Pub Date : 2023-11-17DOI: 10.1007/s13160-023-00625-3
Jun Li, Zhenping Li
In this paper, inspired by the simplified relaxed alternating positive semi-definite splitting preconditioner (Xiong and Li in J Appl Math Comput, 2023), a modified preconditioner is established to solve the three-by-three block saddle point problems. The advantage of the modified preconditioner is that its parameters can be easy to select, which can avoid the work of the calculation of the parameters. Next, the spectral property of the preconditioned matrix with modified preconditioner is also discussed. In the end, three examples are provided to show the effectiveness of the modified preconditioner.
本文受简化松弛交替正半定分裂预条件(Xiong and Li In J applied Math computing, 2023)的启发，建立了一个改进的预条件来求解3 × 3块鞍点问题。改进后的预调节器的优点是其参数易于选择，从而避免了参数计算的工作量。其次，讨论了带修正预条件的预条件矩阵的谱性质。最后，通过三个算例说明了改进预调节器的有效性。
{"title":"A modified preconditioner for three-by-three block saddle point problems","authors":"Jun Li, Zhenping Li","doi":"10.1007/s13160-023-00625-3","DOIUrl":"https://doi.org/10.1007/s13160-023-00625-3","url":null,"abstract":"<p>In this paper, inspired by the simplified relaxed alternating positive semi-definite splitting preconditioner (Xiong and Li in J Appl Math Comput, 2023), a modified preconditioner is established to solve the three-by-three block saddle point problems. The advantage of the modified preconditioner is that its parameters can be easy to select, which can avoid the work of the calculation of the parameters. Next, the spectral property of the preconditioned matrix with modified preconditioner is also discussed. In the end, three examples are provided to show the effectiveness of the modified preconditioner.</p>","PeriodicalId":50264,"journal":{"name":"Japan Journal of Industrial and Applied Mathematics","volume":"17 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138518771","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 : 2023-11-16DOI: 10.1007/s13160-023-00627-1
Noriyuki Kushida, Hiroshi Okuda
Variable preconditioning methods for Krylov-type linear equation solvers have become popular thanks to their faster convergence speed compared to conventional methods, such as, the Incomplete Lower-Upper factorization and point Jacobi methods. Recently, Kushida and Okuda have introduced a variable preconditioning method, which updates the preconditioning matrix using the Broyden–Fletcher–Goldfarb–Shanno scheme, and applied it to the generalized minimum residual recursive scheme (GMRESR), which is a variant of the well-known GMRES method. Although their method indicated a superior performance to the conventional methods, the problems employed in their study were academic, and its performance on practical problems is of interest. In this study, we evaluate the feasibility of their variable preconditioning for practical problems. FrontISTR, which is a well established open-source parallel finite element analysis program and well used in the industrial field, is employed as the framework to implement the above-mentioned Kushida and Okuda’s preconditioning method in GMRESR (Self-Updating Preconditioning GMRESR; SUP-GMRESR). As results, (1) SUP-GMRESR indicated approximately a three-fold faster convergence than GMRES, which is one of the default linear equation solvers implemented on FrontISTR, using a 600 million degrees of freedom problem, and (2) SUP-GMRESR converged even when GMRES suffered from a stagnation.
{"title":"A performance evaluation of a new flexible preconditioning method on a parallel finite element structure analysis program, FrontISTR","authors":"Noriyuki Kushida, Hiroshi Okuda","doi":"10.1007/s13160-023-00627-1","DOIUrl":"https://doi.org/10.1007/s13160-023-00627-1","url":null,"abstract":"<p>Variable preconditioning methods for Krylov-type linear equation solvers have become popular thanks to their faster convergence speed compared to conventional methods, such as, the Incomplete Lower-Upper factorization and point Jacobi methods. Recently, Kushida and Okuda have introduced a variable preconditioning method, which updates the preconditioning matrix using the Broyden–Fletcher–Goldfarb–Shanno scheme, and applied it to the generalized minimum residual recursive scheme (GMRESR), which is a variant of the well-known GMRES method. Although their method indicated a superior performance to the conventional methods, the problems employed in their study were academic, and its performance on practical problems is of interest. In this study, we evaluate the feasibility of their variable preconditioning for practical problems. FrontISTR, which is a well established open-source parallel finite element analysis program and well used in the industrial field, is employed as the framework to implement the above-mentioned Kushida and Okuda’s preconditioning method in GMRESR (Self-Updating Preconditioning GMRESR; SUP-GMRESR). As results, (1) SUP-GMRESR indicated approximately a three-fold faster convergence than GMRES, which is one of the default linear equation solvers implemented on FrontISTR, using a 600 million degrees of freedom problem, and (2) SUP-GMRESR converged even when GMRES suffered from a stagnation.</p>","PeriodicalId":50264,"journal":{"name":"Japan Journal of Industrial and Applied Mathematics","volume":"13 5","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138518772","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 : 2023-11-14DOI: 10.1007/s13160-023-00626-2
Yoshihisa Morita, Yoshitaro Tanaka
{"title":"Existence of spiky stationary solutions to a mass-conserved reaction-diffusion model","authors":"Yoshihisa Morita, Yoshitaro Tanaka","doi":"10.1007/s13160-023-00626-2","DOIUrl":"https://doi.org/10.1007/s13160-023-00626-2","url":null,"abstract":"","PeriodicalId":50264,"journal":{"name":"Japan Journal of Industrial and Applied Mathematics","volume":"64 16","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134901179","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 : 2023-11-08DOI: 10.1007/s13160-023-00621-7
T. Pasayat, A. Patra, M. Sahoo
{"title":"Fractional sight analysis of generalized perturbed Zakharov–Kuznetsov equation using Elzaki transform","authors":"T. Pasayat, A. Patra, M. Sahoo","doi":"10.1007/s13160-023-00621-7","DOIUrl":"https://doi.org/10.1007/s13160-023-00621-7","url":null,"abstract":"","PeriodicalId":50264,"journal":{"name":"Japan Journal of Industrial and Applied Mathematics","volume":"117 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135341597","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 : 2023-11-03DOI: 10.1007/s13160-023-00624-4
N. Zhang, J. K. Liu, B. Tang
{"title":"A three-term projection method based on spectral secant equation for nonlinear monotone equations","authors":"N. Zhang, J. K. Liu, B. Tang","doi":"10.1007/s13160-023-00624-4","DOIUrl":"https://doi.org/10.1007/s13160-023-00624-4","url":null,"abstract":"","PeriodicalId":50264,"journal":{"name":"Japan Journal of Industrial and Applied Mathematics","volume":"10 11","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135821144","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 : 2023-10-27DOI: 10.1007/s13160-023-00620-8
Jianhua Zhang, Yuqing Wang, Jing Zhao
{"title":"On pseudoinverse-free block maximum residual nonlinear Kaczmarz method for solving large-scale nonlinear system of equations","authors":"Jianhua Zhang, Yuqing Wang, Jing Zhao","doi":"10.1007/s13160-023-00620-8","DOIUrl":"https://doi.org/10.1007/s13160-023-00620-8","url":null,"abstract":"","PeriodicalId":50264,"journal":{"name":"Japan Journal of Industrial and Applied Mathematics","volume":"28 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136262149","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 : 2023-10-19DOI: 10.1007/s13160-023-00622-6
Taoshun He, Yong Chen
{"title":"Pricing European options under stochastic looping contagion risk model","authors":"Taoshun He, Yong Chen","doi":"10.1007/s13160-023-00622-6","DOIUrl":"https://doi.org/10.1007/s13160-023-00622-6","url":null,"abstract":"","PeriodicalId":50264,"journal":{"name":"Japan Journal of Industrial and Applied Mathematics","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135731475","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}
{"title":"Scheduling system for automated storage and retrieval system with multiple machines using a time-expanded network","authors":"Hiroki Ishikura, Nariaki Tateiwa, Shingo Egi, Issa Oe, Nozomi Hata, Toru Mitsutake, Keiichiro Yamamura, Miyu Fujii, Katsuki Fujisawa","doi":"10.1007/s13160-023-00619-1","DOIUrl":"https://doi.org/10.1007/s13160-023-00619-1","url":null,"abstract":"","PeriodicalId":50264,"journal":{"name":"Japan Journal of Industrial and Applied Mathematics","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136014659","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 : 2023-10-06DOI: 10.1007/s13160-023-00618-2
Yuma Tamura
{"title":"On a certain martingale representation and the related infinite dimensional moment problem","authors":"Yuma Tamura","doi":"10.1007/s13160-023-00618-2","DOIUrl":"https://doi.org/10.1007/s13160-023-00618-2","url":null,"abstract":"","PeriodicalId":50264,"journal":{"name":"Japan Journal of Industrial and Applied Mathematics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135351194","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 : 2023-09-22DOI: 10.1007/s13160-023-00617-3
Rui Zhang
{"title":"On the spectral bias of coupled frequency predictor–corrector triangular DNN: The convergence analysis","authors":"Rui Zhang","doi":"10.1007/s13160-023-00617-3","DOIUrl":"https://doi.org/10.1007/s13160-023-00617-3","url":null,"abstract":"","PeriodicalId":50264,"journal":{"name":"Japan Journal of Industrial and Applied Mathematics","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136061213","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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