Mathematical Models and Methods in Applied Sciences最新文献_第6页

Nonlocal half-ball vector operators on bounded domains: Poincare inequality and its applications 有界域上的非局部半球向量算子:庞加莱不等式及其应用

Mathematical Models and Methods in Applied Sciences Pub Date : 2023-10-19 DOI: 10.1142/s0218202523500549

Zhaolong Han, Xiaochuan Tian

引用次数: 3

Analyticity and hp discontinuous Galerkin approximation of nonlinear Schrödinger eigenproblems 非线性Schrödinger特征问题的解析性和hp不连续Galerkin逼近

Mathematical Models and Methods in Applied Sciences Pub Date : 2023-10-18 DOI: 10.1142/s0218202523500586

Yvon Maday, Carlo Marcati

引用次数: 5

Reduced Lagrange multiplier approach for non-matching coupling of mixed-dimensional domains 混合维域非匹配耦合的简化拉格朗日乘子方法

Mathematical Models and Methods in Applied Sciences Pub Date : 2023-10-04 DOI: 10.1142/s0218202523500525

Luca Heltai, Paolo Zunino

{"title":"Reduced Lagrange multiplier approach for non-matching coupling of mixed-dimensional domains","authors":"Luca Heltai, Paolo Zunino","doi":"10.1142/s0218202523500525","DOIUrl":"https://doi.org/10.1142/s0218202523500525","url":null,"abstract":"Many physical problems involving heterogeneous spatial scales, such as the flow through fractured porous media, the study of fiber-reinforced materials, or the modeling of the small circulation in living tissues — just to mention a few examples — can be described as coupled partial differential equations defined in domains of heterogeneous dimensions that are embedded into each other. This formulation is a consequence of geometric model reduction techniques that transform the original problems defined in complex three-dimensional domains into more tractable ones. The definition and the approximation of coupling operators suitable for this class of problems is still a challenge. We develop a general mathematical framework for the analysis and the approximation of partial differential equations coupled by non-matching constraints across different dimensions, focusing on their enforcement using Lagrange multipliers. In this context, we address in abstract and general terms the well-posedness, stability, and robustness of the problem with respect to the smallest characteristic length of the embedded domain. We also address the numerical approximation of the problem and we discuss the infsup stability of the proposed numerical scheme for some representative configuration of the embedded domain. The main message of this work is twofold: from the standpoint of the theory of mixed-dimensional problems, we provide general and abstract mathematical tools to formulate coupled problems across dimensions. From the practical standpoint of the numerical approximation, we show the interplay between the mesh characteristic size, the dimension of the Lagrange multiplier space, and the size of the inclusion in representative configurations interesting for applications. The latter analysis is complemented with illustrative numerical examples.","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135547277","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

Sharp Interface Limit of the Cahn-Hilliard Reaction Model for Lithium-ion Batteries 锂离子电池Cahn-Hilliard反应模型的夏普界面极限

Mathematical Models and Methods in Applied Sciences Pub Date : 2023-09-30 DOI: 10.1142/s0218202523500550

Tim Laux, Kerrek Stinson

引用次数: 0

A second-order fully-balanced structure-preserving variational discretization scheme for the Cahn-Hilliard Navier-Stokes system Cahn-Hilliard Navier-Stokes系统的二阶全平衡保结构变分离散化格式

Mathematical Models and Methods in Applied Sciences Pub Date : 2023-09-30 DOI: 10.1142/s0218202523500562

A. Brunk, H. Egger, O. Habrich, M. Lukacova-Medvid'ova

引用次数: 0

Error estimates with low-order polynomial dependence for the fully-discrete finite element Invariant Energy Quadratization scheme of the Allen-Cahn Equation Allen-Cahn方程全离散有限元不变能量二次化格式的低阶多项式依赖误差估计

Mathematical Models and Methods in Applied Sciences Pub Date : 2023-09-30 DOI: 10.1142/s0218202523500537

Guo-Dong Zhang, Xiaofeng Yang

引用次数: 0

Coupling the Navier–Stokes–Fourier equations with the Johnson–Segalman stress-diffusive viscoelastic model: global-in-time and large-data analysis 纳维-斯托克斯-傅里叶方程与约翰逊-塞格曼应力扩散粘弹性模型的耦合：全局实时和大数据分析

Mathematical Models and Methods in Applied Sciences Pub Date : 2023-08-08 DOI: 10.1142/s0218202524500064

Michal Bathory, Miroslav Bul'ivcek, J. M'alek

{"title":"Coupling the Navier–Stokes–Fourier equations with the Johnson–Segalman stress-diffusive viscoelastic model: global-in-time and large-data analysis","authors":"Michal Bathory, Miroslav Bul'ivcek, J. M'alek","doi":"10.1142/s0218202524500064","DOIUrl":"https://doi.org/10.1142/s0218202524500064","url":null,"abstract":"We prove that there exists a~large-data and global-in-time weak solution to a~system of partial differential equations describing an unsteady flow of an incompressible heat-conducting rate-type viscoelastic stress-diffusive fluid filling up a~mechanically and thermally isolated container of any dimension. To overcome the~principle difficulties connected with ill-posedness of the~diffusive Oldroyd-B model in three dimensions, we assume that the~fluid admits a~strengthened dissipation mechanism, at least for excessive elastic deformations. All the~relevant material coefficients are allowed to depend continuously on the~temperature, whose evolution is captured by a~thermodynamically consistent equation. In fact, the~studied model is derived from scratch using only the~balance equations for linear momentum and energy, the~formulation of the~second law of thermodynamics and the~constitutive equation for the~internal energy. The~latter is assumed to be a~linear function of temperature, which simplifies the~model. The~concept of our weak solution incorporates both the~temperature and entropy inequalities, and also the~local balance of total energy provided that the~pressure function exists.","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"69 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139351392","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

A IETI-DP method for discontinuous Galerkin discretizations in isogeometric analysis with inexact local solvers 非精确局部解等几何分析中不连续Galerkin离散的IETI-DP方法

Mathematical Models and Methods in Applied Sciences Pub Date : 2023-08-02 DOI: 10.1142/s0218202523500495

Monica Montardini, Giancarlo Sangalli, Rainer Schneckenleitner, Stefan Takacs, Mattia Tani

{"title":"A IETI-DP method for discontinuous Galerkin discretizations in isogeometric analysis with inexact local solvers","authors":"Monica Montardini, Giancarlo Sangalli, Rainer Schneckenleitner, Stefan Takacs, Mattia Tani","doi":"10.1142/s0218202523500495","DOIUrl":"https://doi.org/10.1142/s0218202523500495","url":null,"abstract":"We construct solvers for an isogeometric multi-patch discretization, where the patches are coupled via a discontinuous Galerkin approach, which allows for the consideration of discretizations that do not match on the interfaces. We solve the resulting linear system using a Dual-Primal IsogEometric Tearing and Interconnecting (IETI-DP) method. We are interested in solving the arising patch-local problems using iterative solvers since this allows for the reduction of the memory footprint. We solve the patch-local problems approximately using the Fast Diagonalization method, which is known to be robust in the grid size and the spline degree. To obtain the tensor structure needed for the application of the Fast Diagonalization method, we introduce an orthogonal splitting of the local function spaces. We present a convergence theory for two-dimensional problems that confirms that the condition number of the preconditioned system only grows poly-logarithmically with the grid size. The numerical experiments confirm this finding. Moreover, they show that the convergence of the overall solver only mildly depends on the spline degree. We observe a mild reduction of the computational times and a significant reduction of the memory requirements in comparison to standard IETI-DP solvers using sparse direct solvers for the local subproblems. Furthermore, the experiments indicate good scaling behavior on distributed memory machines. Additionally, we present an extension of the solver to three-dimensional problems and provide numerical experiments assessing good performance also in that setting.","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"132 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136384633","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

Adaptive isogeometric methods with C1 (truncated) hierarchical splines on planar multi-patch domains 平面多斑块域上C1(截断)层次样条的自适应等几何方法

Mathematical Models and Methods in Applied Sciences Pub Date : 2023-05-31 DOI: 10.1142/s0218202523500434

Cesare Bracco, Carlotta Giannelli, Mario Kapl, Rafael Vazquez

{"title":"Adaptive isogeometric methods with C1 (truncated) hierarchical splines on planar multi-patch domains","authors":"Cesare Bracco, Carlotta Giannelli, Mario Kapl, Rafael Vazquez","doi":"10.1142/s0218202523500434","DOIUrl":"https://doi.org/10.1142/s0218202523500434","url":null,"abstract":"Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well suited for the representation of complex geometries, and to maintain high continuity on general domains special constructions on multi-patch geometries must be used. In this paper, we focus on adaptive isogeometric methods with hierarchical splines, and extend the construction of [Formula: see text] isogeometric spline spaces on multi-patch planar domains to the hierarchical setting. We replace the hypothesis of local linear independence for the basis of each level by a weaker assumption, which still ensures the linear independence of hierarchical splines. We also develop a refinement algorithm that guarantees that the assumption is fulfilled by [Formula: see text] splines on certain suitably graded hierarchical multi-patch mesh configurations, and prove that it has linear complexity. The performance of the adaptive method is tested by solving the Poisson and the biharmonic problems.","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135194798","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

Multigrid solvers for isogeometric discretizations of the second biharmonic problem 二次双调和问题等几何离散化的多网格求解方法

Mathematical Models and Methods in Applied Sciences Pub Date : 2023-05-29 DOI: 10.1142/s0218202523500422

Jarle Sogn, Stefan Takacs

引用次数: 0