Communications in Mathematical Sciences最新文献_第3页

Implicit-explicit Runge-Kutta methods for Landau-Lifshitz equation with arbitrary damping 具有任意阻尼的 Landau-Lifshitz 方程的隐含-显式 Runge-Kutta 方法

IF 1 4区数学

Communications in Mathematical Sciences Pub Date : 2024-07-15 DOI: 10.4310/cms.2024.v22.n5.a9

Yan Gui, Cheng Wang, Jingrun Chen

{"title":"Implicit-explicit Runge-Kutta methods for Landau-Lifshitz equation with arbitrary damping","authors":"Yan Gui, Cheng Wang, Jingrun Chen","doi":"10.4310/cms.2024.v22.n5.a9","DOIUrl":"https://doi.org/10.4310/cms.2024.v22.n5.a9","url":null,"abstract":"Magnetization dynamics in ferromagnetic materials is modeled by the Landau-Lifshitz (LL) equation, a nonlinear system of partial differential equations. Among the numerical approaches, semi-implicit schemes are widely used in the micromagnetics simulation, due to a nice compromise between accuracy and efficiency. At each time step, only a linear system needs to be solved and a projection is then applied to preserve the length of magnetization. However, this linear system contains variable coefficients and a non-symmetric structure, and thus an efficient linear solver is highly desired. If the damping parameter becomes large, it has been realized that efficient solvers are only available to a linear system with constant, symmetric, and positive definite (SPD) structure. In this work, based on the implicit-explicit Runge-Kutta (IMEX-RK) time discretization, we introduce an artificial damping term, which is treated implicitly. The remaining terms are treated explicitly. This strategy leads to a semi-implicit scheme with the following properties: (1) only a few linear systems with constant and SPD structure needs to be solved at each time step; (2) it works for the LL equation with arbitrary damping parameter; (3) high-order accuracy can be obtained with high-order IMEX-RK time discretization. Numerically, second-order and third-order IMEX-RK methods are designed in both the 1-D and 3-D domains. A comparison with the backward differentiation formula scheme is undertaken, in terms of accuracy and efficiency. The robustness of both numerical methods is tested on the first benchmark problem from National Institute of Standards and Technology. The linearized stability estimate and optimal rate convergence analysis are provided for an alternate IMEX-RK2 numerical scheme as well.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"70 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719614","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}

引用次数: 0

Chemotactic reaction enhancement in one dimension 一维的趋化反应增强

IF 1 4区数学

Communications in Mathematical Sciences Pub Date : 2024-07-15 DOI: 10.4310/cms.2024.v22.n5.a5

Yishu Gong, Alexander Kiselev

{"title":"Chemotactic reaction enhancement in one dimension","authors":"Yishu Gong, Alexander Kiselev","doi":"10.4310/cms.2024.v22.n5.a5","DOIUrl":"https://doi.org/10.4310/cms.2024.v22.n5.a5","url":null,"abstract":"Chemotaxis, which involves the directed movement of cells in response to a chemical gradient, plays a crucial role in a broad variety of biological processes. Examples include bacterial motion, the development of single-cell or multicellular organisms, and immune responses. Chemotaxis directs bacteria’s movement to find food (e.g., glucose) by swimming toward the highest concentration of food molecules. In multicellular organisms, chemotaxis is critical to early development (e.g., movement of sperm towards the egg during fertilization). Chemotaxis also helps mobilize phagocytic and immune cells at sites of infection, tissue injury, and thus facilitates immune reactions. In this paper, we study a PDE system that describes chemotactic processes in one dimension, which may correspond to a thin channel, the setting relevant in many applications: for example, spermatozoa progression to the ovum inside a Fallopian tube or immune response in a blood vessel. Our objective is to obtain qualitatively precise estimates on how chemotaxis improves reaction efficiency, when compared to purely diffusive situation. The techniques we use to achieve this goal include a variety of comparison principles and analysis of mass transport for a class of Fokker–Planck operators.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"2 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719559","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}

引用次数: 0

Differentiable Hartman-Grobman Theorem via modulus of continuity: A sharp result on linearization in general Banach space 通过连续性模数的可微哈特曼-格罗布曼定理一般巴拿赫空间线性化的尖锐结果

IF 1 4区数学

Communications in Mathematical Sciences Pub Date : 2024-07-15 DOI: 10.4310/cms.2024.v22.n5.a8

Zhicheng Tong, Yong Li

引用次数: 0

Representation theorem for multivariable totally symmetric functions 多变量完全对称函数的表示定理

IF 1 4区数学

Communications in Mathematical Sciences Pub Date : 2024-07-15 DOI: 10.4310/cms.2024.v22.n5.a2

Chongyao Chen, Ziang Chen, Jianfeng Lu

引用次数: 0

Non-uniqueness of transonic shock solutions to Euler–Poisson system with varying background charges 背景电荷变化的欧拉-泊松系统跨音速冲击解的非唯一性

IF 1 4区数学

Communications in Mathematical Sciences Pub Date : 2024-03-04 DOI: 10.4310/cms.2024.v22.n3.a7

Ben Duan, Haoran Zheng

引用次数: 0

Hydrodynamic traffic flow models including random accidents: A kinetic derivation 包括随机事故在内的水动力交通流模型：动力学推导

IF 1 4区数学

Communications in Mathematical Sciences Pub Date : 2024-03-04 DOI: 10.4310/cms.2024.v22.n3.a10

Felisia Angela Chiarello, Simone Göttlich, Thomas Schillinger, Andrea Tosin

引用次数: 0

Autonomous vehicles driving traffic: The Cauchy problem 自动驾驶汽车在交通中行驶：考奇问题

IF 1 4区数学

Communications in Mathematical Sciences Pub Date : 2024-03-04 DOI: 10.4310/cms.2024.v22.n3.a9

Mauro Garavello, Francesca Marcellini

引用次数: 0

Analysis and computation for the scattering problem of electromagnetic waves in chiral media 手性介质中电磁波散射问题的分析与计算

IF 1 4区数学

Communications in Mathematical Sciences Pub Date : 2024-03-04 DOI: 10.4310/cms.2024.v22.n3.a5

Gang Bao, Lei Zhang

引用次数: 0

Improved uniform error bounds of an exponential wave integrator method for the Klein–Gordon–Schrödinger equation with the small coupling constant 具有小耦合常数的克莱因-戈登-薛定谔方程指数波积分器方法的改进均匀误差边界

IF 1 4区数学

Communications in Mathematical Sciences Pub Date : 2024-03-04 DOI: 10.4310/cms.2024.v22.n3.a1

Jiyong Li

{"title":"Improved uniform error bounds of an exponential wave integrator method for the Klein–Gordon–Schrödinger equation with the small coupling constant","authors":"Jiyong Li","doi":"10.4310/cms.2024.v22.n3.a1","DOIUrl":"https://doi.org/10.4310/cms.2024.v22.n3.a1","url":null,"abstract":"Recently, the long-time numerical simulation and error analysis of PDEs with weak nonlinearity (or small potentials) become an interesting topic. However, the existing results of long-time error analysis mostly focus on the single equations. In this paper, for the Klein–Gordon–Schrödinger equation (KGSE) with a small coupling constant $varepsilon in (0,1]$, we propose an exponential wave integrator Fourier pseudo-spectral (EWIFP) method by reformulating the KGSE into a coupled nonlinear Schrödinger system (CNLSS). Through careful and rigorous analysis, we establish improved error bounds for the numerical solution at $O(h^m + varepsilon tau^2)$ in the long-time domain up to $O(1/varepsilon)$ where $m$ is determined by the regularity conditions, h is the mesh size and τ is the time step, respectively. Compared with the existing results, our analysis shows the long-time errors of numerical solution for the KGSE. In error analysis, in addition to the classical tools such as energy method and cut-off technique, we also adopt the regularity compensation oscillation (RCO) technique which has been developed recently to analyze the accumulation of errors carefully. The numerical experiments support our error estimates and demonstrate the long-term stability of discrete mass and energy. To the best of our knowledge, there has not been any relevant long-time error analysis for the KGSE and any improved uniform error bounds for an exponential wave integrator. Our work is novel and provides a reference for analyzing the improved error bounds of the numerical methods for other coupled equations.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"114 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140035267","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}

引用次数: 0

Global existence and asymptotic behavior of the full Euler system with damping and radiative effects in $mathbb{R}^3$ 在 $mathbb{R}^3$ 中具有阻尼和辐射效应的全欧拉系统的全局存在性和渐近行为

IF 1 4区数学

Communications in Mathematical Sciences Pub Date : 2024-03-04 DOI: 10.4310/cms.2024.v22.n3.a8

Shijin Deng, Wenjun Wang, Feng Xie, Xiongfeng Yang

{"title":"Global existence and asymptotic behavior of the full Euler system with damping and radiative effects in $mathbb{R}^3$","authors":"Shijin Deng, Wenjun Wang, Feng Xie, Xiongfeng Yang","doi":"10.4310/cms.2024.v22.n3.a8","DOIUrl":"https://doi.org/10.4310/cms.2024.v22.n3.a8","url":null,"abstract":"In this paper, we study the global existence and the large-time behavior of solutions to the Cauchy problem of the full Euler system with damping and radiative effects around some constant equilibrium states. It is well-known that the solutions may blow up in finite time without the additional damping and radiative effects, and the global existence of the solutions obtained in this paper shows that these two effects together prevent the formation of the singularity when the initial perturbation is small. Combining the Green’s function method and energy estimates, we consider the pointwise structures of the solutions to obtain a precise description of the system. The construction of the Green’s function includes three steps: singularity removal, long wave-short wave decomposition and weighted energy estimate. Finally, we achieve the pointwise estimates of the solutions in the small perturbation framework by Duhamel’s principle, the pointwise structure of the Green’s function established for the linearized equations and bounded estimates for higher order derivatives of the solutions together.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"9 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140034478","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}

引用次数: 0