Pub Date : 2023-11-01DOI: 10.4208/jcm.2305-m2022-0215
Pratibha Shakya
{"title":"Error Analysis for Parabolic Optimal Control Problems with Measure Data in a Nonconvex Polygonal Domain","authors":"Pratibha Shakya","doi":"10.4208/jcm.2305-m2022-0215","DOIUrl":"https://doi.org/10.4208/jcm.2305-m2022-0215","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139294507","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 : 2023-11-01DOI: 10.4208/jcm.2304-m2022-0185
Jianliang Li, Xiaoli Liu, Bo Zhang and Haiwen Zhang
{"title":"The Nyström Method for Elastic Wave Scattering By Unbounded Rough Surfaces","authors":"Jianliang Li, Xiaoli Liu, Bo Zhang and Haiwen Zhang","doi":"10.4208/jcm.2304-m2022-0185","DOIUrl":"https://doi.org/10.4208/jcm.2304-m2022-0185","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139294940","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 : 2023-11-01DOI: 10.4208/jcm.2305-m2021-0107
Jianchao Bai, Ke Guo, Junli Liang, Yang Jing and H.C. So
{"title":"Accelerated Symmetric ADMM and Its Applications in Large-Scale Signal Processing","authors":"Jianchao Bai, Ke Guo, Junli Liang, Yang Jing and H.C. So","doi":"10.4208/jcm.2305-m2021-0107","DOIUrl":"https://doi.org/10.4208/jcm.2305-m2021-0107","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139301946","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 : 2023-11-01DOI: 10.4208/jcm.2304-m2022-0140
Minghua Chen, Fan Yu, Qingdong Zhang and Zhimin Zhang
In this work, we analyze the three-step backward differentiation formula (BDF3) method for solving the Allen-Cahn equation on variable grids. For BDF2 method, the discrete orthogonal convolution (DOC) kernels are positive, the stability and convergence analysis are well established in [Liao and Zhang, newblock Math. Comp., textbf{90} (2021) 1207--1226; Chen, Yu, and Zhang, newblock SIAM J. Numer. Anal., Major Revised]. However, the numerical analysis for BDF3 method with variable steps seems to be highly nontrivial, since the DOC kernels are not always positive. By developing a novel spectral norm inequality, the unconditional stability and convergence are rigorously proved under the updated step ratio restriction $r_k:=tau_k/tau_{k-1}leq 1.405$ (compared with $r_kleq 1.199$ in [Calvo and Grigorieff, newblock BIT. textbf{42} (2002) 689--701]) for BDF3 method. Finally, numerical experiments are performed to illustrate the theoretical results. To the best of our knowledge, this is the first theoretical analysis of variable steps BDF3 method for the Allen-Cahn equation.
{"title":"Variable Step-Size BDF3 Method for Allen-Cahn Equation","authors":"Minghua Chen, Fan Yu, Qingdong Zhang and Zhimin Zhang","doi":"10.4208/jcm.2304-m2022-0140","DOIUrl":"https://doi.org/10.4208/jcm.2304-m2022-0140","url":null,"abstract":"In this work, we analyze the three-step backward differentiation formula (BDF3) method for solving the Allen-Cahn equation on variable grids. For BDF2 method, the discrete orthogonal convolution (DOC) kernels are positive, the stability and convergence analysis are well established in [Liao and Zhang, newblock Math. Comp., textbf{90} (2021) 1207--1226; Chen, Yu, and Zhang, newblock SIAM J. Numer. Anal., Major Revised]. However, the numerical analysis for BDF3 method with variable steps seems to be highly nontrivial, since the DOC kernels are not always positive. By developing a novel spectral norm inequality, the unconditional stability and convergence are rigorously proved under the updated step ratio restriction $r_k:=tau_k/tau_{k-1}leq 1.405$ (compared with $r_kleq 1.199$ in [Calvo and Grigorieff, newblock BIT. textbf{42} (2002) 689--701]) for BDF3 method. Finally, numerical experiments are performed to illustrate the theoretical results. To the best of our knowledge, this is the first theoretical analysis of variable steps BDF3 method for the Allen-Cahn equation.","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135714975","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 : 2023-11-01DOI: 10.4208/jcm.2305-m2023-0014
Daxin Nie and Weihua Deng
{"title":"Numerical Analysis for Stochastic Time-Space Fractional Diffusion Equation Driven By Fractional Gaussian Noise","authors":"Daxin Nie and Weihua Deng","doi":"10.4208/jcm.2305-m2023-0014","DOIUrl":"https://doi.org/10.4208/jcm.2305-m2023-0014","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139305528","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 : 2023-11-01DOI: 10.4208/jcm.2303-m2021-0309
Sihong Shao, Dong Zhang and Weixi Zhang null
We propose a simple iterative (SI) algorithm for the maxcut problem through fully using an equivalent continuous formulation. It does not need rounding at all and has advantages that all subproblems have explicit analytic solutions, the cut values are monotonically updated and the iteration points converge to a local optima in finite steps via an appropriate subgradient selection. Numerical experiments on G-set demonstrate the performance. In particular, the ratios between the best cut values achieved by SI and the best known ones are at least $0.986$ and can be further improved to at least $0.997$ by a preliminary attempt to break out of local optima.
{"title":"A Simple Iterative Algorithm for Maxcut","authors":"Sihong Shao, Dong Zhang and Weixi Zhang null","doi":"10.4208/jcm.2303-m2021-0309","DOIUrl":"https://doi.org/10.4208/jcm.2303-m2021-0309","url":null,"abstract":"We propose a simple iterative (SI) algorithm for the maxcut problem through fully using an equivalent continuous formulation. It does not need rounding at all and has advantages that all subproblems have explicit analytic solutions, the cut values are monotonically updated and the iteration points converge to a local optima in finite steps via an appropriate subgradient selection. Numerical experiments on G-set demonstrate the performance. In particular, the ratios between the best cut values achieved by SI and the best known ones are at least $0.986$ and can be further improved to at least $0.997$ by a preliminary attempt to break out of local optima.","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135217556","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 : 2023-11-01DOI: 10.4208/jcm.2305-m2022-0268
Jie Xu and Mingbo Zhang
{"title":"Wong-Zakai Approximations for Stochastic Volterra Equations","authors":"Jie Xu and Mingbo Zhang","doi":"10.4208/jcm.2305-m2022-0268","DOIUrl":"https://doi.org/10.4208/jcm.2305-m2022-0268","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139299758","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 : 2023-10-01DOI: 10.4208/jcm.2301-m2022-0088
Jingjun Zhao, Hao Zhou and Yang Xu
{"title":"Modified Split-Step Theta Method for Stochastic Differential Equations Driven By Fractional Brownian Motion","authors":"Jingjun Zhao, Hao Zhou and Yang Xu","doi":"10.4208/jcm.2301-m2022-0088","DOIUrl":"https://doi.org/10.4208/jcm.2301-m2022-0088","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135706056","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 : 2023-10-01DOI: 10.4208/jcm.2307-m2021-0331
Nachuan Xiao and Xin Liu
In this paper, we present a novel penalty model called ExPen for optimization over the Stiefel manifold. Different from existing penalty functions for orthogonality constraints, ExPen adopts a smooth penalty function without using any first-order derivative of the objective function. We show that all the first-order stationary points of ExPen with a sufficiently large penalty parameter are either feasible, namely, are the first-order stationary points of the original optimization problem, or far from the Stiefel manifold. Besides, the original problem and ExPen share the same second-order stationary points. Remarkably, the exact gradient and Hessian of ExPen are easy to compute. As a consequence, abundant algorithm resources in unconstrained optimization can be applied straightforwardly to solve ExPen.
{"title":"Solving Optimization Problems over the Stiefel Manifold by Smooth Exact Penalty Functions","authors":"Nachuan Xiao and Xin Liu","doi":"10.4208/jcm.2307-m2021-0331","DOIUrl":"https://doi.org/10.4208/jcm.2307-m2021-0331","url":null,"abstract":"In this paper, we present a novel penalty model called ExPen for optimization over the Stiefel manifold. Different from existing penalty functions for orthogonality constraints, ExPen adopts a smooth penalty function without using any first-order derivative of the objective function. We show that all the first-order stationary points of ExPen with a sufficiently large penalty parameter are either feasible, namely, are the first-order stationary points of the original optimization problem, or far from the Stiefel manifold. Besides, the original problem and ExPen share the same second-order stationary points. Remarkably, the exact gradient and Hessian of ExPen are easy to compute. As a consequence, abundant algorithm resources in unconstrained optimization can be applied straightforwardly to solve ExPen.","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136094371","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 : 2023-10-01DOI: 10.4208/jcm.2301-m2022-0116
Mengyun Wang, Ye Ji and Chungang Zhu
{"title":"Degree Elevation and Knot Insertion for Generalized Bézier Surfaces and Their Application to Isogeometric Analysis","authors":"Mengyun Wang, Ye Ji and Chungang Zhu","doi":"10.4208/jcm.2301-m2022-0116","DOIUrl":"https://doi.org/10.4208/jcm.2301-m2022-0116","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135706411","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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