Communications on Applied Mathematics and Computation最新文献

{"title":"Mathematical Modeling of Cell Polarity Establishment of Budding Yeast","authors":"Yue Liu, Jun Xie, Hay-Oak Park, W. Lo","doi":"10.1007/s42967-022-00240-y","DOIUrl":"https://doi.org/10.1007/s42967-022-00240-y","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"39 1","pages":"1-18"},"PeriodicalIF":1.6,"publicationDate":"2023-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75085386","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":"Bound-Preserving Discontinuous Galerkin Methods with Modified Patankar Time Integrations for Chemical Reacting Flows","authors":"Fangyao Zhu, Juntao Huang, Yang Yang","doi":"10.1007/s42967-022-00231-z","DOIUrl":"https://doi.org/10.1007/s42967-022-00231-z","url":null,"abstract":"In this paper, we develop bound-preserving discontinuous Galerkin (DG) methods for chemical reactive flows. There are several difficulties in constructing suitable numerical schemes. First of all, the density and internal energy are positive, and the mass fraction of each species is between 0 and 1. Second, due to the rapid reaction rate, the system may contain stiff sources, and the strong-stability-preserving explicit Runge-Kutta method may result in limited time-step sizes. To obtain physically relevant numerical approximations, we apply the bound-preserving technique to the DG methods. Though traditional positivity-preserving techniques can successfully yield positive density, internal energy, and mass fractions, they may not enforce the upper bound 1 of the mass fractions. To solve this problem, we need to (i) make sure the numerical fluxes in the equations of the mass fractions are consistent with that in the equation of the density; (ii) choose conservative time integrations, such that the summation of the mass fractions is preserved. With the above two conditions, the positive mass fractions have summation 1, and then, they are all between 0 and 1. For time discretization, we apply the modified Runge-Kutta/multi-step Patankar methods, which are explicit for the flux while implicit for the source. Such methods can handle stiff sources with relatively large time steps, preserve the positivity of the target variables, and keep the summation of the mass fractions to be 1. Finally, it is not straightforward to combine the bound-preserving DG methods and the Patankar time integrations. The positivity-preserving technique for DG methods requires positive numerical approximations at the cell interfaces, while Patankar methods can keep the positivity of the pre-selected point values of the target variables. To match the degree of freedom, we use $$Q^k$$ polynomials on rectangular meshes for problems in two space dimensions. To evolve in time, we first read the polynomials at the Gaussian points. Then, suitable slope limiters can be applied to enforce the positivity of the solutions at those points, which can be preserved by the Patankar methods, leading to positive updated numerical cell averages. In addition, we use another slope limiter to get positive solutions used for the bound-preserving technique for the flux. Numerical examples are given to demonstrate the good performance of the proposed schemes.","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134915866","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":"A Dynamical System-Based Framework for Dimension Reduction","authors":"Ryeongkyung Yoon, Braxton Osting","doi":"10.1007/s42967-022-00234-w","DOIUrl":"https://doi.org/10.1007/s42967-022-00234-w","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135256579","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":"On the Fractional Derivatives with an Exponential Kernel","authors":"Enyu Fan, Jingshu Wu, Shaoying Zeng","doi":"10.1007/s42967-022-00233-x","DOIUrl":"https://doi.org/10.1007/s42967-022-00233-x","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"33 1","pages":"1655-1673"},"PeriodicalIF":1.6,"publicationDate":"2023-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80990039","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":"On High-Resolution Entropy-Consistent Flux with Slope Limiter for Hyperbolic Conservation Laws","authors":"Xuan Ren, Jian-hu Feng, Supei Zheng, Xiaohan Cheng, Y. Li","doi":"10.1007/s42967-022-00232-y","DOIUrl":"https://doi.org/10.1007/s42967-022-00232-y","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"2 1","pages":"1616-1643"},"PeriodicalIF":1.6,"publicationDate":"2023-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79515929","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":"On Fixed-Parameter Solvability of the Minimax Path Location Problem","authors":"Hao-Chen Lin, Cheng He","doi":"10.1007/s42967-022-00238-6","DOIUrl":"https://doi.org/10.1007/s42967-022-00238-6","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"193 6 1","pages":"1644-1654"},"PeriodicalIF":1.6,"publicationDate":"2023-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83666743","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":"High-Order Method with Moving Frames to Compute the Covariant Derivatives of Vectors on General 2D Curved Surfaces","authors":"Sehun Chun","doi":"10.1007/s42967-022-00225-x","DOIUrl":"https://doi.org/10.1007/s42967-022-00225-x","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"48 1","pages":"1-30"},"PeriodicalIF":1.6,"publicationDate":"2023-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86705383","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":"Growth of RB Population in the Conversion Phase of Chlamydia Life Cycle","authors":"Frederic Y. M. Wan","doi":"10.1007/s42967-022-00226-w","DOIUrl":"https://doi.org/10.1007/s42967-022-00226-w","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"156 1","pages":"1-23"},"PeriodicalIF":1.6,"publicationDate":"2023-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78070381","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":"A Combination of Residual Distribution and the Active Flux Formulations or a New Class of Schemes That Can Combine Several Writings of the Same Hyperbolic Problem: Application to the 1D Euler Equations.","authors":"R Abgrall","doi":"10.1007/s42967-021-00175-w","DOIUrl":"https://doi.org/10.1007/s42967-021-00175-w","url":null,"abstract":"<p><p>We show how to combine in a natural way (i.e., without any test nor switch) the conservative and non-conservative formulations of an hyperbolic system that has a conservative form. This is inspired from two different classes of schemes: the residual distribution one (Abgrall in Commun Appl Math Comput 2(3): 341-368, 2020), and the active flux formulations (Eyman and Roe in 49th AIAA Aerospace Science Meeting, 2011; Eyman in active flux. PhD thesis, University of Michigan, 2013; Helzel et al. in J Sci Comput 80(3): 35-61, 2019; Barsukow in J Sci Comput 86(1): paper No. 3, 34, 2021; Roe in J Sci Comput 73: 1094-1114, 2017). The solution is globally continuous, and as in the active flux method, described by a combination of point values and average values. Unlike the \"classical\" active flux methods, the meaning of the point-wise and cell average degrees of freedom is different, and hence follow different forms of PDEs; it is a conservative version of the cell average, and a possibly non-conservative one for the points. This new class of scheme is proved to satisfy a Lax-Wendroff-like theorem. We also develop a method to perform non-linear stability. We illustrate the behaviour on several benchmarks, some quite challenging.</p>","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"5 1","pages":"370-402"},"PeriodicalIF":1.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9925591/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10762392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Efficient Finite Difference/Spectral Method for the Time Fractional Ito Equation Using Fast Fourier Transform Technic","authors":"Dakang Cen, Zhibo Wang, Seakweng Vong","doi":"10.1007/s42967-022-00223-z","DOIUrl":"https://doi.org/10.1007/s42967-022-00223-z","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"7 1","pages":"1591-1600"},"PeriodicalIF":1.6,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89067824","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}