-am.so-2022-0038
Yi Lu and Chunhua Jin
{"title":"Global Solvability and Decay Properties for a $p$-Laplacian Diffusive Keller-Segel Model","authors":"Yi Lu and Chunhua Jin","doi":"10.4208/csiam-am.so-2022-0038","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2022-0038","url":null,"abstract":"","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141841988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-01DOI: 10.4208/csiam-am.so-2023-0021
Wei Wang and Chengyun Yang
{"title":"Total Variations for Hue, Saturation, and Value of a Color Image","authors":"Wei Wang and Chengyun Yang","doi":"10.4208/csiam-am.so-2023-0021","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2023-0021","url":null,"abstract":"","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141030281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-01DOI: 10.4208/csiam-am.so-2023-0045
Yannan Chen, Kaidong Fu, Can Li and Qi Ye
. Scattered data interpolation aims to reconstruct a continuous (smooth) function that approximates the underlying function by fitting (meshless) data points. There are extensive applications of scattered data interpolation in computer graphics, fluid dynamics, inverse kinematics, machine learning, etc. In this paper, we consider a novel generalized Mercel kernel in the reproducing kernel Banach space for scattered data interpolation. The system of interpolation equations is formulated as a multilinear sys-tem with a structural tensor, which is an absolutely and uniformly convergent infinite series of symmetric rank-one tensors. Then we design a fast numerical method for computing the product of the structural tensor and any vector in arbitrary precision. Whereafter, a scalable optimization approach equipped with limited-memory BFGS and Wolfe line-search techniques is customized for solving these multilinear systems. Using the Łojasiewicz inequality, we prove that the proposed scalable optimization approach is a globally convergent algorithm and possesses a linear or sublinear convergence rate. Numerical experiments illustrate that the proposed scalable optimization approach can improve the accuracy of interpolation fitting and computational efficiency.
{"title":"A Scalable Optimization Approach for the Multilinear System Arising from Scattered Data Interpolation","authors":"Yannan Chen, Kaidong Fu, Can Li and Qi Ye","doi":"10.4208/csiam-am.so-2023-0045","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2023-0045","url":null,"abstract":". Scattered data interpolation aims to reconstruct a continuous (smooth) function that approximates the underlying function by fitting (meshless) data points. There are extensive applications of scattered data interpolation in computer graphics, fluid dynamics, inverse kinematics, machine learning, etc. In this paper, we consider a novel generalized Mercel kernel in the reproducing kernel Banach space for scattered data interpolation. The system of interpolation equations is formulated as a multilinear sys-tem with a structural tensor, which is an absolutely and uniformly convergent infinite series of symmetric rank-one tensors. Then we design a fast numerical method for computing the product of the structural tensor and any vector in arbitrary precision. Whereafter, a scalable optimization approach equipped with limited-memory BFGS and Wolfe line-search techniques is customized for solving these multilinear systems. Using the Łojasiewicz inequality, we prove that the proposed scalable optimization approach is a globally convergent algorithm and possesses a linear or sublinear convergence rate. Numerical experiments illustrate that the proposed scalable optimization approach can improve the accuracy of interpolation fitting and computational efficiency.","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141049387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-01DOI: 10.4208/csiam-am.so-2023-0032
Yabing Sun and Weidong Zhao
{"title":"Stochastic Runge-Kutta Methods for Preserving Maximum Bound Principle of Semilinear Parabolic Equations. Part I: Gaussian Quadrature Rule","authors":"Yabing Sun and Weidong Zhao","doi":"10.4208/csiam-am.so-2023-0032","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2023-0032","url":null,"abstract":"","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141058444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-01DOI: 10.4208/csiam-am.so-2023-0023
Wangtao Lu, Jun Lai and Haijun Wu
. This paper proposes a novel method to establish the well-posedness of uni-axial perfectly matched layer (UPML) method for a two-dimensional acoustic scattering from a compactly supported source in a two-layered medium. We solve a long standing problem by showing that the truncated layered medium scattering problem is always resonance free regardless of the thickness and absorbing strength of UPML. The main idea is based on analyzing an auxiliary waveguide problem obtained by truncating the layered medium scattering problem through PML in the vertical direction only. The Green function for this waveguide problem can be constructed explicitly based on the separation of variables and Fourier transform. We prove that such a construction is always well-defined regardless of the absorbing strength. The well-posedness of the fully UPML truncated scattering problem follows by assembling the waveguide Green function through periodic extension.
{"title":"On the Well-Posedness of UPML Method for Wave Scattering in Layered Media","authors":"Wangtao Lu, Jun Lai and Haijun Wu","doi":"10.4208/csiam-am.so-2023-0023","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2023-0023","url":null,"abstract":". This paper proposes a novel method to establish the well-posedness of uni-axial perfectly matched layer (UPML) method for a two-dimensional acoustic scattering from a compactly supported source in a two-layered medium. We solve a long standing problem by showing that the truncated layered medium scattering problem is always resonance free regardless of the thickness and absorbing strength of UPML. The main idea is based on analyzing an auxiliary waveguide problem obtained by truncating the layered medium scattering problem through PML in the vertical direction only. The Green function for this waveguide problem can be constructed explicitly based on the separation of variables and Fourier transform. We prove that such a construction is always well-defined regardless of the absorbing strength. The well-posedness of the fully UPML truncated scattering problem follows by assembling the waveguide Green function through periodic extension.","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140278951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-01DOI: 10.4208/csiam-am.so-2022-0018
Waixiang Cao, Lueling Jia and Zhimin Zhang
{"title":"A $C^1$-Conforming Gauss Collocation Method for Elliptic Equations and Superconvergence Analysis Over Rectangular Meshes","authors":"Waixiang Cao, Lueling Jia and Zhimin Zhang","doi":"10.4208/csiam-am.so-2022-0018","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2022-0018","url":null,"abstract":"","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140273281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-01DOI: 10.4208/csiam-am.so-2023-0049
Manyi Zheng, Zhishan Qiu, Feng Jiao and Qiwen Sun
{"title":"A Novel Computational Method for Two-State Transcription Model with Non-Exponential ON and OFF Durations","authors":"Manyi Zheng, Zhishan Qiu, Feng Jiao and Qiwen Sun","doi":"10.4208/csiam-am.so-2023-0049","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2023-0049","url":null,"abstract":"","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140281002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-01DOI: 10.4208/csiam-am.so-2023-0013
Zhengyang Qiao, Yicheng Liu and Xiao Wang
{"title":"Flocking Behaviors of a Body Attitude Coordination Model with Velocity Alignment","authors":"Zhengyang Qiao, Yicheng Liu and Xiao Wang","doi":"10.4208/csiam-am.so-2023-0013","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2023-0013","url":null,"abstract":"","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139453670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-01DOI: 10.4208/csiam-am.so-2023-0022
Yunqing Huang and Shangyou Zhang
{"title":"On the Optimal Order Approximation of the Partition of Unity Finite Element Method","authors":"Yunqing Huang and Shangyou Zhang","doi":"10.4208/csiam-am.so-2023-0022","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2023-0022","url":null,"abstract":"","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139636116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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