{"title":"双鞍点问题的改进型交替正半有限分裂预处理器","authors":"Jun Li, Shu-Xin Miao, Xiangtuan Xiong","doi":"10.1007/s12190-024-02165-6","DOIUrl":null,"url":null,"abstract":"<p>In this paper, to further enhance the efficiency of the improved alternating positive semi-definite splitting (IAPSS) preconditioner proposed by Ren et al. (Numer Algorithms 91:1363–1379, 2022. https://doi.org/10.1007/s11075-022-01305-y), the modified IAPSS preconditioner is established, which can be applied to GMRES method to solve the double saddle point problems. The construction idea of the preconditioner is to modify several sub-matrices in the IAPSS preconditioner. Theoretically, the iteration method generated by the proposed preconditioner is unconditionally convergent for all positive parameters. Furthermore, the selection of the parameters is discussed in detail. Finally, the performance of the preconditioner is verified by the two examples of the liquid crystal director model and the mixed Stokes/Darcy model.</p>","PeriodicalId":15034,"journal":{"name":"Journal of Applied Mathematics and Computing","volume":"241 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A modified improved alternating positive semi-definite splitting preconditioner for double saddle point problems\",\"authors\":\"Jun Li, Shu-Xin Miao, Xiangtuan Xiong\",\"doi\":\"10.1007/s12190-024-02165-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, to further enhance the efficiency of the improved alternating positive semi-definite splitting (IAPSS) preconditioner proposed by Ren et al. (Numer Algorithms 91:1363–1379, 2022. https://doi.org/10.1007/s11075-022-01305-y), the modified IAPSS preconditioner is established, which can be applied to GMRES method to solve the double saddle point problems. The construction idea of the preconditioner is to modify several sub-matrices in the IAPSS preconditioner. Theoretically, the iteration method generated by the proposed preconditioner is unconditionally convergent for all positive parameters. Furthermore, the selection of the parameters is discussed in detail. Finally, the performance of the preconditioner is verified by the two examples of the liquid crystal director model and the mixed Stokes/Darcy model.</p>\",\"PeriodicalId\":15034,\"journal\":{\"name\":\"Journal of Applied Mathematics and Computing\",\"volume\":\"241 1\",\"pages\":\"\"},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2024-07-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Mathematics and Computing\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s12190-024-02165-6\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mathematics and Computing","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s12190-024-02165-6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
A modified improved alternating positive semi-definite splitting preconditioner for double saddle point problems
In this paper, to further enhance the efficiency of the improved alternating positive semi-definite splitting (IAPSS) preconditioner proposed by Ren et al. (Numer Algorithms 91:1363–1379, 2022. https://doi.org/10.1007/s11075-022-01305-y), the modified IAPSS preconditioner is established, which can be applied to GMRES method to solve the double saddle point problems. The construction idea of the preconditioner is to modify several sub-matrices in the IAPSS preconditioner. Theoretically, the iteration method generated by the proposed preconditioner is unconditionally convergent for all positive parameters. Furthermore, the selection of the parameters is discussed in detail. Finally, the performance of the preconditioner is verified by the two examples of the liquid crystal director model and the mixed Stokes/Darcy model.
期刊介绍：
JAMC is a broad based journal covering all branches of computational or applied mathematics with special encouragement to researchers in theoretical computer science and mathematical computing. Major areas, such as numerical analysis, discrete optimization, linear and nonlinear programming, theory of computation, control theory, theory of algorithms, computational logic, applied combinatorics, coding theory, cryptograhics, fuzzy theory with applications, differential equations with applications are all included. A large variety of scientific problems also necessarily involve Algebra, Analysis, Geometry, Probability and Statistics and so on. The journal welcomes research papers in all branches of mathematics which have some bearing on the application to scientific problems, including papers in the areas of Actuarial Science, Mathematical Biology, Mathematical Economics and Finance.
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