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Adjustment of the scaling parameter of Dai-Kou type conjugate gradient methods with application to motion control Dai-Kou型共轭梯度法标度参数的调整及其在运动控制中的应用
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-11-12 DOI: 10.21136/AM.2024.0006-24
Mahbube Akbari, Saeed Nezhadhosein, Aghile Heydari
{"title":"Adjustment of the scaling parameter of Dai-Kou type conjugate gradient methods with application to motion control","authors":"Mahbube Akbari,&nbsp;Saeed Nezhadhosein,&nbsp;Aghile Heydari","doi":"10.21136/AM.2024.0006-24","DOIUrl":"10.21136/AM.2024.0006-24","url":null,"abstract":"<div><p>We introduce a new scaling parameter for the Dai-Kou family of conjugate gradient algorithms (2013), which is one of the most numerically efficient methods for unconstrained optimization. The suggested parameter is based on eigenvalue analysis of the search direction matrix and minimizing the measure function defined by Dennis and Wolkowicz (1993). The corresponding search direction of conjugate gradient method has the sufficient descent property and the extended conjugacy condition. The global convergence of the proposed algorithm is given for both uniformly convex and general nonlinear objective functions. Also, numerical experiments on a set of test functions of the CUTER collections and the practical problem of the manipulator of robot movement control show that the proposed method is effective.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 6","pages":"829 - 845"},"PeriodicalIF":0.6,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142845014","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 modeling flow between adjacent surfaces where the fluid is governed by implicit algebraic constitutive relations 在流体由隐式代数本构关系控制的相邻表面之间的流动建模
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-11-12 DOI: 10.21136/AM.2024.0131-24
Andreas Almqvist, Evgeniya Burtseva, Kumbakonam R. Rajagopal, Peter Wall
{"title":"On modeling flow between adjacent surfaces where the fluid is governed by implicit algebraic constitutive relations","authors":"Andreas Almqvist,&nbsp;Evgeniya Burtseva,&nbsp;Kumbakonam R. Rajagopal,&nbsp;Peter Wall","doi":"10.21136/AM.2024.0131-24","DOIUrl":"10.21136/AM.2024.0131-24","url":null,"abstract":"<div><p>We consider pressure-driven flow between adjacent surfaces, where the fluid is assumed to have constant density. The main novelty lies in using implicit algebraic constitutive relations to describe the fluid’s response to external stimuli, enabling the modeling of fluids whose responses cannot be accurately captured by conventional methods. When the implicit algebraic constitutive relations cannot be solved for the Cauchy stress in terms of the symmetric part of the velocity gradient, the traditional approach of inserting the expression for the Cauchy stress into the equation for the balance of linear momentum to derive the governing equation for the velocity becomes inapplicable. Instead, a non-standard system of first-order equations governs the flow. This system is highly complex, making it important to develop simplified models. Our primary contribution is the development of a framework for achieving this. Additionally, we apply our findings to a fluid that exhibits an S-shaped curve in the shear stress versus shear rate plot, as observed in some colloidal solutions.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 6","pages":"725 - 746"},"PeriodicalIF":0.6,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2024.0131-24.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142845012","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: 0
Special issue dedicated to Professor Ivo Babuška, the founder of the journal Applications of Mathematics: Editorial 专为伊沃教授Babuška，杂志的创始人数学的应用：社论
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2024-10-31 DOI: 10.21136/AM.2024.0185-24
Vít Dolejší, Michal Křížek, Jan Zeman
{"title":"Special issue dedicated to Professor Ivo Babuška, the founder of the journal Applications of Mathematics: Editorial","authors":"Vít Dolejší,&nbsp;Michal Křížek,&nbsp;Jan Zeman","doi":"10.21136/AM.2024.0185-24","DOIUrl":"10.21136/AM.2024.0185-24","url":null,"abstract":"","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 5","pages":"541 - 544"},"PeriodicalIF":0.7,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145122611","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
Morley finite element analysis for fourth-order elliptic equations under a semi-regular mesh condition 半规则网格条件下四阶椭圆方程的莫里有限元分析
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-10-21 DOI: 10.21136/AM.2024.0103-24
Hiroki Ishizaka
{"title":"Morley finite element analysis for fourth-order elliptic equations under a semi-regular mesh condition","authors":"Hiroki Ishizaka","doi":"10.21136/AM.2024.0103-24","DOIUrl":"10.21136/AM.2024.0103-24","url":null,"abstract":"<div><p>We present a precise anisotropic interpolation error estimate for the Morley finite element method (FEM) and apply it to fourth-order elliptic equations. We do not impose the shape-regularity mesh condition in the analysis. Anisotropic meshes can be used for this purpose. The main contributions of this study include providing a new proof of the term consistency. This enables us to obtain an anisotropic consistency error estimate. The core idea of the proof involves using the relationship between the Raviart-Thomas and Morley finite-element spaces. Our results indicate optimal convergence rates and imply that the modified Morley FEM may be effective for errors.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 6","pages":"769 - 805"},"PeriodicalIF":0.6,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142844857","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
Error estimation for finite element solutions on meshes that contain thin elements 含薄单元网格有限元解的误差估计
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2024-10-14 DOI: 10.21136/AM.2024.0047-24
Kenta Kobayashi, Takuya Tsuchiya
{"title":"Error estimation for finite element solutions on meshes that contain thin elements","authors":"Kenta Kobayashi,&nbsp;Takuya Tsuchiya","doi":"10.21136/AM.2024.0047-24","DOIUrl":"10.21136/AM.2024.0047-24","url":null,"abstract":"<div><p>In an error estimation of finite element solutions to the Poisson equation, we usually impose the shape regularity assumption on the meshes to be used. In this paper, we show that even if the shape regularity condition is violated, the standard error estimation can be obtained if “bad” elements that violate the shape regularity or maximum angle condition are covered virtually by simplices that satisfy the minimum angle condition. A numerical experiment illustrates the theoretical result.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 5","pages":"571 - 588"},"PeriodicalIF":0.7,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121854","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
Ill-posedness for the Navier-Stokes and Euler equations in Besov spaces 贝索夫空间中的纳维-斯托克斯方程和欧拉方程的假定性
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-10-10 DOI: 10.21136/AM.2024.0089-24
Yanghai Yu, Fang Liu
{"title":"Ill-posedness for the Navier-Stokes and Euler equations in Besov spaces","authors":"Yanghai Yu,&nbsp;Fang Liu","doi":"10.21136/AM.2024.0089-24","DOIUrl":"10.21136/AM.2024.0089-24","url":null,"abstract":"<div><p>We construct a new initial data to prove the ill-posedness of both Navier-Stokes and Euler equations in weaker Besov spaces in the sense that the solution maps to these equations starting from <i>u</i><sub>0</sub> are discontinuous at <i>t</i> = 0.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 6","pages":"757 - 767"},"PeriodicalIF":0.6,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142844859","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
Stability analysis for acoustic waveguides. Part 3: impedance boundary conditions 声波导的稳定性分析。第三部分：阻抗边界条件
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2024-10-08 DOI: 10.21136/AM.2024.0080-24
Leszek Demkowicz, Jay Gopalakrishnan, Norbert Heuer
{"title":"Stability analysis for acoustic waveguides. Part 3: impedance boundary conditions","authors":"Leszek Demkowicz,&nbsp;Jay Gopalakrishnan,&nbsp;Norbert Heuer","doi":"10.21136/AM.2024.0080-24","DOIUrl":"10.21136/AM.2024.0080-24","url":null,"abstract":"<div><p>A model two-dimensional acoustic waveguide with lateral impedance boundary conditions (and outgoing boundary conditions at the waveguide outlet) is considered. The governing operator is proved to be bounded below with a stability constant inversely proportional to the length of the waveguide. The presence of impedance boundary conditions leads to a non self-adjoint operator which considerably complicates the analysis. The goal of this paper is to elucidate these complications and tools that are applicable, as simply as possible. This work is a continuation of prior waveguide studies (where self-adjoint operators arose) by J. M. Melenk et al. (2023), and L. Demkowicz et al. (2024).</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 5","pages":"633 - 651"},"PeriodicalIF":0.7,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121685","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
Guaranteed a-posteriori error estimation for finite element solutions of nonstationary heat conduction problems based on their elliptic reconstructions 基于椭圆重构的非平稳热传导问题有限元解的保证后验误差估计
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2024-09-17 DOI: 10.21136/AM.2024.0085-24
Theofanis Strouboulis, Delin Wang
{"title":"Guaranteed a-posteriori error estimation for finite element solutions of nonstationary heat conduction problems based on their elliptic reconstructions","authors":"Theofanis Strouboulis,&nbsp;Delin Wang","doi":"10.21136/AM.2024.0085-24","DOIUrl":"10.21136/AM.2024.0085-24","url":null,"abstract":"<div><p>We deal with the a-posteriori estimation of the error for finite element solutions of nonstationary heat conduction problems with mixed boundary conditions on bounded polygonal domains. The a-posteriori error estimates are constucted by solving stationary “reconstruction” problems, obtained by replacing the time derivative of the exact solution by the time derivative of the finite element solution. The main result is that the reconstructed solutions, or reconstructions, are superconvergent approximations of the exact solution (they are more accurate than the finite element solution) when the error is measured in the gradient or the energy-norm. Because of this, the error in the gradient of the finite element solution can be estimated reliably, by computing its difference from the gradient of its reconstructions. Numerical examples show that “reconstruction estimates” are reliable for the most general classes of solutions which can occur in practical computations.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 5","pages":"589 - 619"},"PeriodicalIF":0.7,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145122073","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
Exact solutions of generalized Lane-Emden equations of the second kind 第二类广义Lane-Emden方程的精确解
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-09-13 DOI: 10.21136/AM.2024.0220-23
Kismet Kasapoǧlu
{"title":"Exact solutions of generalized Lane-Emden equations of the second kind","authors":"Kismet Kasapoǧlu","doi":"10.21136/AM.2024.0220-23","DOIUrl":"10.21136/AM.2024.0220-23","url":null,"abstract":"<div><p>Contact and Lie point symmetries of a certain class of second order differential equations using the Lie symmetry theory are obtained. Generators of these symmetries are used to obtain first integrals and exact solutions of the equations. This class of equations is transformed into the so-called generalized Lane-Emden equations of the second kind</p><div><div><span>$$y^{primeprime}(x)+{kover{x}}y^{prime}(x)+ g(x){rm {e}}^{ny}=0.$$</span></div></div><p>Then we consider two types of functions <i>g</i>(<i>x</i>) and present first integrals and exact solutions of the Lane-Emden equation for them. One of the considered cases is new.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 6","pages":"747 - 755"},"PeriodicalIF":0.6,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142845019","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
Thermo-viscous fluid flow in porous slab bounded between two impermeable parallel plates in relative motion: Four stage algorithm approach 多孔板中的热粘性流体在两块不透水的平行板之间的相对运动中流动：四阶段算法方法
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-09-03 DOI: 10.21136/AM.2024.0144-23
Nalimela Pothanna, Podila Aparna, M. Pavankumar Reddy, R. Archana Reddy, M. Clement Joe Anand
{"title":"Thermo-viscous fluid flow in porous slab bounded between two impermeable parallel plates in relative motion: Four stage algorithm approach","authors":"Nalimela Pothanna,&nbsp;Podila Aparna,&nbsp;M. Pavankumar Reddy,&nbsp;R. Archana Reddy,&nbsp;M. Clement Joe Anand","doi":"10.21136/AM.2024.0144-23","DOIUrl":"10.21136/AM.2024.0144-23","url":null,"abstract":"<div><p>The problem of an approximate solution of thermo-viscous fluid flow in a porous slab bounded between two impermeable parallel plates in relative motion is examined in this paper. The two plates are kept at two different temperatures and the flow is generated by a constant pressure gradient together with the motion of one of the plates relative to the other. The velocity and temperature distributions have been obtained by a four-stage algorithm approach. It is worth mentioning that reverse effects are noticed on velocity and temperature distributions. These effects can be attributed to Darcy’s friction offered by the medium. The approximation results obtained in the present paper are in good agreement with the earlier numerical results of thermo-viscous fluid flows in plane geometry.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 6","pages":"807 - 827"},"PeriodicalIF":0.6,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176627","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
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