Applied Numerical Mathematics最新文献_第9页

Error estimates with polynomial growth O(ε−1) for the HHO method on polygonal meshes of the Allen-Cahn model

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-01-13 DOI: 10.1016/j.apnum.2025.01.001

Naresh Kumar , Ajeet Singh , Ram Jiwari , J.Y. Yuan

{"title":"Error estimates with polynomial growth O(ε−1) for the HHO method on polygonal meshes of the Allen-Cahn model","authors":"Naresh Kumar , Ajeet Singh , Ram Jiwari , J.Y. Yuan","doi":"10.1016/j.apnum.2025.01.001","DOIUrl":"10.1016/j.apnum.2025.01.001","url":null,"abstract":"<div><div>A novel approach is presented to tackle the Allen-Cahn equation arising from phase separation in alloys, by utilizing the hybrid high-order (HHO) method on polygonal meshes. The primary challenge in this equation lies in employing a straightforward Gronwall inequality-type argument for error estimation with exponential growth factor <span><math><msup><mrow><mi>e</mi></mrow><mrow><mo>(</mo><mi>C</mi><mi>T</mi><mo>/</mo><msup><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></msup></math></span> as <em>ε</em> approaches zero. The application of the discrete Lyapunov functional and the discrete HHO spectrum estimate of the linearized Allen-Cahn operator <span><math><msubsup><mrow><mi>λ</mi></mrow><mrow><mi>A</mi><mi>C</mi></mrow><mrow><mi>H</mi><mi>H</mi><mi>O</mi></mrow></msubsup></math></span> are used to overcome this exponential growth factor and achieve polynomial growth of order <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></math></span> for error bounds in error estimations. Rigorous convergence analyses are established for the fully implicit schemes, which are energy stable. However, due to the implicit processing of the nonlinear term, the computational cost significantly increases. To enhance computational efficiency, a static condensation process is hired by using the HHO method, resulting in optimal convergence rates in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norm. Finally, various numerical experiments on diverse meshes are conducted to validate our theoretical findings.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"211 ","pages":"Pages 78-102"},"PeriodicalIF":2.2,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143141886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 distributed stochastic forward-backward-forward self-adaptive algorithm for Cartesian stochastic variational inequalities

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-01-09 DOI: 10.1016/j.apnum.2025.01.003

Liya Liu , Xiaolong Qin , Jen-Chih Yao

{"title":"A distributed stochastic forward-backward-forward self-adaptive algorithm for Cartesian stochastic variational inequalities","authors":"Liya Liu , Xiaolong Qin , Jen-Chih Yao","doi":"10.1016/j.apnum.2025.01.003","DOIUrl":"10.1016/j.apnum.2025.01.003","url":null,"abstract":"<div><div>In this paper, we consider a Cartesian stochastic variational inequality with a high dimensional solution space. This mathematical formulation captures a wide range of optimization problems including stochastic Nash games and stochastic minimization problems. By combining the advantages of the forward-backward-forward method and the stochastic approximated method, a novel distributed algorithm is developed for addressing this large-scale problem without any kind of monotonicity. A salient feature of the proposed algorithm is to compute two independent queries of a stochastic oracle at each iteration. The main contributions include: (i) The necessary condition imposed on the involved operator is related merely to the Lipschitz continuity, which are quite general. (ii) At each iteration, the suggested algorithm only requires one computation of the projection onto each feasible set, which can be easily evaluated. (iii) The distributed implementation of the stochastic approximation based Armijo-type line search strategy is adopted to weaken the line search condition and define variable adaptive non-monotonic stepsizes, when the Lipschitz constant is unknown. Some theoretical results of the almost sure convergence, the optimal rate statement, and the oracle complexity bound are established with conditions weaker than the conditions of other methods studied in the literature. Finally, preliminary numerical results are presented to show the efficiency and the competitiveness of our algorithm.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"211 ","pages":"Pages 17-41"},"PeriodicalIF":2.2,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143141893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 fitted space-time finite element method for an advection-diffusion problem with moving interfaces

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-01-09 DOI: 10.1016/j.apnum.2025.01.002

Quang Huy Nguyen , Van Chien Le , Phuong Cuc Hoang , Thi Thanh Mai Ta

引用次数: 0

A numerical study of WENO approximations to sharp propagating fronts for reaction-diffusion systems

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-01-07 DOI: 10.1016/j.apnum.2024.12.014

Jiaxi Gu , Daniel Olmos-Liceaga , Jae-Hun Jung

引用次数: 0

Analysis for implicit and implicit-explicit ADER and DeC methods for ordinary differential equations, advection-diffusion and advection-dispersion equations

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-01-07 DOI: 10.1016/j.apnum.2024.12.013

Philipp Öffner , Louis Petri , Davide Torlo

{"title":"Analysis for implicit and implicit-explicit ADER and DeC methods for ordinary differential equations, advection-diffusion and advection-dispersion equations","authors":"Philipp Öffner , Louis Petri , Davide Torlo","doi":"10.1016/j.apnum.2024.12.013","DOIUrl":"10.1016/j.apnum.2024.12.013","url":null,"abstract":"<div><div>In this manuscript, we present the development of implicit and implicit-explicit ADER and DeC methodologies within the DeC framework using the two-operators formulation, with a focus on their stability analysis both as solvers for ordinary differential equations (ODEs) and within the context of linear partial differential equations (PDEs). To analyze their stability, we reinterpret these methods as Runge-Kutta schemes and uncover significant variations in stability behavior, ranging from A-stable to bounded stability regions, depending on the chosen order, method, and quadrature nodes. This differentiation contrasts with their explicit counterparts. When applied to advection-diffusion and advection-dispersion equations employing finite difference spatial discretization, the von Neumann stability analysis demonstrates stability under CFL-like conditions. Particularly noteworthy is the stability maintenance observed for the advection-diffusion equation, even under spatial-independent constraints. Furthermore, we establish precise boundaries for relevant coefficients and provide suggestions regarding the suitability of specific schemes for different problem.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"212 ","pages":"Pages 110-134"},"PeriodicalIF":2.2,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143155013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Inexact proximal penalty alternating linearization decomposition scheme of nonsmooth convex constrained optimization problems

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-01-07 DOI: 10.1016/j.apnum.2024.12.016

Si-Da Lin , Ya-Jing Zhang , Ming Huang , Jin-Long Yuan , Hong-Han Bei

{"title":"Inexact proximal penalty alternating linearization decomposition scheme of nonsmooth convex constrained optimization problems","authors":"Si-Da Lin , Ya-Jing Zhang , Ming Huang , Jin-Long Yuan , Hong-Han Bei","doi":"10.1016/j.apnum.2024.12.016","DOIUrl":"10.1016/j.apnum.2024.12.016","url":null,"abstract":"<div><div>In this paper, the convex constrained optimization problems are studied via the alternating linearization approach. The objective function <em>f</em> is assumed to be complex, and its exact oracle information (function values and subgradients) is not easy to obtain, while the constraint function <em>h</em> is expected to be “simple” relatively. With the help of the exact penalty function, we present an alternating linearization method with inexact information. In this method, the penalty problem is replaced by two relatively simple linear subproblems with regularized form which are needed to be solved successively in each iteration. An approximate solution is utilized instead of an exact form to solve each of the two subproblems. Moreover, it is proved that the generated sequence converges to some solution of the original problem. The dual form of this approach is discussed and described. Finally, some preliminary numerical test results are reported. Numerical experiences provided show that the inexact scheme has good performance, certificate and reliability.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"211 ","pages":"Pages 42-60"},"PeriodicalIF":2.2,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143141892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Analysis of a new BFGS algorithm and conjugate gradient algorithms and their applications in image restoration and machine learning

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-01-07 DOI: 10.1016/j.apnum.2024.12.015

Yijia Wang , Chen Ouyang , Liangfu Lv , Gonglin Yuan

{"title":"Analysis of a new BFGS algorithm and conjugate gradient algorithms and their applications in image restoration and machine learning","authors":"Yijia Wang , Chen Ouyang , Liangfu Lv , Gonglin Yuan","doi":"10.1016/j.apnum.2024.12.015","DOIUrl":"10.1016/j.apnum.2024.12.015","url":null,"abstract":"<div><div>Renowned for offering a more precise approximation of the objective function, a third-order tensor expansion is deemed superior to the traditional second-order Taylor expansion, a viewpoint supported by various academics. Despite its acknowledged benefits, the adoption of this advanced expansion within the widely utilized quasi-Newton method remains notably rare. This research endeavors to construct update equations for the quasi-Newton method, based on a third-order tensor expansion, and to introduce an innovative quasi-Newton equation. The main contributions of this study include: (i) the development of a unique quasi-Newton equation based on a third-order tensor expansion; (ii) a detailed comparative analysis of the new BFGS quasi-Newton update method versus the traditional BFGS methodologies; (iii) the demonstration of convergence outcomes for the newly developed BFGS quasi-Newton technique; and (iv) the introduction of novel methodologies for conjugate gradients inspired by this distinctive quasi-Newton formula. Through exhaustive numerical experimentation, the algorithms derived from this pioneering quasi-Newton equation have shown superior performance.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"210 ","pages":"Pages 199-221"},"PeriodicalIF":2.2,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143175063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Discrete maximum principles with computable mesh conditions for nonlinear elliptic finite element problems

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-01-02 DOI: 10.1016/j.apnum.2024.12.009

M.T. Bahlibi , J. Karátson , S. Korotov

引用次数: 0

Numerical derivation of multivariate functions

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-12-31 DOI: 10.1016/j.apnum.2024.12.011

Nadaniela Egidi, Josephin Giacomini, Pierluigi Maponi

引用次数: 0

A new scale-invariant hybrid WENO scheme for steady Euler and Navier-Stokes equations

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-12-31 DOI: 10.1016/j.apnum.2024.12.012

Yifei Wan

{"title":"A new scale-invariant hybrid WENO scheme for steady Euler and Navier-Stokes equations","authors":"Yifei Wan","doi":"10.1016/j.apnum.2024.12.012","DOIUrl":"10.1016/j.apnum.2024.12.012","url":null,"abstract":"<div><div>The steady-state convergence property of prevalent weighted essentially non-oscillatory (WENO) schemes usually relies on the sensitivity parameter. On the one hand, it is discovered that relatively large sensitivity parameter is conducive to attaining the steady-state convergence, however, large sensitivity parameter may result in some oscillations in the numerical solutions. On the other hand, relatively small sensitivity parameter can prevent some non-physical oscillations, but this choice may degrade the accuracy of WENO schemes. To address this issue, we design a fifth-order scale-invariant WENO scheme for steady problems to drag the residual of numerical solutions into machine-zero level. A new effective smoothness detector is introduced in this scheme, then the whole computational domain is classified into smooth, non-smooth and transition regions accordingly. The optimal fifth-order linear reconstruction is used in smooth region, the mixed WENO reconstruction is utilized in non-smooth region, and a interpolation technique is adapted in transition region to ensure robust steady-state convergence. In particular, the essentially non-oscillatory (ENO) property of the mixed reconstruction is verified by investigating the smoothness indicator of the mixed polynomial. Moreover, the scheme further achieves the scale-invariant property in theory, and maintains the fifth-order accuracy regardless of the order of critical points. Numerical experiments demonstrate that the scale-invariant error of this WENO scheme is close to machine zero, and the ENO property is still retained for small scale problems. What's more, the scheme is robust for the steady-state convergence across extensive benchmark examples of Euler and Navier-Stokes (NS) equations, and still displays the ENO property for the problems involving strong discontinuities.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"210 ","pages":"Pages 177-198"},"PeriodicalIF":2.2,"publicationDate":"2024-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143175062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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