Pub Date : 2023-04-20DOI: 10.1007/s42967-023-00258-w
Wei Zheng, Yan Xu
{"title":"High-Order Decoupled and Bound Preserving Local Discontinuous Galerkin Methods for a Class of Chemotaxis Models","authors":"Wei Zheng, Yan Xu","doi":"10.1007/s42967-023-00258-w","DOIUrl":"https://doi.org/10.1007/s42967-023-00258-w","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"32 1","pages":"1-27"},"PeriodicalIF":1.6,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85208207","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}
Pub Date : 2023-04-20DOI: 10.1007/s42967-023-00263-z
Xiyin Liang, J. Lei
{"title":"Oscillatory Dynamics of Heterogeneous Stem Cell Regeneration","authors":"Xiyin Liang, J. Lei","doi":"10.1007/s42967-023-00263-z","DOIUrl":"https://doi.org/10.1007/s42967-023-00263-z","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"159 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73938209","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}
Pub Date : 2023-04-19DOI: 10.1007/s42967-023-00262-0
Liqun Qi
{"title":"Motion, Dual Quaternion Optimization and Motion Optimization","authors":"Liqun Qi","doi":"10.1007/s42967-023-00262-0","DOIUrl":"https://doi.org/10.1007/s42967-023-00262-0","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"11 1","pages":"1-11"},"PeriodicalIF":1.6,"publicationDate":"2023-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75388919","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}
Pub Date : 2023-04-11DOI: 10.1007/s42967-023-00257-x
Zhen Wang
In this paper, a class of discrete Gronwall inequalities is proposed. It is efficiently applied to analyzing the constructed L1/local discontinuous Galerkin (LDG) finite element methods which are used for numerically solving the Caputo-Hadamard time fractional diffusion equation. The derived numerical methods are shown to be -robust using the newly established Gronwall inequalities, that is, it remains valid when . Numerical experiments are given to demonstrate the theoretical statements.
{"title":"L1/LDG Method for Caputo-Hadamard Time Fractional Diffusion Equation.","authors":"Zhen Wang","doi":"10.1007/s42967-023-00257-x","DOIUrl":"10.1007/s42967-023-00257-x","url":null,"abstract":"<p><p>In this paper, a class of discrete Gronwall inequalities is proposed. It is efficiently applied to analyzing the constructed L1/local discontinuous Galerkin (LDG) finite element methods which are used for numerically solving the Caputo-Hadamard time fractional diffusion equation. The derived numerical methods are shown to be <math><mi>α</mi></math>-robust using the newly established Gronwall inequalities, that is, it remains valid when <math><mrow><mi>α</mi><mo>→</mo><msup><mn>1</mn><mo>-</mo></msup></mrow></math>. Numerical experiments are given to demonstrate the theoretical statements.</p>","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":" ","pages":"1-25"},"PeriodicalIF":1.6,"publicationDate":"2023-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10088693/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9714950","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}
Pub Date : 2023-04-11DOI: 10.1007/s42967-023-00267-9
J. Holmes, B. Keyfitz
{"title":"Nonuniform Dependence on the Initial Data for Solutions of Conservation Laws","authors":"J. Holmes, B. Keyfitz","doi":"10.1007/s42967-023-00267-9","DOIUrl":"https://doi.org/10.1007/s42967-023-00267-9","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"37 1","pages":"1-12"},"PeriodicalIF":1.6,"publicationDate":"2023-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73203444","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}
Pub Date : 2023-04-03DOI: 10.1007/s42967-022-00241-x
Wasilij Barsukow, Jonas P. Berberich
Active Flux is a third order accurate numerical method which evolves cell averages and point values at cell interfaces independently. It naturally uses a continuous reconstruction, but is stable when applied to hyperbolic problems. In this work, the Active Flux method is extended for the first time to a nonlinear hyperbolic system of balance laws, namely, to the shallow water equations with bottom topography. We demonstrate how to achieve an Active Flux method that is well-balanced, positivity preserving, and allows for dry states in one spatial dimension. Because of the continuous reconstruction all these properties are achieved using new approaches. To maintain third order accuracy, we also propose a novel high-order approximate evolution operator for the update of the point values. A variety of test problems demonstrates the good performance of the method even in presence of shocks.
{"title":"A Well-Balanced Active Flux Method for the Shallow Water Equations with Wetting and Drying","authors":"Wasilij Barsukow, Jonas P. Berberich","doi":"10.1007/s42967-022-00241-x","DOIUrl":"https://doi.org/10.1007/s42967-022-00241-x","url":null,"abstract":"Active Flux is a third order accurate numerical method which evolves cell averages and point values at cell interfaces independently. It naturally uses a continuous reconstruction, but is stable when applied to hyperbolic problems. In this work, the Active Flux method is extended for the first time to a nonlinear hyperbolic system of balance laws, namely, to the shallow water equations with bottom topography. We demonstrate how to achieve an Active Flux method that is well-balanced, positivity preserving, and allows for dry states in one spatial dimension. Because of the continuous reconstruction all these properties are achieved using new approaches. To maintain third order accuracy, we also propose a novel high-order approximate evolution operator for the update of the point values. A variety of test problems demonstrates the good performance of the method even in presence of shocks.","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136329116","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}
Pub Date : 2023-04-03DOI: 10.1007/s42967-023-00251-3
Vitaliy Gyrya, Evan Lieberman, Mark Kenamond, Mikhail Shashkov
To accurately model flows with shock waves using staggered-grid Lagrangian hydrodynamics, the artificial viscosity has to be introduced to convert kinetic energy into internal energy, thereby increasing the entropy across shocks. Determining the appropriate strength of the artificial viscosity is an art and strongly depends on the particular problem and experience of the researcher. The objective of this study is to pose the problem of finding the appropriate strength of the artificial viscosity as an optimization problem and solve this problem using machine learning (ML) tools, specifically using surrogate models based on Gaussian Process regression (GPR) and Bayesian analysis. We describe the optimization method and discuss various practical details of its implementation. The shock-containing problems for which we apply this method all have been implemented in the LANL code FLAG (Burton in Connectivity structures and differencing techniques for staggered-grid free-Lagrange hydrodynamics, Tech. Rep. UCRL-JC-110555, Lawrence Livermore National Laboratory, Livermore, CA, 1992, 1992, in Consistent finite-volume discretization of hydrodynamic conservation laws for unstructured grids, Tech. Rep. CRL-JC-118788, Lawrence Livermore National Laboratory, Livermore, CA, 1992, 1994, Multidimensional discretization of conservation laws for unstructured polyhedral grids, Tech. Rep. UCRL-JC-118306, Lawrence Livermore National Laboratory, Livermore, CA, 1992, 1994, in FLAG, a multi-dimensional, multiple mesh, adaptive free-Lagrange, hydrodynamics code. In: NECDC, 1992). First, we apply ML to find optimal values to isolated shock problems of different strengths. Second, we apply ML to optimize the viscosity for a one-dimensional (1D) propagating detonation problem based on Zel’dovich-von Neumann-Doring (ZND) (Fickett and Davis in Detonation: theory and experiment. Dover books on physics. Dover Publications, Mineola, 2000) detonation theory using a reactive burn model. We compare results for default (currently used values in FLAG) and optimized values of the artificial viscosity for these problems demonstrating the potential for significant improvement in the accuracy of computations.
为了使用交错网格拉格朗日流体力学准确地模拟激波流动，必须引入人工粘度将动能转化为内能，从而增加跨激波的熵。确定人工粘度的适当强度是一门艺术，在很大程度上取决于研究人员的具体问题和经验。本研究的目的是将寻找合适的人工粘度强度的问题作为一个优化问题，并使用机器学习(ML)工具解决这个问题，特别是使用基于高斯过程回归(GPR)和贝叶斯分析的代理模型。我们描述了优化方法，并讨论了其实现的各种实际细节。我们应用该方法的包含激波的问题都已经在LANL代码FLAG(伯顿在交错网格自由拉格朗日流体力学的连性结构和差分技术中)中实现，UCRL-JC-110555，劳伦斯利弗莫尔国家实验室，加利福尼亚州利弗莫尔，1992年，1992年，在非结构化网格的流体动力守恒定律的一致有限体积离散化中，技术代表CRL-JC-118788，劳伦斯利弗莫尔国家实验室，加利福尼亚州利弗莫尔，1992,1994，非结构多面体网格守恒定律的多维离散化，技术代表UCRL-JC-118306，劳伦斯利弗莫尔国家实验室，利弗莫尔，CA, 1992,1994，在FLAG中，一个多维，多网格，自适应自由拉格朗日，流体力学代码。见:NECDC, 1992)。首先，我们应用机器学习来寻找不同强度的孤立冲击问题的最优值。其次，基于Zel ' ovich-von Neumann-Doring (ZND) (Fickett and Davis在detonation: theory and experiment)一书中的理论和实验，我们应用ML对一维传播爆轰问题的粘度进行优化。多佛物理学方面的书。Dover Publications, Mineola, 2000)使用反应性燃烧模型的爆轰理论。我们比较了这些问题的默认值(目前在FLAG中使用的值)和优化后的人工粘度值的结果，证明了计算精度有显著提高的潜力。
{"title":"Optimization of Artificial Viscosity in Production Codes Based on Gaussian Regression Surrogate Models","authors":"Vitaliy Gyrya, Evan Lieberman, Mark Kenamond, Mikhail Shashkov","doi":"10.1007/s42967-023-00251-3","DOIUrl":"https://doi.org/10.1007/s42967-023-00251-3","url":null,"abstract":"To accurately model flows with shock waves using staggered-grid Lagrangian hydrodynamics, the artificial viscosity has to be introduced to convert kinetic energy into internal energy, thereby increasing the entropy across shocks. Determining the appropriate strength of the artificial viscosity is an art and strongly depends on the particular problem and experience of the researcher. The objective of this study is to pose the problem of finding the appropriate strength of the artificial viscosity as an optimization problem and solve this problem using machine learning (ML) tools, specifically using surrogate models based on Gaussian Process regression (GPR) and Bayesian analysis. We describe the optimization method and discuss various practical details of its implementation. The shock-containing problems for which we apply this method all have been implemented in the LANL code FLAG (Burton in Connectivity structures and differencing techniques for staggered-grid free-Lagrange hydrodynamics, Tech. Rep. UCRL-JC-110555, Lawrence Livermore National Laboratory, Livermore, CA, 1992, 1992, in Consistent finite-volume discretization of hydrodynamic conservation laws for unstructured grids, Tech. Rep. CRL-JC-118788, Lawrence Livermore National Laboratory, Livermore, CA, 1992, 1994, Multidimensional discretization of conservation laws for unstructured polyhedral grids, Tech. Rep. UCRL-JC-118306, Lawrence Livermore National Laboratory, Livermore, CA, 1992, 1994, in FLAG, a multi-dimensional, multiple mesh, adaptive free-Lagrange, hydrodynamics code. In: NECDC, 1992). First, we apply ML to find optimal values to isolated shock problems of different strengths. Second, we apply ML to optimize the viscosity for a one-dimensional (1D) propagating detonation problem based on Zel’dovich-von Neumann-Doring (ZND) (Fickett and Davis in Detonation: theory and experiment. Dover books on physics. Dover Publications, Mineola, 2000) detonation theory using a reactive burn model. We compare results for default (currently used values in FLAG) and optimized values of the artificial viscosity for these problems demonstrating the potential for significant improvement in the accuracy of computations.","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135416691","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}
Pub Date : 2023-03-28DOI: 10.1007/s42967-022-00242-w
Weitao Chen, C. Kao
{"title":"Review of Computational Approaches to Optimization Problems in Inhomogeneous Rods and Plates","authors":"Weitao Chen, C. Kao","doi":"10.1007/s42967-022-00242-w","DOIUrl":"https://doi.org/10.1007/s42967-022-00242-w","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"16 1","pages":"1-21"},"PeriodicalIF":1.6,"publicationDate":"2023-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90699677","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}
Pub Date : 2023-03-27DOI: 10.1007/s42967-023-00250-4
Mikhail Shashkov, Konstantin Lipnikov
We explore an intersection-based remap method between meshes consisting of isoparametric elements. We present algorithms for the case of serendipity isoparametric elements (QUAD8 elements) and piece-wise constant (cell-centered) discrete fields. We demonstrate convergence properties of this remap method with a few numerical experiments.
{"title":"Remapping Between Meshes with Isoparametric Cells: a Case Study","authors":"Mikhail Shashkov, Konstantin Lipnikov","doi":"10.1007/s42967-023-00250-4","DOIUrl":"https://doi.org/10.1007/s42967-023-00250-4","url":null,"abstract":"We explore an intersection-based remap method between meshes consisting of isoparametric elements. We present algorithms for the case of serendipity isoparametric elements (QUAD8 elements) and piece-wise constant (cell-centered) discrete fields. We demonstrate convergence properties of this remap method with a few numerical experiments.","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135891039","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}
Pub Date : 2023-03-27DOI: 10.1007/s42967-022-00246-6
Xuechun Liu, Haijin Wang, Jue Yan, Xinghui Zhong
{"title":"Superconvergence of Direct Discontinuous Galerkin Methods: Eigen-structure Analysis Based on Fourier Approach","authors":"Xuechun Liu, Haijin Wang, Jue Yan, Xinghui Zhong","doi":"10.1007/s42967-022-00246-6","DOIUrl":"https://doi.org/10.1007/s42967-022-00246-6","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"51 1","pages":"1-22"},"PeriodicalIF":1.6,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79393637","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}
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