Applications of Mathematics最新文献_第2页

Modeling pressure-driven flow between adjacent surfaces of viscoplastic and seemingly viscoplastic materials 模拟粘塑性和似粘塑性材料相邻表面之间的压力驱动流动

IF 0.7 4区数学

Applications of Mathematics Pub Date : 2026-01-08 DOI: 10.21136/AM.2026.0146-25

Andreas Almqvist, Evgeniya Burtseva, Kumbakonam Rajagopal, Peter Wall

引用次数: 0

An improved two-step method for inverse singular value problems 奇异值反问题的改进两步法

IF 0.7 4区数学

Applications of Mathematics Pub Date : 2026-01-07 DOI: 10.21136/AM.2026.0096-25

Wei Ma

引用次数: 0

Efficient Karhunen-Loève expansions via Legendre-Galerkin discretization and tensor structure 基于legende - galerkin离散化和张量结构的高效karhunen - lo<e:1>展开

IF 0.7 4区数学

Applications of Mathematics Pub Date : 2025-12-05 DOI: 10.21136/AM.2025.0163-25

Michal Béreš

引用次数: 0

The least squares solution of inconsistent discretized elliptic problems using the FETI method 非一致离散椭圆型问题的最小二乘解

IF 0.7 4区数学

Applications of Mathematics Pub Date : 2025-12-04 DOI: 10.21136/AM.2025.0189-25

Zdeněk Dostál, David Horák

引用次数: 0

Memories of Professor Radim Blaheta Radim Blaheta教授的回忆

IF 0.7 4区数学

Applications of Mathematics Pub Date : 2025-12-02 DOI: 10.21136/AM.2025.0246-25

Stanislav Sysala

引用次数: 0

Fitted norm preconditioners for the Hodge-Laplacian in mixed form 混合形式Hodge-Laplacian的拟合范数前提条件

IF 0.7 4区数学

Applications of Mathematics Pub Date : 2025-12-01 DOI: 10.21136/AM.2025.0185-25

Wietse M. Boon, Johannes Kraus, Tomáš Luber, Maria Lymbery

引用次数: 0

An adaptive mesh refinement scheme for hierarchical hybrid grids 一种层次混合网格的自适应网格细化方案

IF 0.7 4区数学

Applications of Mathematics Pub Date : 2025-11-28 DOI: 10.21136/AM.2025.0186-25

Benjamin Mann, Ulrich Rüde

{"title":"An adaptive mesh refinement scheme for hierarchical hybrid grids","authors":"Benjamin Mann, Ulrich Rüde","doi":"10.21136/AM.2025.0186-25","DOIUrl":"10.21136/AM.2025.0186-25","url":null,"abstract":"<div><p>This work introduces an adaptive mesh refinement technique for hierarchical hybrid grids with the goal to reach scalability and maintain excellent performance on massively parallel computer systems. On the block-structured hierarchical hybrid grids, this is accomplished by using classical, unstructured refinement only on the coarsest level of the hierarchy, while keeping the number of structured refinement levels constant over the whole domain. This leads to a compromise, where the excellent performance characteristics of hierarchical hybrid grids can be maintained at the price that the flexibility of generating locally refined meshes is constrained. Furthermore, the mesh adaptivity often relies on a posteriori error estimators or error indicators, which tend to become computationally expensive. Again, with the goal of preserving scalability and performance, a method is proposed that leverages the grid hierarchy and the full multigrid scheme. Utilizing the sequence of approximations on the nested hierarchy of grids permits the computation of a cheap error estimator that is well-suited for large-scale parallel computing. We present the theoretical foundations for both global and local error estimates, and present a rigorous analysis of their effectivity. The proposed method, including the error estimator and the adaptive coarse grid refinement, is implemented in the finite element framework H<span>y</span>T<span>e</span>G. Extensive numerical experiments are conducted to validate the effectiveness, as well as performance and scalability.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 6","pages":"875 - 905"},"PeriodicalIF":0.7,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754500","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

State-based approach to the numerical solution of Dirichlet boundary optimal control problems for the Laplace equation 拉普拉斯方程Dirichlet边界最优控制问题数值解的基于状态的方法

IF 0.7 4区数学

Applications of Mathematics Pub Date : 2025-11-21 DOI: 10.21136/AM.2025.0166-25

Ulrich Langer, Richard Löscher, Olaf Steinbach, Huidong Yang

引用次数: 0

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