Pub Date : 2022-07-01DOI: 10.1016/j.amc.2022.127085
Ruihan Chen, Moxuan Guo, Song Zhu, Yongqiang Qi, Min Wang, Junhao Hu
{"title":"Reachable set bounding for linear systems with mixed delays and state constraints","authors":"Ruihan Chen, Moxuan Guo, Song Zhu, Yongqiang Qi, Min Wang, Junhao Hu","doi":"10.1016/j.amc.2022.127085","DOIUrl":"https://doi.org/10.1016/j.amc.2022.127085","url":null,"abstract":"","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"1 1","pages":"127085"},"PeriodicalIF":0.0,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90691330","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 : 2022-06-30DOI: 10.48550/arXiv.2207.00063
Ondvrej Kincl, I. Peshkov, M. Pavelka, V. Klika
Smoothed Particle Hydrodynamics (SPH) methods are advantageous in simulations of fluids in domains with free boundary. Special SPH methods have also been developed to simulate solids. However, there are situations where the matter behaves partly as a fluid and partly as a solid, for instance, the solidification front in 3D printing, or any system involving both fluid and solid phases. We develop an SPH-like method that is suitable for both fluids and solids at the same time. Instead of the typical discretization of hydrodynamics, we discretize the Symmetric Hyperbolic Thermodynamically Compatible equations (SHTC), which describe both fluids, elastic solids, and visco-elasto-plastic solids within a single framework. The resulting SHTC-SPH method is then tested on various benchmarks from the hydrodynamics and dynamics of solids and shows remarkable agreement with the data.
{"title":"Unified description of fluids and solids in Smoothed Particle Hydrodynamics","authors":"Ondvrej Kincl, I. Peshkov, M. Pavelka, V. Klika","doi":"10.48550/arXiv.2207.00063","DOIUrl":"https://doi.org/10.48550/arXiv.2207.00063","url":null,"abstract":"Smoothed Particle Hydrodynamics (SPH) methods are advantageous in simulations of fluids in domains with free boundary. Special SPH methods have also been developed to simulate solids. However, there are situations where the matter behaves partly as a fluid and partly as a solid, for instance, the solidification front in 3D printing, or any system involving both fluid and solid phases. We develop an SPH-like method that is suitable for both fluids and solids at the same time. Instead of the typical discretization of hydrodynamics, we discretize the Symmetric Hyperbolic Thermodynamically Compatible equations (SHTC), which describe both fluids, elastic solids, and visco-elasto-plastic solids within a single framework. The resulting SHTC-SPH method is then tested on various benchmarks from the hydrodynamics and dynamics of solids and shows remarkable agreement with the data.","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"12 1","pages":"127579"},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86270705","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 : 2022-05-05DOI: 10.48550/arXiv.2205.02931
R. Treinen
We consider capillary surfaces that are constructed by bounded generating curves. This class of surfaces includes radially symmetric and lower dimensional fluid-fluid interfaces. We use the arc-length representation of the differential equations for these surfaces to allow for vertical points and inflection points along the generating curve. These considerations admit capillary tubes, sessile drops, and fluids in annular tubes as well as other examples. We present a pseudo-spectral method for approximating solutions to the associated boundary value problems based on interpolation by Chebyshev polynomials. This method is observably more stable than the traditional shooting method and it is computationally lean and fast. The algorithm is also adaptive, but does not use the adaptive automation in Chebfun.
{"title":"Spectral Methods for capillary surfaces described by bounded generating curves","authors":"R. Treinen","doi":"10.48550/arXiv.2205.02931","DOIUrl":"https://doi.org/10.48550/arXiv.2205.02931","url":null,"abstract":"We consider capillary surfaces that are constructed by bounded generating curves. This class of surfaces includes radially symmetric and lower dimensional fluid-fluid interfaces. We use the arc-length representation of the differential equations for these surfaces to allow for vertical points and inflection points along the generating curve. These considerations admit capillary tubes, sessile drops, and fluids in annular tubes as well as other examples. We present a pseudo-spectral method for approximating solutions to the associated boundary value problems based on interpolation by Chebyshev polynomials. This method is observably more stable than the traditional shooting method and it is computationally lean and fast. The algorithm is also adaptive, but does not use the adaptive automation in Chebfun.","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"4 1","pages":"127886"},"PeriodicalIF":0.0,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81022801","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 : 2022-04-29DOI: 10.48550/arXiv.2205.06659
Xicui Li, Bin Wang
In this paper, we rigorously analyze the energy, momentum and magnetic moment behaviours of two splitting methods for solving charged-particle dynamics. The near-conservations of these invariants are given for the system under constant magnetic field or quadratic electric potential. By the approach named as backward error analysis, we derive the modified equations and modified invariants of the splitting methods and based on which, the near-conservations over long times are proved. Some numerical experiments are presented to demonstrate these long time behaviours.
{"title":"Long term analysis of splitting methods for charged-particle dynamics","authors":"Xicui Li, Bin Wang","doi":"10.48550/arXiv.2205.06659","DOIUrl":"https://doi.org/10.48550/arXiv.2205.06659","url":null,"abstract":"In this paper, we rigorously analyze the energy, momentum and magnetic moment behaviours of two splitting methods for solving charged-particle dynamics. The near-conservations of these invariants are given for the system under constant magnetic field or quadratic electric potential. By the approach named as backward error analysis, we derive the modified equations and modified invariants of the splitting methods and based on which, the near-conservations over long times are proved. Some numerical experiments are presented to demonstrate these long time behaviours.","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"2010 1","pages":"127682"},"PeriodicalIF":0.0,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82601724","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 : 2022-04-15DOI: 10.48550/arXiv.2204.14089
Benjamin F. Zwick, G. Bourantas, F. Alkhatib, A. Wittek, K. Miller
A new recovery technique based on discretization corrected particle strength exchange (DC PSE) operators is developed in this paper. DC PSE is a collocation method that can be used to compute derivatives directly at nodal points, instead of by projection from Gauss points as is done in many finite element-based recovery techniques. The proposed method is truly meshless and does not require patches of elements to be defined, which makes it generally applicable to point clouds and arbitrary element topologies. Numerical examples show that the proposed method is accurate and robust.
{"title":"Recovery by discretization corrected particle strength exchange (DC PSE) operators","authors":"Benjamin F. Zwick, G. Bourantas, F. Alkhatib, A. Wittek, K. Miller","doi":"10.48550/arXiv.2204.14089","DOIUrl":"https://doi.org/10.48550/arXiv.2204.14089","url":null,"abstract":"A new recovery technique based on discretization corrected particle strength exchange (DC PSE) operators is developed in this paper. DC PSE is a collocation method that can be used to compute derivatives directly at nodal points, instead of by projection from Gauss points as is done in many finite element-based recovery techniques. The proposed method is truly meshless and does not require patches of elements to be defined, which makes it generally applicable to point clouds and arbitrary element topologies. Numerical examples show that the proposed method is accurate and robust.","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"48 1","pages":"127923"},"PeriodicalIF":0.0,"publicationDate":"2022-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83972487","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 : 2022-04-01DOI: 10.1016/j.amc.2021.126825
Han Tang, Xiangfeng Yang
{"title":"Moment estimation in uncertain differential equations based on the Milstein scheme","authors":"Han Tang, Xiangfeng Yang","doi":"10.1016/j.amc.2021.126825","DOIUrl":"https://doi.org/10.1016/j.amc.2021.126825","url":null,"abstract":"","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"36 1","pages":"126825"},"PeriodicalIF":0.0,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72847001","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 : 2022-04-01DOI: 10.1016/j.amc.2021.126826
H. Mehboob, K. Maqbool, Hameed Ullah, A. Siddiqui
{"title":"Computational analysis of an axisymmetric flow of Jeffrey fluid in a permeable micro channel","authors":"H. Mehboob, K. Maqbool, Hameed Ullah, A. Siddiqui","doi":"10.1016/j.amc.2021.126826","DOIUrl":"https://doi.org/10.1016/j.amc.2021.126826","url":null,"abstract":"","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"2015 1","pages":"126826"},"PeriodicalIF":0.0,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87817774","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 : 2022-04-01DOI: 10.1016/j.amc.2021.126822
Boris Furtula, S. Radenković, Izudin Redžepović, Niko Tratnik, Petra Zigert
{"title":"The generalized Zhang-Zhang polynomial of benzenoid systems - theory and applications","authors":"Boris Furtula, S. Radenković, Izudin Redžepović, Niko Tratnik, Petra Zigert","doi":"10.1016/j.amc.2021.126822","DOIUrl":"https://doi.org/10.1016/j.amc.2021.126822","url":null,"abstract":"","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"115 1","pages":"126822"},"PeriodicalIF":0.0,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91115908","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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