Pub Date : 2023-03-29DOI: 10.48550/arXiv.2303.16508
Harald Monsuur, R. Stevenson
We consider an ultra-weak first order system discretization of the Helmholtz equation. When employing the optimal test norm, the `ideal' method yields the best approximation to the pair of the Helmholtz solution and its scaled gradient w.r.t.~the norm on $L_2(Omega)times L_2(Omega)^d$ from the selected finite element trial space. On convex polygons, the `practical', implementable method is shown to be pollution-free essentially whenever the order $tilde{p}$ of the finite element test space grows proportionally with $max(log kappa,p^2)$, with $p$ being the order at trial side. Numerical results also on other domains show a much better accuracy than for the Galerkin method.
{"title":"A pollution-free ultra-weak FOSLS discretization of the Helmholtz equation","authors":"Harald Monsuur, R. Stevenson","doi":"10.48550/arXiv.2303.16508","DOIUrl":"https://doi.org/10.48550/arXiv.2303.16508","url":null,"abstract":"We consider an ultra-weak first order system discretization of the Helmholtz equation. When employing the optimal test norm, the `ideal' method yields the best approximation to the pair of the Helmholtz solution and its scaled gradient w.r.t.~the norm on $L_2(Omega)times L_2(Omega)^d$ from the selected finite element trial space. On convex polygons, the `practical', implementable method is shown to be pollution-free essentially whenever the order $tilde{p}$ of the finite element test space grows proportionally with $max(log kappa,p^2)$, with $p$ being the order at trial side. Numerical results also on other domains show a much better accuracy than for the Galerkin method.","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87059560","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 : 2023-03-22DOI: 10.1007/s40314-022-02165-x
Pingfan Dai, Jinping Li, Shaoyu Zhao
{"title":"Infinity norm bounds for the inverse for $$textrm{GSDD}_1$$ matrices using scaling matrices","authors":"Pingfan Dai, Jinping Li, Shaoyu Zhao","doi":"10.1007/s40314-022-02165-x","DOIUrl":"https://doi.org/10.1007/s40314-022-02165-x","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82197056","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 : 2023-03-22DOI: 10.48550/arXiv.2303.12459
Federico Herrero-Herv'as, M. Negreanu, A. M. Vargas
This article studies a parabolic-elliptic system modelling the pattern formation in E. coli bacteria in response to a chemoattractant known as acylhomoserine lactone concentration (AHL). The system takes into account certain bacterial strains with motility regulation, and the parameters of the equations represent the bacterial logistic growth, AHL diffusion and the rates of production and degradation of AHL. We consider the numerical solution to the system using the Generalized Finite Difference (GFD) Method, a meshless method known to effectively compute numerical solutions to nonlinear problems. The paper is organized to first explain the derivation of the explicit formulae of the method, followed by the study of the convergence of the explicit scheme. Then, several examples over regular and irregular meshes are given.
{"title":"Convergence of a meshless numerical method for a chemotaxis system with density-suppressed motility","authors":"Federico Herrero-Herv'as, M. Negreanu, A. M. Vargas","doi":"10.48550/arXiv.2303.12459","DOIUrl":"https://doi.org/10.48550/arXiv.2303.12459","url":null,"abstract":"This article studies a parabolic-elliptic system modelling the pattern formation in E. coli bacteria in response to a chemoattractant known as acylhomoserine lactone concentration (AHL). The system takes into account certain bacterial strains with motility regulation, and the parameters of the equations represent the bacterial logistic growth, AHL diffusion and the rates of production and degradation of AHL. We consider the numerical solution to the system using the Generalized Finite Difference (GFD) Method, a meshless method known to effectively compute numerical solutions to nonlinear problems. The paper is organized to first explain the derivation of the explicit formulae of the method, followed by the study of the convergence of the explicit scheme. Then, several examples over regular and irregular meshes are given.","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89335136","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 : 2023-03-14DOI: 10.1007/s40314-023-02255-4
L. Doss, L. Aishwarya
{"title":"An $$H^{1}-$$Galerkin mixed finite element method for rosenau equation","authors":"L. Doss, L. Aishwarya","doi":"10.1007/s40314-023-02255-4","DOIUrl":"https://doi.org/10.1007/s40314-023-02255-4","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76512633","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":"Semi-monolithic formulation based on a projection method for simulating fluid-structure interaction problems","authors":"S. Ha, H. Choi","doi":"10.2139/ssrn.4093620","DOIUrl":"https://doi.org/10.2139/ssrn.4093620","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75182375","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 : 2023-03-01DOI: 10.48550/arXiv.2203.15570
L. Calatroni, S. Morigi, S. Parisotto, G. Recupero
{"title":"Fast and stable schemes for non-linear osmosis filtering","authors":"L. Calatroni, S. Morigi, S. Parisotto, G. Recupero","doi":"10.48550/arXiv.2203.15570","DOIUrl":"https://doi.org/10.48550/arXiv.2203.15570","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74252271","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 : 2023-02-23DOI: 10.1007/s40314-023-02239-4
H. Tamimi, S. Saiedinezhad, M. Ghaemi
{"title":"Study on the integro-differential equations on $${C^1}({mathbb {R}}_{+})$$","authors":"H. Tamimi, S. Saiedinezhad, M. Ghaemi","doi":"10.1007/s40314-023-02239-4","DOIUrl":"https://doi.org/10.1007/s40314-023-02239-4","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77849460","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 : 2023-02-15DOI: 10.48550/arXiv.2302.07786
R. Schoof, G. Castelli, W. Dörfler
Next-generation lithium-ion batteries with silicon anodes have positive characteristics due to higher energy densities compared to state-of-the-art graphite anodes. However, the large volume expansion of silicon anodes can cause high mechanical stresses, especially if the battery active particle cannot expand freely. In this article, a thermodynamically consistent continuum model for coupling chemical and mechanical effects of electrode particles is extended by a change in the boundary condition for the displacement via a variational inequality. This switch represents a limited enlargement of the particle swelling or shrinking due to lithium intercalation or deintercalation in the host material, respectively. For inequality constraints as boundary condition a smaller time step size is need as well as a locally finer mesh. The combination of a primal-dual active set algorithm, interpreted as semismooth Newton method, and a spatial and temporal adaptive algorithm allows the efficient numerical investigation based on a finite element method. Using the example of silicon, the chemical and mechanical behavior of one- and two-dimensional representative geometries for a charge-discharge cycle is investigated. Furthermore, the efficiency of the adaptive algorithm is demonstrated. It turns out that the size of the gap has a significant influence on the maximal stress value and the slope of the increase. Especially in two dimension, the obstacle can cause an additional region with a lithium-poor phase.
{"title":"Simulation of the Deformation for Cycling Chemo-Mechanically Coupled Battery Active Particles with Mechanical Constraints","authors":"R. Schoof, G. Castelli, W. Dörfler","doi":"10.48550/arXiv.2302.07786","DOIUrl":"https://doi.org/10.48550/arXiv.2302.07786","url":null,"abstract":"Next-generation lithium-ion batteries with silicon anodes have positive characteristics due to higher energy densities compared to state-of-the-art graphite anodes. However, the large volume expansion of silicon anodes can cause high mechanical stresses, especially if the battery active particle cannot expand freely. In this article, a thermodynamically consistent continuum model for coupling chemical and mechanical effects of electrode particles is extended by a change in the boundary condition for the displacement via a variational inequality. This switch represents a limited enlargement of the particle swelling or shrinking due to lithium intercalation or deintercalation in the host material, respectively. For inequality constraints as boundary condition a smaller time step size is need as well as a locally finer mesh. The combination of a primal-dual active set algorithm, interpreted as semismooth Newton method, and a spatial and temporal adaptive algorithm allows the efficient numerical investigation based on a finite element method. Using the example of silicon, the chemical and mechanical behavior of one- and two-dimensional representative geometries for a charge-discharge cycle is investigated. Furthermore, the efficiency of the adaptive algorithm is demonstrated. It turns out that the size of the gap has a significant influence on the maximal stress value and the slope of the increase. Especially in two dimension, the obstacle can cause an additional region with a lithium-poor phase.","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87423492","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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