Pub Date : 2023-02-25DOI: 10.4208/csiam-am.so-2023-0001
Tianjiao Wang, Yi-Jhou Lin, Xiang-Yang Xu
This paper investigates the elastic scattering by unbounded deterministic and random rough surfaces, which both are assumed to be graphs of Lipschitz continuous functions. For the deterministic case, an a priori bound explicitly dependent on frequencies is derived by the variational approach. For the scattering by random rough surfaces with a random source, well-posedness of the corresponding variation problem is proved. Moreover, a similar bound with explicit dependence on frequencies for the random case is also established based upon the deterministic result, Pettis measurability theorem and Bochner's integrability Theorem.
{"title":"A Priori Bounds for Elastic Scattering by Deterministic and Random Unbounded Rough Surfaces","authors":"Tianjiao Wang, Yi-Jhou Lin, Xiang-Yang Xu","doi":"10.4208/csiam-am.so-2023-0001","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2023-0001","url":null,"abstract":"This paper investigates the elastic scattering by unbounded deterministic and random rough surfaces, which both are assumed to be graphs of Lipschitz continuous functions. For the deterministic case, an a priori bound explicitly dependent on frequencies is derived by the variational approach. For the scattering by random rough surfaces with a random source, well-posedness of the corresponding variation problem is proved. Moreover, a similar bound with explicit dependence on frequencies for the random case is also established based upon the deterministic result, Pettis measurability theorem and Bochner's integrability Theorem.","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43638477","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 : 2023-01-01DOI: 10.4208/csiam-am.so-2022-0007
Ben Duan, Zhen Luo null, Yu-Hang Xing
{"title":"Radial Transonic Shock Solutions to Euler-Poisson System with Varying Background Charge in an Annulus","authors":"Ben Duan, Zhen Luo null, Yu-Hang Xing","doi":"10.4208/csiam-am.so-2022-0007","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2022-0007","url":null,"abstract":"","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516494","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 : 2023-01-01DOI: 10.4208/csiam-am.so-2021-0006
Jialin He, Jie Ma null, Tianchi Yang
{"title":"Some Exact Results on 4-Cycles: Stability and Supersaturation","authors":"Jialin He, Jie Ma null, Tianchi Yang","doi":"10.4208/csiam-am.so-2021-0006","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2021-0006","url":null,"abstract":"","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516401","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 : 2023-01-01DOI: 10.4208/csiam-am.so-2022-0012
Shanshan Tong, Wei Wang, Zhenwu Fu, Bo Han
{"title":"Iterative Runge-Kutta-Type Methods with Convex Penalty for Inverse Problems in Hilbert Spaces","authors":"Shanshan Tong, Wei Wang, Zhenwu Fu, Bo Han","doi":"10.4208/csiam-am.so-2022-0012","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2022-0012","url":null,"abstract":"","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516953","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 : 2022-08-31DOI: 10.4208/csiam-am.so-2022-0049
Kai Jiang, Juan Zhang, Qishang Zhou
Matrix splitting iteration methods play a vital role in solving large sparse linear systems. Their performance heavily depends on the splitting parameters, however, the approach of selecting optimal splitting parameters has not been well developed. In this paper, we present a multitask kernel-learning parameter prediction method to automatically obtain relatively optimal splitting parameters, which contains simultaneous multiple parameters prediction and a data-driven kernel learning. For solving time-dependent linear systems, including linear differential systems and linear matrix systems, we give a new matrix splitting Kronecker product method, as well as its convergence analysis and preconditioning strategy. Numerical results illustrate our methods can save an enormous amount of time in selecting the relatively optimal splitting parameters compared with the exists methods. Moreover, our iteration method as a preconditioner can effectively accelerate GMRES. As the dimension of systems increases, all the advantages of our approaches becomes significantly. Especially, for solving the differential Sylvester matrix equation, the speedup ratio can reach tens to hundreds of times when the scale of the system is larger than one hundred thousand.
{"title":"Multitask Kernel-Learning Parameter Prediction Method for Solving Time-Dependent Linear Systems","authors":"Kai Jiang, Juan Zhang, Qishang Zhou","doi":"10.4208/csiam-am.so-2022-0049","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2022-0049","url":null,"abstract":"Matrix splitting iteration methods play a vital role in solving large sparse linear systems. Their performance heavily depends on the splitting parameters, however, the approach of selecting optimal splitting parameters has not been well developed. In this paper, we present a multitask kernel-learning parameter prediction method to automatically obtain relatively optimal splitting parameters, which contains simultaneous multiple parameters prediction and a data-driven kernel learning. For solving time-dependent linear systems, including linear differential systems and linear matrix systems, we give a new matrix splitting Kronecker product method, as well as its convergence analysis and preconditioning strategy. Numerical results illustrate our methods can save an enormous amount of time in selecting the relatively optimal splitting parameters compared with the exists methods. Moreover, our iteration method as a preconditioner can effectively accelerate GMRES. As the dimension of systems increases, all the advantages of our approaches becomes significantly. Especially, for solving the differential Sylvester matrix equation, the speedup ratio can reach tens to hundreds of times when the scale of the system is larger than one hundred thousand.","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44948823","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 : 2022-06-01DOI: 10.4208/csiam-am.2020-0216
Xiangcheng Zheng null, Hong Wang
{"title":"An Error Estimate of a Modified Method of Characteristics Modeling Advective-Diffusive Transport in Randomly Heterogeneous Porous Media","authors":"Xiangcheng Zheng null, Hong Wang","doi":"10.4208/csiam-am.2020-0216","DOIUrl":"https://doi.org/10.4208/csiam-am.2020-0216","url":null,"abstract":"","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43236440","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 : 2022-06-01DOI: 10.4208/csiam-am.so-2021-0018
Li Deng null, Xu Zhang
. In this paper, we present our optimality results on optimal control problems for ordinary differential equations on Riemannian manifolds. For the problems with free states at the terminal time, we obtain the first and second-order necessary conditions, dynamical programming principle, and their relations. Then, we consider the problems with the initial and final states satisfying some inequality-type and equality-type constraints, and establish the corresponding first and second-order necessary conditions of optimal pairs in the sense of either spike or convex variations. For each of the above results concerning second-order optimality conditions, the curvature tensor of the underlying manifold plays a crucial role.
{"title":"A Survey of Optimal Control Problems Evolved on Riemannian Manifolds","authors":"Li Deng null, Xu Zhang","doi":"10.4208/csiam-am.so-2021-0018","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2021-0018","url":null,"abstract":". In this paper, we present our optimality results on optimal control problems for ordinary differential equations on Riemannian manifolds. For the problems with free states at the terminal time, we obtain the first and second-order necessary conditions, dynamical programming principle, and their relations. Then, we consider the problems with the initial and final states satisfying some inequality-type and equality-type constraints, and establish the corresponding first and second-order necessary conditions of optimal pairs in the sense of either spike or convex variations. For each of the above results concerning second-order optimality conditions, the curvature tensor of the underlying manifold plays a crucial role.","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41947093","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 : 2022-06-01DOI: 10.4208/csiam-am.so-2021-0039
Shuangshuang Wu, Yuchao Tang null, T. Zeng
{"title":"Relaxed Alternating Minimization Algorithm for Separable Convex Programming with Applications to Imaging","authors":"Shuangshuang Wu, Yuchao Tang null, T. Zeng","doi":"10.4208/csiam-am.so-2021-0039","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2021-0039","url":null,"abstract":"","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48761792","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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