Applications of Mathematics最新文献_第5页

Algebraic multilevel preconditioning in spectral fractional diffusion 谱分数扩散中的代数多层预处理

IF 0.7 4区数学

Applications of Mathematics Pub Date : 2025-11-13 DOI: 10.21136/AM.2025.0101-25

Svetozar Margenov

{"title":"Algebraic multilevel preconditioning in spectral fractional diffusion","authors":"Svetozar Margenov","doi":"10.21136/AM.2025.0101-25","DOIUrl":"10.21136/AM.2025.0101-25","url":null,"abstract":"<div><p>The numerical solution of linear systems obtained as a result of discretization of a spectral fractional diffusion problem is studied. The finite element method is applied to the considered boundary value problem. The system matrix is a fractional power of the product of the inverse of the mass matrix and the stiffness matrix. The matrix thus defined is symmetric and positive definite (SPD) with respect to the inner product associated with the mass matrix, but is dense, which is consistent with the nonlocal nature of fractional diffusion. The presented results are in the spirit of the BURA (Best Uniform Rational Approximation) method. BURA reduces numerical solution of the dense linear system to the solution of <i>k</i> systems with sparse SPD diffusion-reaction matrices, where <i>k</i> is the degree of rational approximation. We prove the existence of algebraic multilevel iteration (AMLI) methods for preconditioning such type of emergent matrices that satisfy the conditions for optimal computational complexity. Both multiplicative and additive AMLI preconditioners have been developed, determining the minimum possible degree <i>θ</i> of the hierarchical <i>θ</i>-refinement of the mesh.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 6","pages":"851 - 874"},"PeriodicalIF":0.7,"publicationDate":"2025-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754342","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

A stabilized formulation for the mortar method with non-linear contact constraints 具有非线性接触约束的砂浆法的稳定公式

IF 0.7 4区数学

Applications of Mathematics Pub Date : 2025-11-11 DOI: 10.21136/AM.2025.0149-25

Daniele Moretto, Andrea Franceschini, Massimiliano Ferronato

{"title":"A stabilized formulation for the mortar method with non-linear contact constraints","authors":"Daniele Moretto, Andrea Franceschini, Massimiliano Ferronato","doi":"10.21136/AM.2025.0149-25","DOIUrl":"10.21136/AM.2025.0149-25","url":null,"abstract":"<div><p>The mortar method is a powerful technique to enforce constraints between non-conforming discretizations by introducing a set of Lagrange multipliers on the connecting interface. Usually, the multipliers are not obtained explicitly because they can be eliminated with the aid of the so-called mortar interpolation operator. However, their explicit computation becomes essential when the contact constraint is governed by some non-linear law, and in this situation it is necessary to guarantee that discrete spaces of the primary variables and multipliers are inf-sup stable. In this work, we investigate the issue of inf-sup stability when using various families of piecewise linear and piecewise constant multipliers. The focus is on the role of the mesh resolution and the enforcement of boundary conditions, which are important factors in practical applications. Then, we develop a stabilized formulation for piecewise-constant multipliers inspired by the framework of minimal stabilization. The effectiveness of the proposed approach is demonstrated through numerical benchmarks and examples.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 6","pages":"825 - 849"},"PeriodicalIF":0.7,"publicationDate":"2025-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2025.0149-25.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754315","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

First- and second-order adjoint methods for stochastic identification problems 随机辨识问题的一阶和二阶伴随方法

IF 0.7 4区数学

Applications of Mathematics Pub Date : 2025-11-04 DOI: 10.21136/AM.2025.0151-25

Nguyen Thi Van Anh, Adrian Heldt, Akhtar Ali Khan, Christiane Tammer

{"title":"First- and second-order adjoint methods for stochastic identification problems","authors":"Nguyen Thi Van Anh, Adrian Heldt, Akhtar Ali Khan, Christiane Tammer","doi":"10.21136/AM.2025.0151-25","DOIUrl":"10.21136/AM.2025.0151-25","url":null,"abstract":"<div><p>We present a unified framework for estimating stochastic parameters in general variational problems. This nonlinear inverse problem is formulated as a stochastic optimization problem using the output least-squares (OLS) objective, which minimizes the discrepancy between observed data and the computed solution. A key challenge in OLS-based formulations is the efficient computation of first- and second-order derivatives of the OLS functional, which depend on the corresponding derivatives of the parameter-to-solution map often costly and difficult to evaluate, especially in stochastic settings. To address this, we develop a rigorous computational approach based on first- and second-order adjoint methods for inverse problems governed by stochastic variational problems. Specifically, we propose a new first-order adjoint method for computing the gradient of the OLS objective and introduce two novel second-order adjoint methods for Hessian evaluation. A stochastic Galerkin discretization framework is employed, enabling efficient implementation of the adjoint-based derivative computations. Numerical experiments demonstrate the accuracy and efficiency of the proposed computational framework.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 6","pages":"763 - 795"},"PeriodicalIF":0.7,"publicationDate":"2025-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754325","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

Stable computation of Laplacian eigenfunctions corresponding to clustered eigenvalues 聚类特征值对应的拉普拉斯特征函数的稳定计算

IF 0.7 4区数学

Applications of Mathematics Pub Date : 2025-10-30 DOI: 10.21136/AM.2025.0132-25

Ryoki Endo, Xuefeng Liu

引用次数: 0

An accelerated gradient descent method based on a non-monotone backtracking line search scheme for unconstrained optimization and image restoration problems 一种基于非单调回溯线搜索的加速梯度下降法，用于无约束优化和图像恢复问题

IF 0.7 4区数学

Applications of Mathematics Pub Date : 2025-10-27 DOI: 10.21136/AM.2025.0131-25

Ali Ashrafi, Seyed Hamzeh Mirzaei

引用次数: 0

On parameter identification in the Stokes system with threshold leak boundary conditions 具有阈值泄漏边界条件的Stokes系统参数辨识

IF 0.7 4区数学

Applications of Mathematics Pub Date : 2025-10-27 DOI: 10.21136/AM.2025.0142-25

Raino A. E. Mäkinen, Jaroslav Haslinger

引用次数: 0

Two-grid penalty Arrow-Hurwicz iterative finite element methods for the stationary magnetohydrodynamics flow 静止磁流体流动的双网格罚Arrow-Hurwicz迭代有限元方法

IF 0.7 4区数学

Applications of Mathematics Pub Date : 2025-10-01 DOI: 10.21136/AM.2025.0141-23

Yun-Bo Yang, Yan-De Xia

引用次数: 0

A robust coefficient of determination based on implicit weighting 基于隐式加权的鲁棒决定系数

IF 0.7 4区数学

Applications of Mathematics Pub Date : 2025-10-01 DOI: 10.21136/AM.2025.0105-25

Jan Kalina

{"title":"A robust coefficient of determination based on implicit weighting","authors":"Jan Kalina","doi":"10.21136/AM.2025.0105-25","DOIUrl":"10.21136/AM.2025.0105-25","url":null,"abstract":"<div><p>In the linear regression model, the standard coefficient of determination <i>R</i><sup>2</sup> and its weighted counterpart are commonly used to assess the quality of the linear fit. However, both metrics are susceptible to the influence of outliers and heteroskedasticity within the dataset. This paper introduces a robust version of <i>R</i><sup>2</sup>, based on the least weighted squares (LWS) estimator, and examines its statistical properties in detail. We investigate the impact of data quantization on <i>R</i><sup>2</sup> and its robust variants, and propose a hypothesis test for assessing the equality of expected values between two <i>R</i><sup>2</sup> versions. Numerical experiments on 29 publicly available datasets reveal that confidence intervals for the LWS-based coefficient of determination are generally narrower than those for existing measures, especially in homoskedastic settings. In contrast, under heteroskedasticity, narrower intervals do not necessarily imply greater robustness, highlighting the nuanced behavior of these estimators. The comparison with the well-known least trimmed squares (LTS) estimator underscores the promise of the LWS approach, which exhibits favorable efficiency properties and more reliable interval estimation in many practical scenarios.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 5","pages":"647 - 670"},"PeriodicalIF":0.7,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2025.0105-25.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145442885","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

Global weak solutions to a 3D self-consistent chemotaxis-Stokes system with nonlinear resource consumption 具有非线性资源消耗的三维自洽趋化- stokes系统的全局弱解

IF 0.7 4区数学

Applications of Mathematics Pub Date : 2025-09-26 DOI: 10.21136/AM.2025.0041-25

Kwang-Ok Ri, Yong-Ho Kim, Jong-Chol Paek, Song-Chol Hong

引用次数: 0

Analysis and optimal control of a fractional tuberculosis model 分级结核模型的分析与最优控制

IF 0.7 4区数学

Applications of Mathematics Pub Date : 2025-09-24 DOI: 10.21136/AM.2025.0075-25

Hamadoum Dicko, Ali Traoré, Rosaire Ouedraogo

引用次数: 0