Advances in Applied Mathematics and Mechanics最新文献_第10页

A Compact Eulerian Interface–Capturing Algorithm for Compressible Multimaterial Elastic–Plastic Flows with Mie–Gr ¨uneisen Equation of State 基于Mie-Gr¨uneisen状态方程的可压缩多材料弹塑性流的紧凑欧拉界面捕获算法

IF 1.4 4区工程技术

Advances in Applied Mathematics and Mechanics Pub Date : 2023-01-01 DOI: 10.4208/aamm.oa-2021-0019

Xiang Li, D. Ma, Nan-Sheng Liu null, Pei Wang

引用次数: 0

A Total Variation Based Method for Multivariate Time Series Segmentation 一种基于全变分的多元时间序列分割方法

IF 1.4 4区工程技术

Advances in Applied Mathematics and Mechanics Pub Date : 2023-01-01 DOI: 10.4208/aamm.oa-2021-0209

Min Li, Yumei Huang null, Y. Wen

引用次数: 1

An SAV Method for Imaginary Time Gradient Flow Model in Density Functional Theory 密度泛函理论中虚时间梯度流模型的SAV方法

IF 1.4 4区工程技术

Advances in Applied Mathematics and Mechanics Pub Date : 2023-01-01 DOI: 10.4208/aamm.oa-2021-0363

Tingxiu Wang, Jie Zhou null, G. Hu

引用次数: 1

A Scale-Invariant Fifth Order WCNS Scheme for Hyperbolic Conservation Laws 双曲守恒律的一个尺度不变的五阶WCNS格式

IF 1.4 4区工程技术

Advances in Applied Mathematics and Mechanics Pub Date : 2022-12-01 DOI: 10.4208/aamm.oa-2022-0196

Zixuan Zhang, Yidao Dong, Huaibao Zhang, Shichao Deng

引用次数: 0

Arbitrarily High-Order Energy-Preserving Schemes for the Camassa-Holm Equation Based on the Quadratic Auxiliary Variable Approach 基于二次辅助变量法的Camassa-Holm方程任意高阶保能格式

IF 1.4 4区工程技术

Advances in Applied Mathematics and Mechanics Pub Date : 2022-12-01 DOI: 10.4208/aamm.oa-2022-0188

Yuezheng Gong, Qi Hong, Chunwu Wang and Yushun Wang

引用次数: 1

Influence of the Radial Inertia Effect on the Propagation Law of Stress Waves in Thin-Walled Tubes 径向惯性效应对薄壁管中应力波传播规律的影响

IF 1.4 4区工程技术

Advances in Applied Mathematics and Mechanics Pub Date : 2022-12-01 DOI: 10.4208/aamm.oa-2022-0247

Shitang Zhang

引用次数: 0

Numerical Simulations of the Richtmyer–Meshkov Instability of Solid-Vacuum Interface 固体-真空界面Richtmyer–Meshkov不稳定性的数值模拟

IF 1.4 4区工程技术

Advances in Applied Mathematics and Mechanics Pub Date : 2022-11-01 DOI: 10.4208/aamm.oa-2022-0282

X. Liu, Zhiye Zhao, Nansheng Liu and Xiyun Lu

引用次数: 0

A Self-Adaptive Algorithm of the Clean Numerical Simulation (CNS) for Chaos 混沌洁净数值模拟(CNS)的自适应算法

IF 1.4 4区工程技术

Advances in Applied Mathematics and Mechanics Pub Date : 2022-11-01 DOI: 10.4208/aamm.OA-2022-0340

Shijie Qin, S. Liao

{"title":"A Self-Adaptive Algorithm of the Clean Numerical Simulation (CNS) for Chaos","authors":"Shijie Qin, S. Liao","doi":"10.4208/aamm.OA-2022-0340","DOIUrl":"https://doi.org/10.4208/aamm.OA-2022-0340","url":null,"abstract":"The background numerical noise $varepsilon_{0} $ is determined by the maximum of truncation error and round-off error. For a chaotic system, the numerical error $varepsilon(t)$ grows exponentially, say, $varepsilon(t) = varepsilon_{0} exp(kappa,t)$, where $kappa>0$ is the so-called noise-growing exponent. This is the reason why one can not gain a convergent simulation of chaotic systems in a long enough interval of time by means of traditional algorithms in double precision, since the background numerical noise $varepsilon_{0}$ might stop decreasing because of the use of double precision. This restriction can be overcome by means of the clean numerical simulation (CNS), which can decrease the background numerical noise $varepsilon_{0}$ to any required tiny level. A lot of successful applications show the novelty and validity of the CNS. In this paper, we further propose some strategies to greatly increase the computational efficiency of the CNS algorithms for chaotic dynamical systems. It is highly suggested to keep a balance between truncation error and round-off error and besides to progressively enlarge the background numerical noise $varepsilon_{0}$, since the exponentially increasing numerical noise $varepsilon(t)$ is much larger than it. Some examples are given to illustrate the validity of our strategies for the CNS.","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42621923","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Reconstructed Discontinuous Approximation to Monge-Ampère Equation in Least Square Formulation Monge-Ampère方程的最小二乘重构间断逼近

IF 1.4 4区工程技术

Advances in Applied Mathematics and Mechanics Pub Date : 2022-10-01 DOI: 10.4208/aamm.oa-2022-0047

Ruo Li and Fanyi Yang

引用次数: 0

Avoiding Small Denominator Problems by Means of the Homotopy Analysis Method 用同伦分析法避免小分母问题

IF 1.4 4区工程技术

Advances in Applied Mathematics and Mechanics Pub Date : 2022-08-03 DOI: 10.4208/aamm.OA-2022-0260

S. Liao

{"title":"Avoiding Small Denominator Problems by Means of the Homotopy Analysis Method","authors":"S. Liao","doi":"10.4208/aamm.OA-2022-0260","DOIUrl":"https://doi.org/10.4208/aamm.OA-2022-0260","url":null,"abstract":"The so-called ``small denominator problem'' was a fundamental problem of dynamics, as pointed out by Poincar'{e}. Small denominators appear most commonly in perturbative theory. The Duffing equation is the simplest example of a non-integrable system exhibiting all problems due to small denominators. In this paper, using the forced Duffing equation as an example, we illustrate that the famous ``small denominator problems'' never appear if a non-perturbative approach based on the homotopy analysis method (HAM), namely ``the method of directly defining inverse mapping'' (MDDiM), is used. The HAM-based MDDiM provides us great freedom to directly define the inverse operator of an undetermined linear operator so that all small denominators can be completely avoided and besides the convergent series of multiple limit-cycles of the forced Duffing equation with high nonlinearity are successfully obtained. So, from the viewpoint of the HAM, the famous ``small denominator problems'' are only artifacts of perturbation methods. Therefore, completely abandoning perturbation methods but using the HAM-based MDDiM, one would be never troubled by ``small denominators''. The HAM-based MDDiM has general meanings in mathematics and thus can be used to attack many open problems related to the so-called ``small denominators''.","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46469524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2