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Meshfree methods for nonlinear equilibrium radiation diffusion equation with jump coefficient 具有跳跃系数的非线性平衡辐射扩散方程的无网格法
Comput. Math. Appl. Pub Date : 2023-10-01 DOI: 10.2139/ssrn.4359801
Haowei Liu, Zhiyong Liu, Qiuyan Xu, Jiye Yang
{"title":"Meshfree methods for nonlinear equilibrium radiation diffusion equation with jump coefficient","authors":"Haowei Liu, Zhiyong Liu, Qiuyan Xu, Jiye Yang","doi":"10.2139/ssrn.4359801","DOIUrl":"https://doi.org/10.2139/ssrn.4359801","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76631292","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}
引用次数: 0
Second-order linear adaptive time-stepping schemes for the fractional Allen-Cahn equation 分数阶Allen-Cahn方程的二阶线性自适应时间步进格式
Comput. Math. Appl. Pub Date : 2023-09-01 DOI: 10.2139/ssrn.4359792
Linlin Bu, Jianhua Wu, Liquan Mei, Y. Wang
{"title":"Second-order linear adaptive time-stepping schemes for the fractional Allen-Cahn equation","authors":"Linlin Bu, Jianhua Wu, Liquan Mei, Y. Wang","doi":"10.2139/ssrn.4359792","DOIUrl":"https://doi.org/10.2139/ssrn.4359792","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90829957","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}
引用次数: 0
A family of edge-centered finite volume schemes for heterogeneous and anisotropic diffusion problems on unstructured meshes 非结构网格上非均质和各向异性扩散问题的一类边心有限体积格式
Comput. Math. Appl. Pub Date : 2023-09-01 DOI: 10.2139/ssrn.4359794
Ziqi Liu, Shuai Miao, Zhimin Zhang
{"title":"A family of edge-centered finite volume schemes for heterogeneous and anisotropic diffusion problems on unstructured meshes","authors":"Ziqi Liu, Shuai Miao, Zhimin Zhang","doi":"10.2139/ssrn.4359794","DOIUrl":"https://doi.org/10.2139/ssrn.4359794","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77253330","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}
引用次数: 1
Effects of prefilmer edge configuration on primary liquid film breakup: A lattice Boltzmann study 预膜器边缘结构对初液膜破裂的影响:晶格玻尔兹曼研究
Comput. Math. Appl. Pub Date : 2023-09-01 DOI: 10.2139/ssrn.4359809
Xun Zhou, Miaomiao Liu, B. Dong, Weizhong Li, Kunfeng Liang
{"title":"Effects of prefilmer edge configuration on primary liquid film breakup: A lattice Boltzmann study","authors":"Xun Zhou, Miaomiao Liu, B. Dong, Weizhong Li, Kunfeng Liang","doi":"10.2139/ssrn.4359809","DOIUrl":"https://doi.org/10.2139/ssrn.4359809","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76910494","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}
引用次数: 0
A Banach spaces-based fully-mixed finite element method for the stationary chemotaxis-Navier-Stokes problem 基于Banach空间的平稳趋化- navier - stokes问题全混合有限元方法
Comput. Math. Appl. Pub Date : 2023-09-01 DOI: 10.2139/ssrn.4359790
Sergio Caucao, Eligio Colmenares, G. Gatica, Cristian Inzunza
{"title":"A Banach spaces-based fully-mixed finite element method for the stationary chemotaxis-Navier-Stokes problem","authors":"Sergio Caucao, Eligio Colmenares, G. Gatica, Cristian Inzunza","doi":"10.2139/ssrn.4359790","DOIUrl":"https://doi.org/10.2139/ssrn.4359790","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85832827","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}
引用次数: 6
Application of flux limiters to passive scalar advection for the lattice Boltzmann method 点阵玻尔兹曼法中通量限制器在被动标量平流中的应用
Comput. Math. Appl. Pub Date : 2023-08-01 DOI: 10.2139/ssrn.4368195
Brian Devincentis, John A. Thomas
{"title":"Application of flux limiters to passive scalar advection for the lattice Boltzmann method","authors":"Brian Devincentis, John A. Thomas","doi":"10.2139/ssrn.4368195","DOIUrl":"https://doi.org/10.2139/ssrn.4368195","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83179513","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}
引用次数: 2
Stabilized bi-cubic Hermite Bézier finite element method with application to gas-plasma interactions occurring during massive material injection in tokamaks 稳定双立方Hermite bsamzier有限元法及其在托卡马克大量材料注入过程中气等离子体相互作用的应用
Comput. Math. Appl. Pub Date : 2023-07-01 DOI: 10.2139/ssrn.4359796
A. Bhole, B. Nkonga, José Costa, G. Huijsmans, S. Pamela, M. Hoelzl
{"title":"Stabilized bi-cubic Hermite Bézier finite element method with application to gas-plasma interactions occurring during massive material injection in tokamaks","authors":"A. Bhole, B. Nkonga, José Costa, G. Huijsmans, S. Pamela, M. Hoelzl","doi":"10.2139/ssrn.4359796","DOIUrl":"https://doi.org/10.2139/ssrn.4359796","url":null,"abstract":"Development of a numerical tool based upon the high-order, high-resolution Galerkin finite element method (FEM) often encounters two challenges: First, the Galerkin FEMs give central approximations to the differential operators and their use in the simulation of the convection-dominated flows may lead to the dispersion errors yielding entirely wrong numerical solutions. Secondly, high-order, high-resolution numerical methods are known to produce high wave-number oscillations in the vicinity of shocks/discontinuities in the numerical solution adversely affecting the stability of the method. We present the stabilized finite element method for plasma fluid models to address the two challenges. The numerical stabilization is based on two strategies: Variational Multiscale (VMS) and the shock-capturing approach. The former strategy takes into account (the approximation of) the effect of the unresolved scales onto resolved scales to introduce upwinding in the Galerkin FEM. The latter adaptively adds the artificial viscosity only in the vicinity of shocks. These numerical stabilization strategies are applied to stabilize the bi-cubic Hermite B´ezier FEM in the computational framework of the nonlinear magnetohy-drodynamics (MHD) code JOREK. The application of the stabilized FEM to the challenging simulation of Shattered Pellet Injection (SPI) in JET-like plasma is presented. It is shown that","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83066834","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}
引用次数: 1
The robust physics-informed neural networks for a typical fourth-order phase field model 典型四阶相场模型的鲁棒物理信息神经网络
Comput. Math. Appl. Pub Date : 2023-06-01 DOI: 10.2139/ssrn.4359806
Wen Zhang, Jun Yu Li
{"title":"The robust physics-informed neural networks for a typical fourth-order phase field model","authors":"Wen Zhang, Jun Yu Li","doi":"10.2139/ssrn.4359806","DOIUrl":"https://doi.org/10.2139/ssrn.4359806","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77460988","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}
引用次数: 0
On the convergence rate of the splitting-up scheme for rough partial differential equations 粗糙偏微分方程分裂格式的收敛速度
Comput. Math. Appl. Pub Date : 2023-06-01 DOI: 10.2139/ssrn.4222885
Yuchen He
{"title":"On the convergence rate of the splitting-up scheme for rough partial differential equations","authors":"Yuchen He","doi":"10.2139/ssrn.4222885","DOIUrl":"https://doi.org/10.2139/ssrn.4222885","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74725221","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}
引用次数: 0
Scalable DPG Multigrid Solver for Helmholtz Problems: A Study on Convergence Helmholtz问题的可伸缩DPG多网格求解器:收敛性研究
Comput. Math. Appl. Pub Date : 2023-04-04 DOI: 10.48550/arXiv.2304.01728
Jacob Badger, Stefan Henneking, S. Petrides, L. Demkowicz
{"title":"Scalable DPG Multigrid Solver for Helmholtz Problems: A Study on Convergence","authors":"Jacob Badger, Stefan Henneking, S. Petrides, L. Demkowicz","doi":"10.48550/arXiv.2304.01728","DOIUrl":"https://doi.org/10.48550/arXiv.2304.01728","url":null,"abstract":"This paper presents a scalable multigrid preconditioner targeting large-scale systems arising from discontinuous Petrov-Galerkin (DPG) discretizations of high-frequency wave operators. This work is built on previously developed multigrid preconditioning techniques of Petrides and Demkowicz (Comput. Math. Appl. 87 (2021) pp. 12-26) and extends the convergence results from $mathcal{O}(10^7)$ degrees of freedom (DOFs) to $mathcal{O}(10^9)$ DOFs using a new scalable parallel MPI/OpenMP implementation. Novel contributions of this paper include an alternative definition of coarse-grid systems based on restriction of fine-grid operators, yielding superior convergence results. In the uniform refinement setting, a detailed convergence study is provided, demonstrating h and p robust convergence and linear dependence with respect to the wave frequency. The paper concludes with numerical results on hp-adaptive simulations including a large-scale seismic modeling benchmark problem with high material contrast.","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91511336","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}
引用次数: 2
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