Communications on Applied Mathematics and Computation最新文献

{"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}

{"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}

{"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}

{"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}

{"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}

{"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}

{"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}

{"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}

{"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}

{"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}