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Perfectly matched layers in time domain. A simplified two-dimensional error analysis 在时域上完全匹配层。简化的二维误差分析
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2026-01-29 DOI: 10.21136/AM.2026.0055-25
Kurt M. Bryan, Michael S. Vogelius
{"title":"Perfectly matched layers in time domain. A simplified two-dimensional error analysis","authors":"Kurt M. Bryan,&nbsp;Michael S. Vogelius","doi":"10.21136/AM.2026.0055-25","DOIUrl":"10.21136/AM.2026.0055-25","url":null,"abstract":"<div><p>Perfectly Matched Layers (PML) has become a very common method for the numerical approximation of wave and wave-like equations on unbounded domains. This technique allows one to obtain accurate solutions while working on a finite computational domain, and the technique is relatively simple to implement. Results concerning the accuracy of the PML method have been obtained, but mostly with regard to problems at a fixed frequency. In this paper we provide very explicit time-domain bounds on the accuracy of PML for the inhomogeneous two-dimensional wave equation with a particular type of forcing term, and illustrate our conclusions with some numerical examples.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 1","pages":"31 - 57"},"PeriodicalIF":0.7,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342624","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
100 years since the birth of Professor Miloš Zlámal 米洛什教授诞辰100周年Zlámal
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2026-01-20 DOI: 10.21136/AM.2026.0273-25
Jan Franců, Michal Křížek
{"title":"100 years since the birth of Professor Miloš Zlámal","authors":"Jan Franců,&nbsp;Michal Křížek","doi":"10.21136/AM.2026.0273-25","DOIUrl":"10.21136/AM.2026.0273-25","url":null,"abstract":"<div><p>After a brief biography of Professor Miloš Zlámal we recall his most important mathematical achievements. First, he dealt with various properties of analytical solutions of ordinary and partial differential equations. He then laid the theoretical foundation for the finite element method as the minimum angle condition, curved finite elements, the numerical solution of heat conduction problem and semiconductor equations, and superconvergence. He developed the so-called mortar finite elements used to cover a strip between two different types of finite elements. Complete chronological list of Zlámal’s publications closes the contribution.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 1","pages":"127 - 135"},"PeriodicalIF":0.7,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147340534","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
Failure extropy properties of mixed system with application 混合系统的失效熵特性及其应用
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2026-01-15 DOI: 10.21136/AM.2026.0203-25
Aman Pandey, Chanchal Kundu
{"title":"Failure extropy properties of mixed system with application","authors":"Aman Pandey,&nbsp;Chanchal Kundu","doi":"10.21136/AM.2026.0203-25","DOIUrl":"10.21136/AM.2026.0203-25","url":null,"abstract":"<div><p>Recent research has shown growing interest in quantifying uncertainty in system lifetimes. This paper investigates the failure extropy (FEx) of an <i>n</i>-component mixed system, conditioned on the failure of all components by a given time <i>t.</i> Using the concept of system signature, explicit expressions for the FEx of the system lifetime are derived, along with key properties and informative bounds. To extend this framework, a divergence measure based on FEx is proposed to assess the complexity of system structures. A new discrimination measure is also proposed, serving as a valuable tool to assess how closely a system resembles a parallel system. An application to redundancy allocation has been carried out to demonstrate the practical relevance of the proposed results and provide insights into optimal system design under uncertainty.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 1","pages":"89 - 105"},"PeriodicalIF":0.7,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147339456","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
Evolution of acceleration wave and interaction with a strong shock in a plasma with axial magnetic field and dust particles 具有轴向磁场和尘埃粒子的等离子体中加速波的演化及其与强激波的相互作用
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2026-01-15 DOI: 10.21136/AM.2026.0201-24
Nishi Deepa Palo, Jasobanta Jena
{"title":"Evolution of acceleration wave and interaction with a strong shock in a plasma with axial magnetic field and dust particles","authors":"Nishi Deepa Palo,&nbsp;Jasobanta Jena","doi":"10.21136/AM.2026.0201-24","DOIUrl":"10.21136/AM.2026.0201-24","url":null,"abstract":"<div><p>The paper examines the evolution of a weak discontinuity, specifically, an acceleration wave in a one-dimensional unsteady plasma flow influenced by an axial magnetic field in the presence of dust particles. We obtained self-similar solutions through the application of Lie group transformations. This study also explores the idea of interaction between the acceleration wave and a strong shock wave, with particular emphasis on the roles played by dust particles and the magnetic field. The effects of various parameters involved in the flow are examined. Additionally, the reflected and transmitted waves following the interactions are analyzed and the results are depicted.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 1","pages":"107 - 126"},"PeriodicalIF":0.7,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147339457","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
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
{"title":"Modeling pressure-driven flow between adjacent surfaces of viscoplastic and seemingly viscoplastic materials","authors":"Andreas Almqvist,&nbsp;Evgeniya Burtseva,&nbsp;Kumbakonam Rajagopal,&nbsp;Peter Wall","doi":"10.21136/AM.2026.0146-25","DOIUrl":"10.21136/AM.2026.0146-25","url":null,"abstract":"<div><p>A simplified model is derived for pressure-driven flow between adjacent surfaces of materials modeled as seemingly viscoplastic or truly viscoplastic. The material response to external forces is traditionally described by constitutive relations in which the extra stress tensor <b>S</b> is expressed as a function of the symmetric part of the velocity gradient <b>D</b>. However, for viscoplastic materials, <b>S</b> cannot, in general, be written as a function of <b>D</b>, whereas <b>D</b> can be expressed in terms of <b>S</b>. Motivated by this observation, a model based on constitutive relations of the form <b>D</b> = <i>f</i>(<b>S</b>) is proposed, leading to a system of first-order partial differential equations. A local Poiseuille law is also formulated, and a reduced-dimensional equation for the pressure is derived. Explicit velocity profiles are obtained for selected cases.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 1","pages":"1 - 30"},"PeriodicalIF":0.7,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2026.0146-25.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337863","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
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
{"title":"An improved two-step method for inverse singular value problems","authors":"Wei Ma","doi":"10.21136/AM.2026.0096-25","DOIUrl":"10.21136/AM.2026.0096-25","url":null,"abstract":"<div><p>Based on the technique of T. Ogita and K. Aishima (2020) and J. A. Ezquerro and M. A. Hernández (2012), we designed an improved two-step method for solving the inverse singular value problems. Compared with other existing two-step methods, the proposed method has comparable computational cost. However, computing the product of matrices is simpler than solving linear equations and has no instability problem caused by ill-conditioning in solving linear equations, and thus it seems more stable and greatly reducing computational costs. Under appropriate assumptions, the proposed method is proved to be convergent with the cubic root-convergence rate. The proposed method is applied to the noise reduction for modal parameters estimation and indicates that it can significantly remove noise from measured signals and accurately estimate the modal frequencies and damping ratios. The numerical results demonstrate the effectiveness of the improved method.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 1","pages":"59 - 88"},"PeriodicalIF":0.7,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337807","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
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
{"title":"Efficient Karhunen-Loève expansions via Legendre-Galerkin discretization and tensor structure","authors":"Michal Béreš","doi":"10.21136/AM.2025.0163-25","DOIUrl":"10.21136/AM.2025.0163-25","url":null,"abstract":"<div><p>We develop an efficient framework for Karhunen-Loève expansions of isotropic Gaussian random fields on hyper-rectangular domains. The approach approximates the co-variance kernel by a positive mixture of squared-exponentials, fitted via Newton optimization with a theoretically informed initialization; we also provide convergence estimates for this Gaussian-mixture approximation. The resulting separable kernel enables a Legendre-Galerkin discretization with a Kronecker product structure across dimensions, together with submatrices exhibiting even/odd parity. For assembly, we employ a Duffy-type transformation followed by Gaussian quadrature. These structural properties substantially reduce memory usage and arithmetic cost compared with naive formulations. All algorithms and numerical experiments are released in an open-source repository that reproduces every figure and table. For completeness, a concise derivation of the three-term recurrence for Legendre polynomials is included in appendix.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 6","pages":"941 - 991"},"PeriodicalIF":0.7,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754428","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
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
{"title":"The least squares solution of inconsistent discretized elliptic problems using the FETI method","authors":"Zdeněk Dostál,&nbsp;David Horák","doi":"10.21136/AM.2025.0189-25","DOIUrl":"10.21136/AM.2025.0189-25","url":null,"abstract":"<div><p>The variants of FETI (finite element tearing and interconnecting) based domain decomposition methods are well-established, massively parallel algorithms for solving huge linear systems arising from the discretization of elliptic partial differential equations. Here, we adapt the FETI method for solving the large least squares problems associated with inconsistent systems of linear equations arising from the discretization of elliptic partial differential equations. We briefly review the symmetric least squares problems and the FETI method, explain how FETI can find the least squares solution, prove the optimal rate of convergence, and present the results of numerical experiments demonstrating the efficiency of the proposed method in solving the least squares problem defined by the Poisson equation with inconsistent Neumann conditions.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 6","pages":"929 - 939"},"PeriodicalIF":0.7,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754367","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
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
{"title":"Memories of Professor Radim Blaheta","authors":"Stanislav Sysala","doi":"10.21136/AM.2025.0246-25","DOIUrl":"10.21136/AM.2025.0246-25","url":null,"abstract":"<div><p>This special issue is a nice opportunity to honor Professor Radim Blaheta, a well-known Czech numerical mathematician. It was supported by his former collaborators, colleagues, friends, and students. Some of them have also contributed to this issue.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 6","pages":"729 - 733"},"PeriodicalIF":0.7,"publicationDate":"2025-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754255","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
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
{"title":"Fitted norm preconditioners for the Hodge-Laplacian in mixed form","authors":"Wietse M. Boon,&nbsp;Johannes Kraus,&nbsp;Tomáš Luber,&nbsp;Maria Lymbery","doi":"10.21136/AM.2025.0185-25","DOIUrl":"10.21136/AM.2025.0185-25","url":null,"abstract":"<div><p>We use the practical framework for abstract perturbed saddle-point problems recently introduced by Hong et al. to analyze the mixed formulation of the Hodge-Laplace problem on a Hilbert complex. We compose two parameter-dependent norms in which the uniform continuity and stability of the problem follow. This not only guarantees the well-posedness of the corresponding variational formulation on the continuous level, but also of related compatible discrete models.</p><p>We further simplify the obtained norms and, in both cases, arrive at the same norm-equivalent preconditioner that is easily implementable. The efficiency and uniformity of the preconditioner are demonstrated numerically by the fast convergence and uniformly bounded number of preconditioned MinRes iterations required to solve various instances of Hodge-Laplace problems in two and three space dimensions.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 6","pages":"907 - 927"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2025.0185-25.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754254","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
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