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On a new computational algorithm for impacts of elastic bodies 一种新的弹性体碰撞计算算法
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2022-05-30 DOI: 10.21136/AM.2022.0129-21
Hynek Štekbauer, Ivan Němec, Rostislav Lang, Daniel Burkart, Jiří Vala
{"title":"On a new computational algorithm for impacts of elastic bodies","authors":"Hynek Štekbauer,&nbsp;Ivan Němec,&nbsp;Rostislav Lang,&nbsp;Daniel Burkart,&nbsp;Jiří Vala","doi":"10.21136/AM.2022.0129-21","DOIUrl":"10.21136/AM.2022.0129-21","url":null,"abstract":"<div><p>Computational modelling of contact problems is still one of the most difficult aspects of non-linear analysis in engineering mechanics. The article introduces an original efficient explicit algorithm for evaluation of impacts of bodies, satisfying the conservation of both momentum and energy exactly. The algorithm is described in its linearized 2-dimensional formulation in details, as open to numerous generalizations including 3-dimensional ones, and supplied by numerical examples obtained from its software implementation.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2022.0129-21.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50054789","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}
引用次数: 1
Analysis of pattern formation using numerical continuation 用数值延拓分析模式形成
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2022-05-02 DOI: 10.21136/AM.2022.0126-21
Vladimír Janovský
{"title":"Analysis of pattern formation using numerical continuation","authors":"Vladimír Janovský","doi":"10.21136/AM.2022.0126-21","DOIUrl":"10.21136/AM.2022.0126-21","url":null,"abstract":"<div><p>The paper deals with the issue of self-organization in applied sciences. It is particularly related to the emergence of Turing patterns. The goal is to analyze the domain size driven instability: We introduce the parameter <i>L</i>, which scales the size of the domain. We investigate a particular reaction-diffusion model in 1-D for two species. We consider and analyze the steady-state solution. We want to compute the solution branches by numerical continuation. The model in question has certain symmetries. We define and classify them. Our goal is to calculate a global bifurcation diagram.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50003901","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 attractors for a tropical climate model 热带气候模式的全球吸引子
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2022-04-08 DOI: 10.21136/AM.2022.0230-21
Pigong Han, Keke Lei, Chenggang Liu, Xuewen Wang
{"title":"Global attractors for a tropical climate model","authors":"Pigong Han,&nbsp;Keke Lei,&nbsp;Chenggang Liu,&nbsp;Xuewen Wang","doi":"10.21136/AM.2022.0230-21","DOIUrl":"10.21136/AM.2022.0230-21","url":null,"abstract":"<div><p>This paper is devoted to the global attractors of the tropical climate model. We first establish the global well-posedness of the system. Then by studying the existence of bounded absorbing sets, the global attractor is constructed. The estimates of the Hausdorff dimension and of the fractal dimension of the global attractor are obtained in the end.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50013903","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
Resilient asynchronous primal Schur method 弹性异步原始Schur方法
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2022-04-05 DOI: 10.21136/AM.2022.0146-21
Guillaume Gbikpi-Benissan, Frédéric Magoulès
{"title":"Resilient asynchronous primal Schur method","authors":"Guillaume Gbikpi-Benissan,&nbsp;Frédéric Magoulès","doi":"10.21136/AM.2022.0146-21","DOIUrl":"10.21136/AM.2022.0146-21","url":null,"abstract":"<div><p>This paper introduces the application of asynchronous iterations theory within the framework of the primal Schur domain decomposition method. A suitable relaxation scheme is designed, whose asynchronous convergence is established under classical spectral radius conditions. For the usual case where local Schur complement matrices are not constructed, suitable splittings based only on explicitly generated matrices are provided. Numerical experiments are conducted on a supercomputer for both Poisson’s and linear elasticity problems. The asynchronous Schur solver outperformed the classical conjugate-gradient-based one in case of computing node failures.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2022.0146-21.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50009160","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}
引用次数: 3
Professor Michal Křížek, associate editor-in-chief of Applications of Mathematics, is seventy 迈克尔教授Křížek，《数学应用》的副主编，今年70岁
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2022-03-19 DOI: 10.21136/AM.2022.0031-22
Karel Segeth
{"title":"Professor Michal Křížek, associate editor-in-chief of Applications of Mathematics, is seventy","authors":"Karel Segeth","doi":"10.21136/AM.2022.0031-22","DOIUrl":"10.21136/AM.2022.0031-22","url":null,"abstract":"By the Charter of April 7, 1348, King of Bohemia and Holy Roman Emperor Charles IV of Luxembourg, a member of the Czech House of Přemyslid from his mother’s side, founded in Prague a university with four faculties (theology, liberal arts, medicine, and law). In 1920, in the Czechoslovak Republic just established in 1918, after several centuries of its successful development, the university was given the name Charles University. The Faculty of Science was established the same year. In 1952, a new faculty separated from this faculty, the Faculty of Mathematics and Physics. However, this was not the only important event of the year 1952. On March 8, 1952, Michal Křížek was born in Prague.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50037803","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
On surrogate learning for linear stability assessment of Navier-Stokes Equations with stochastic viscosity 随机黏度Navier-Stokes方程线性稳定性评价的代理学习
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2022-03-01 DOI: 10.21136/AM.2022.0046-21
Bedřich Sousedík, Howard C. Elman, Kookjin Lee, Randy Price
{"title":"On surrogate learning for linear stability assessment of Navier-Stokes Equations with stochastic viscosity","authors":"Bedřich Sousedík,&nbsp;Howard C. Elman,&nbsp;Kookjin Lee,&nbsp;Randy Price","doi":"10.21136/AM.2022.0046-21","DOIUrl":"10.21136/AM.2022.0046-21","url":null,"abstract":"We study linear stability of solutions to the Navier-Stokes equations with stochastic viscosity. Specifically, we assume that the viscosity is given in the form of a stochastic expansion. Stability analysis requires a solution of the steady-state Navier-Stokes equation and then leads to a generalized eigenvalue problem, from which we wish to characterize the real part of the rightmost eigenvalue. While this can be achieved by Monte Carlo simulation, due to its computational cost we study three surrogates based on generalized polynomial chaos, Gaussian process regression and a shallow neural network. The results of linear stability analysis assessment obtained by the surrogates are compared to that of Monte Carlo simulation using a set of numerical experiments.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49999478","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: 1
On the parameter in augmented Lagrangian preconditioning for isogeometric discretizations of the Navier-Stokes equations Navier-Stokes方程等几何离散化增广拉格朗日预处理中的参数
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2022-02-17 DOI: 10.21136/AM.2022.0130-21
Jiří Egermaier, Hana Horníková
{"title":"On the parameter in augmented Lagrangian preconditioning for isogeometric discretizations of the Navier-Stokes equations","authors":"Jiří Egermaier,&nbsp;Hana Horníková","doi":"10.21136/AM.2022.0130-21","DOIUrl":"10.21136/AM.2022.0130-21","url":null,"abstract":"<div><p>In this paper, we deal with the optimal choice of the parameter <i>γ</i> for augmented Lagrangian preconditioning of GMRES method for efficient solution of linear systems obtained from discretization of the incompressible Navier-Stokes equations. We consider discretization of the equations using the B-spline based isogeometric analysis approach. We are interested in the dependence of the convergence on the parameter <i>γ</i> for various problem parameters (Reynolds number, mesh refinement) and especially for various isogeometric discretizations (degree and interelement continuity of the B-spline discretization bases). The idea is to be able to determine the optimal value of <i>γ</i> for a problem that is relatively cheap to compute and, based on this value, predict suitable values for other problems, e.g., with finer mesh, different discretization, etc. The influence of inner solvers (direct or iterative based on multigrid method) is also discussed.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50034184","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
Low Mach number limit of a compressible Euler-Korteweg model 可压缩Euler-Korteweg模型的低马赫数极限
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2022-02-16 DOI: 10.21136/AM.2022.0067-21
Yajie Wang, Jianwei Yang
{"title":"Low Mach number limit of a compressible Euler-Korteweg model","authors":"Yajie Wang,&nbsp;Jianwei Yang","doi":"10.21136/AM.2022.0067-21","DOIUrl":"10.21136/AM.2022.0067-21","url":null,"abstract":"<div><p>This article deals with the low Mach number limit of the compressible Euler-Korteweg equations. It is justified rigorously that solutions of the compressible Euler-Korteweg equations converge to those of the incompressible Euler equations as the Mach number tends to zero. Furthermore, the desired convergence rates are also obtained.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49999556","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: 1
Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term 具有非线性记忆项的波动方程解的连续依赖和一般衰减
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2022-02-08 DOI: 10.21136/AM.2022.0200-21
Doan Thi Nhu Quynh, Nguyen Huu Nhan, Le Thi Phuong Ngoc, Nguyen Thanh Long
{"title":"Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term","authors":"Doan Thi Nhu Quynh,&nbsp;Nguyen Huu Nhan,&nbsp;Le Thi Phuong Ngoc,&nbsp;Nguyen Thanh Long","doi":"10.21136/AM.2022.0200-21","DOIUrl":"10.21136/AM.2022.0200-21","url":null,"abstract":"<div><p>We study existence, uniqueness, continuous dependence, general decay of solutions of an initial boundary value problem for a viscoelastic wave equation with strong damping and nonlinear memory term. At first, we state and prove a theorem involving local existence and uniqueness of a weak solution. Next, we establish a sufficient condition to get an estimate of the continuous dependence of the solution with respect to the kernel function and the nonlinear terms. Finally, under suitable conditions to obtain the global solution, we prove the general decay property with positive initial energy for this global solution.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50029062","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
Steady Boussinesq System with Mixed Boundary Conditions Including Friction Conditions 含摩擦条件的混合边界条件稳态Boussinesq系统
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2022-01-26 DOI: 10.21136/AM.2022.0031-21
Tujin Kim
{"title":"Steady Boussinesq System with Mixed Boundary Conditions Including Friction Conditions","authors":"Tujin Kim","doi":"10.21136/AM.2022.0031-21","DOIUrl":"10.21136/AM.2022.0031-21","url":null,"abstract":"<div><p>In this paper we are concerned with the steady Boussinesq system with mixed boundary conditions. The boundary conditions for fluid may include Tresca slip, leak, one-sided leak, velocity, vorticity, pressure and stress conditions together and the conditions for temperature may include Dirichlet, Neumann and Robin conditions together. For the problem involving the static pressure and stress boundary conditions, it is proved that if the data of the problem are small enough, then there exists a solution and the solution with small norm is unique. For the problem involving the total pressure and total stress boundary conditions, the existence of a solution is proved without smallness of the data.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50102930","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: 1
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