{"title":"Tracing Isomanifolds in (mathbb{R}) d in Time Polynomial in d using Coxeter-Freudenthal-Kuhn Triangulations","authors":"J. Boissonnat, S. Kachanovich, M. Wintraecken","doi":"10.1137/21m1412918","DOIUrl":"https://doi.org/10.1137/21m1412918","url":null,"abstract":"","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":"AES-3 1","pages":"452-486"},"PeriodicalIF":0.0,"publicationDate":"2023-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84468125","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}
. The block Cimmino is a parallel hybrid row-block projection iterative method suc-4 cessfully used for solving general sparse linear systems. However, the convergence of the method 5 degrades when angles between subspaces spanned by the row-blocks are far from being orthogonal. 6 The density of columns as well as the numerical values of their nonzeros are more likely to contribute 7 to the non-orthogonality between row blocks. We propose a novel scheme to handle such “dense” 8 columns. The proposed scheme forms a reduced system by separating these columns and the re-9 spective rows from the original coefficient matrix and handling them via Schur complement. Then, 10 the angles between subspaces spanned by the row-blocks of the reduced system are expected to be 11 closer to orthogonal and the reduced system is solved efficiently by the block Conjugate Gradient 12 accelerated block Cimmino in fewer iterations. We also propose a novel metric for selecting “dense” 13 columns considering the numerical values. The proposed metric establishes an upper bound on the 14 sum of inner–products between row-blocks. Then, we propose an efficient algorithm for computing 15 the proposed metric for the columns. Extensive numerical experiments for a wide range of linear 16 systems confirm the effectiveness of the proposed scheme by achieving fewer iterations and faster 17 parallel solution time compared to the classical CG accelerated block Cimmino algorithm. 18
{"title":"Enhancing Block Cimmino for Sparse Linear Systems with Dense Columns via Schur Complement","authors":"F. S. Torun, Murat Manguoglu, C. Aykanat","doi":"10.1137/21m1453475","DOIUrl":"https://doi.org/10.1137/21m1453475","url":null,"abstract":". The block Cimmino is a parallel hybrid row-block projection iterative method suc-4 cessfully used for solving general sparse linear systems. However, the convergence of the method 5 degrades when angles between subspaces spanned by the row-blocks are far from being orthogonal. 6 The density of columns as well as the numerical values of their nonzeros are more likely to contribute 7 to the non-orthogonality between row blocks. We propose a novel scheme to handle such “dense” 8 columns. The proposed scheme forms a reduced system by separating these columns and the re-9 spective rows from the original coefficient matrix and handling them via Schur complement. Then, 10 the angles between subspaces spanned by the row-blocks of the reduced system are expected to be 11 closer to orthogonal and the reduced system is solved efficiently by the block Conjugate Gradient 12 accelerated block Cimmino in fewer iterations. We also propose a novel metric for selecting “dense” 13 columns considering the numerical values. The proposed metric establishes an upper bound on the 14 sum of inner–products between row-blocks. Then, we propose an efficient algorithm for computing 15 the proposed metric for the columns. Extensive numerical experiments for a wide range of linear 16 systems confirm the effectiveness of the proposed scheme by achieving fewer iterations and faster 17 parallel solution time compared to the classical CG accelerated block Cimmino algorithm. 18","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":"10 1","pages":"49-"},"PeriodicalIF":0.0,"publicationDate":"2023-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90225952","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}
{"title":"Mass-, Energy-, and Momentum-Preserving Spectral Scheme for Klein-Gordon-Schrödinger System on Infinite Domains","authors":"Shimin Guo, Liquan Mei, Wenjing Yan, Ying Li","doi":"10.1137/22m1484109","DOIUrl":"https://doi.org/10.1137/22m1484109","url":null,"abstract":"","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":"14 1","pages":"200-"},"PeriodicalIF":0.0,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88465329","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}
{"title":"A Novel Density Based Approach for Topology Optimization of Stokes Flow","authors":"Johannes Haubner, Franziska Neumann, M. Ulbrich","doi":"10.1137/21m143114x","DOIUrl":"https://doi.org/10.1137/21m143114x","url":null,"abstract":"","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":"33 1","pages":"338-"},"PeriodicalIF":0.0,"publicationDate":"2023-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80276323","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}
{"title":"Symplectic Model Reduction of Hamiltonian Systems on Nonlinear Manifolds and Approximation with Weakly Symplectic Autoencoder","authors":"Patrick Buchfink, Silke Glas, B. Haasdonk","doi":"10.1137/21m1466657","DOIUrl":"https://doi.org/10.1137/21m1466657","url":null,"abstract":"","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":"34 1","pages":"289-"},"PeriodicalIF":0.0,"publicationDate":"2023-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82488394","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}
In this talk, we focus our investigation on providing long-term estimates of the Hamiltonian deviation computed along numerical approximations to the solutions of stochastic Hamiltonian systems, both of Itô and Statonovich types. It is well-known that the expected Hamiltonian of an Itô Hamiltonian system with additive noise exhibits a linear drift in time [2], while the Hamiltonian function is conserved along the exact flow of a Stratonovich Hamiltonian system [3, 4]. Here, we address our attention to providing modified differential equations associated to suitable discretizations for above problems, by means of weak backward error analysis arguments [1, 5, 6]. Then, long-term estimates are provided both for Itô and Stratonovich Hamiltonian systems, revealing the presence of parasitic terms affecting the overall conservation accuracy. Finally, selected numerical experiments are provided to confirm the theoretical analysis. This talk is based on a joint work with Raffaele D’Ambrosio (University of L’Aquila).
{"title":"Long-Term Analysis of Stochastic Hamiltonian Systems Under Time Discretizations","authors":"R. D'Ambrosio, Stefano Di Giovacchino","doi":"10.1137/21m1458612","DOIUrl":"https://doi.org/10.1137/21m1458612","url":null,"abstract":"In this talk, we focus our investigation on providing long-term estimates of the Hamiltonian deviation computed along numerical approximations to the solutions of stochastic Hamiltonian systems, both of Itô and Statonovich types. It is well-known that the expected Hamiltonian of an Itô Hamiltonian system with additive noise exhibits a linear drift in time [2], while the Hamiltonian function is conserved along the exact flow of a Stratonovich Hamiltonian system [3, 4]. Here, we address our attention to providing modified differential equations associated to suitable discretizations for above problems, by means of weak backward error analysis arguments [1, 5, 6]. Then, long-term estimates are provided both for Itô and Stratonovich Hamiltonian systems, revealing the presence of parasitic terms affecting the overall conservation accuracy. Finally, selected numerical experiments are provided to confirm the theoretical analysis. This talk is based on a joint work with Raffaele D’Ambrosio (University of L’Aquila).","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":"21 1","pages":"257-"},"PeriodicalIF":0.0,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83516073","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}
{"title":"On Min Sum Vertex Cover and Generalized Min Sum Set Cover","authors":"N. Bansal, Jatin Batra, M. Farhadi, P. Tetali","doi":"10.1137/21m1434052","DOIUrl":"https://doi.org/10.1137/21m1434052","url":null,"abstract":"","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":"37 1","pages":"327-357"},"PeriodicalIF":0.0,"publicationDate":"2023-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75518233","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}
{"title":"A Graph-Based Algorithm for the Approximation of the Spectrum of the Curl Operator","authors":"Ana Alonso Rodríguez, J. Camaño","doi":"10.1137/21m1460557","DOIUrl":"https://doi.org/10.1137/21m1460557","url":null,"abstract":"","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":"29 1","pages":"147-"},"PeriodicalIF":0.0,"publicationDate":"2023-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76440468","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}
{"title":"A Generic and Strictly Banded Spectral Petrov-Galerkin Method for Differential Equations with Polynomial Coefficients","authors":"M. Mortensen","doi":"10.1137/22m1492842","DOIUrl":"https://doi.org/10.1137/22m1492842","url":null,"abstract":"","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":"213 1","pages":"123-"},"PeriodicalIF":0.0,"publicationDate":"2023-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88062667","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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