International journal of numerical analysis & modeling. Series B最新文献_第2页

A Splitting Spectral Method for the Nonlinear Dirac-Poisson Equations 非线性Dirac-Poisson方程的分裂谱方法

International journal of numerical analysis & modeling. Series B Pub Date : 2023-06-01 DOI: 10.4208/ijnam2023-1025

Dandan Wang, Yong Zhang null, Hanquan Wang

引用次数: 0

Monolithic and Partitioned Finite Element Schemes for Fsi Based on an Ale Divergence-Free Hdg Fluid Solver and a Tdnns Structural Solver 基于Ale无散度Hdg流体解算器和Tdnns结构解算器的Fsi整体和分区有限元格式

International journal of numerical analysis & modeling. Series B Pub Date : 2023-01-01 DOI: 10.4208/ijnam2023-1011

G. Fu

引用次数: 0

Optimal Block Preconditioner for an Efficient Numerical Solution of the Elliptic Optimal Control Problems Using Gmres Solver 用Gmres求解器求解椭圆型最优控制问题的最优块预调节器

International journal of numerical analysis & modeling. Series B Pub Date : 2023-01-01 DOI: 10.4208/ijnam2023-1003

K. Muzhinji

{"title":"Optimal Block Preconditioner for an Efficient Numerical Solution of the Elliptic Optimal Control Problems Using Gmres Solver","authors":"K. Muzhinji","doi":"10.4208/ijnam2023-1003","DOIUrl":"https://doi.org/10.4208/ijnam2023-1003","url":null,"abstract":". Optimal control problems are a class of optimisation problems with partial diﬀer- ential equations as constraints. These problems arise in many application areas of science and engineering. The ﬁnite element method was used to transform the optimal control problems of an elliptic partial diﬀerential equation into a system of linear equations of saddle point form. The main focus of this paper is to characterise and exploit the structure of the coeﬃcient matrix of the saddle point system to build an eﬃcient numerical process. These systems are of large dimension, block, sparse, indeﬁnite and ill conditioned. The numerical solution of saddle point problems is a computational task since well known numerical schemes perform poorly if they are not properly preconditioned. The main task of this paper is to construct a preconditioner the mimic the structure of the system coeﬃcient matrix to accelerate the convergence of the generalised minimal residual method. Explicit expression of the eigenvalue and eigenvectors for the preconditioned matrix are derived. The main outcome is to achieve optimal convergence results in a small number of iterations with respect to the decreasing mesh size h and the changes in δ the regularisation problem parameters. The numerical results demonstrate the eﬀectiveness and performance of the proposed preconditioner compared to the other existing preconditioners and conﬁrm theoretical results.","PeriodicalId":90552,"journal":{"name":"International journal of numerical analysis & modeling. Series B","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70520519","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

A Spring–Beam System with Signorini’S Condition and the Normal Compliance Condition 具有sigorini条件和正常柔度条件的弹簧梁系统

International journal of numerical analysis & modeling. Series B Pub Date : 2023-01-01 DOI: 10.4208/ijnam2023-1004

J. Ahn, N. Tate

引用次数: 0

Isogeometric Solution of Helmholtz Equation with Dirichlet Boundary Condition in Regions with Irregular Boundary: Numerical Experiences 不规则边界区域具有Dirichlet边界条件的Helmholtz方程等几何解:数值经验

International journal of numerical analysis & modeling. Series B Pub Date : 2023-01-01 DOI: 10.4208/ijnam2023-1001

V. Mederos, I. A. Ugalde, R. Alfonso, Domenico Lahaye null, Valia Guerra Ones

{"title":"Isogeometric Solution of Helmholtz Equation with Dirichlet Boundary Condition in Regions with Irregular Boundary: Numerical Experiences","authors":"V. Mederos, I. A. Ugalde, R. Alfonso, Domenico Lahaye null, Valia Guerra Ones","doi":"10.4208/ijnam2023-1001","DOIUrl":"https://doi.org/10.4208/ijnam2023-1001","url":null,"abstract":". In this paper we use the Isogeometric Analysis (IgA) to solve the Helmholtz equa- tion with Dirichlet boundary condition over a bounded physical 2D domain. Starting from the variational formulation of the problem, we show how to apply IgA to obtain an approximated solution based on biquadratic B-spline functions. We focus the attention on problems where the physical domain has very irregular boundary. To solve these problems successfully a high quality parametrization of the domain must be constructed. This parametrization is also a biquadratic tensor product B-spline function, with control points computed as the vertices of a quadrilateral mesh with optimal geometric properties. We study experimentally the inﬂuence of the wave number and the parametrization of the physical domain in the accuracy of the approximated solution. A comparison with classical Finite Element Method is also included. The power of IgA is shown solving several diﬃcult model problems, which are particular cases of the Helmholtz equation and where the solution has discontinuous gradient in some points, or it is highly oscillatory. For all model problems we explain how to select the knots of B-spline quadratic functions and how to insert knew knots in order to obtain good approximations. The results obtained with our implementation of the method prove that IgA approach is successful, even on regions with irregular boundary, since it is able to oﬀer smooth solutions having at the same time some singular points and high number of oscillations.","PeriodicalId":90552,"journal":{"name":"International journal of numerical analysis & modeling. Series B","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70520413","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

Optimal Control of a Quasistatic Frictional Contact Problem with History-Dependent Operators 一类具有历史相关算子的拟静态摩擦接触问题的最优控制

International journal of numerical analysis & modeling. Series B Pub Date : 2023-01-01 DOI: 10.4208/ijnam2023-1002

Yujie Li, Xiaoliang Cheng, Xilu Wang

引用次数: 1

The Mixed Finite Volume Methods for Stokes Problem Based on Mini Element Pair 基于小单元对的Stokes问题的混合有限体积法

International journal of numerical analysis & modeling. Series B Pub Date : 2023-01-01 DOI: 10.4208/ijnam2023-1006

Hongtao Yang, Yonghai Li

引用次数: 1

Numerical analysis of a structure-preserving space-discretization for an anisotropic and heterogeneous boundary controlled N-dimensional wave equation as port-Hamiltonian system 各向异性非均质边界控制n维波动方程的保结构空间离散化数值分析

International journal of numerical analysis & modeling. Series B Pub Date : 2020-06-26 DOI: 10.4208/ijnam2023-1005

Ghislain Haine, D. Matignon, A. Serhani

引用次数: 9

A MATHEMATICAL ANALYSIS OF PHYSIOLOGICAL AND MOLECULAR MECHANISMS THAT MODULATE PRESSURE GRADIENTS AND FACILITATE VENTRICULAR EXPANSION IN HYDROCEPHALUS. 脑积水中调节压力梯度和促进心室扩张的生理和分子机制的数学分析。

International journal of numerical analysis & modeling. Series B Pub Date : 2012-01-01

Kathleen P Wilkie, Gurjit Nagra, Miles Johnston

{"title":"A MATHEMATICAL ANALYSIS OF PHYSIOLOGICAL AND MOLECULAR MECHANISMS THAT MODULATE PRESSURE GRADIENTS AND FACILITATE VENTRICULAR EXPANSION IN HYDROCEPHALUS.","authors":"Kathleen P Wilkie, Gurjit Nagra, Miles Johnston","doi":"","DOIUrl":"","url":null,"abstract":"Perhaps the greatest paradox in the hydrocephalus field is the failure of researchers to consistently measure transmantle pressure gradients (ventricle to subarachnoid space) in either human or animal models of the communicating form of the disorder. Without such a gradient, conceptualization of how ventricular distention occurs is difficult. Based on evidence from both a mathematical model [35] and experiments in skin [51], we observed that the intraventricular injection of anti-β1 integrin antibodies in rat brains results in a reduction of periventricular pressures to values below those monitored in the ventricles. In addition, many of these animals developed hydrocephalus [30]. We conclude that the dissociation of β1 integrins from the surrounding matrix fibers generates pressure gradients favouring ventricular expansion suggesting a novel mechanism for hydrocephalus development. Several issues, however, need further clarification. If hydrostatic pressure declines in the periventricular tissues then fluid absorption must occur. Aquaporin-4 (AQP4) is a likely candidate for this absorption as it is the predominant water channel in the brain. Indeed, when capillary function is negated, periventricular interstitial fluid pressures increase after anti-β1 integrin antibody administration. This suggests that capillary absorption of parenchymal water may play a pivotal role in the generation of pressure gradients in our hydrocephalus model. Focusing on these issues, we present two poroelastic models to investigate the role of intramantle pressure gradients in ventriculomegaly and to determine if integrin-matrix disassociation represents a complete causative mechanism for hydrocephalus development.","PeriodicalId":90552,"journal":{"name":"International journal of numerical analysis & modeling. Series B","volume":"316 ","pages":"65-81"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4322945/pdf/nihms-620932.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33052813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A MATHEMATICAL INVESTIGATION OF THE ROLE OF INTRACRANIAL PRESSURE PULSATIONS AND SMALL GRADIENTS IN THE PATHOGENESIS OF HYDROCEPHALUS. 颅内压力搏动和小梯度在脑积水发病机制中的作用的数学研究。

International journal of numerical analysis & modeling. Series B Pub Date : 2012-01-01

Kathleen P Wilkie, Corina S Drapaca, Sivabal Sivaloganathan

{"title":"A MATHEMATICAL INVESTIGATION OF THE ROLE OF INTRACRANIAL PRESSURE PULSATIONS AND SMALL GRADIENTS IN THE PATHOGENESIS OF HYDROCEPHALUS.","authors":"Kathleen P Wilkie, Corina S Drapaca, Sivabal Sivaloganathan","doi":"","DOIUrl":"","url":null,"abstract":"Cerebrospinal fluid (CSF) pulsations have been proposed as a possible causative mechanism for the ventricular enlargement that characterizes the neurological condition known as hydrocephalus. This paper summarizes recent work by the authors to anaylze the effect of CSF pulsations on brain tissue to determine if they are mechanically capable of enlarging the cerebral ventricles. First a poroelastic model is presented to analyze the interactions that occur between the fluid and porous solid constituents of brain tissue due to CSF pulsations. A viscoelastic model is then presented to analyze the effects of the fluid pulsations on the solid brain tissue. The combined results indicate that CSF pulsations in a healthy brain are incapable of causing tissue damage and thus the ventricular enlargement observed in hydrocephalus. Therefore they cannot be the primary cause of this condition. Finally, a hyper-viscoelastic model is presented and used to demonstrate that small long-term transmantle pressure gradients may be a possible cause of communicating hydrocephalus in infants.","PeriodicalId":90552,"journal":{"name":"International journal of numerical analysis & modeling. Series B","volume":"3 1","pages":"36-51"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4286312/pdf/nihms620937.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"32967372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0