Applied Numerical Mathematics最新文献_第10页

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

A new primal-dual hybrid gradient scheme for solving minimax problems with nonlinear term

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-12-27 DOI: 10.1016/j.apnum.2024.12.010

Renkai Wu, Zexian Liu

{"title":"A new primal-dual hybrid gradient scheme for solving minimax problems with nonlinear term","authors":"Renkai Wu, Zexian Liu","doi":"10.1016/j.apnum.2024.12.010","DOIUrl":"10.1016/j.apnum.2024.12.010","url":null,"abstract":"<div><div>Primal-dual hybrid gradient (PDHG) methods are popular for solving minimax problems. The proximal terms in the corresponding subproblems play an important role in the convergence analysis and for numerical performance of PDHG methods. However, it is observed that the function values generated by some PDHG algorithms might suffer from intense oscillation as the iteration progresses. To address the drawback, we take advantage of an inertial point to exploit a new proximal term, construct a new quadratic approximation for the nonlinear term in the minimax problem, and present a new primal-dual hybrid gradient algorithm for solving minimax problems with nonlinear terms. The new proximal term is different from other commonly used proximal terms and is used in the <em>x</em>-subproblem of the proposed algorithm. The quadratic approximation is used to replace the common linear approximation in the subproblem of the proposed algorithm to accelerate the proposed method. The local convergence of the proposed algorithm is established under mild assumptions. Numerical experiments on two examples confirm the compelling numerical performance of the proposed method.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"210 ","pages":"Pages 147-164"},"PeriodicalIF":2.2,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143175059","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

Strongly consistent low-dissipation WENO schemes for finite elements

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-12-18 DOI: 10.1016/j.apnum.2024.12.008

Joshua Vedral , Andreas Rupp , Dmitri Kuzmin

{"title":"Strongly consistent low-dissipation WENO schemes for finite elements","authors":"Joshua Vedral , Andreas Rupp , Dmitri Kuzmin","doi":"10.1016/j.apnum.2024.12.008","DOIUrl":"10.1016/j.apnum.2024.12.008","url":null,"abstract":"<div><div>We propose a way to maintain strong consistency and perform error analysis in the context of dissipation-based WENO stabilization for continuous and discontinuous Galerkin discretizations of conservation laws. Following Kuzmin and Vedral (J. Comput. Phys. 487:112153, 2023) and Vedral (arXiv preprint <span><span>arXiv:2309.12019</span><svg><path></path></svg></span>), we use WENO shock detectors to determine appropriate amounts of low-order artificial viscosity. In contrast to existing WENO methods, our approach blends candidate polynomials using residual-based nonlinear weights. The shock-capturing terms of our stabilized Galerkin methods vanish if residuals do. This enables us to achieve improved accuracy compared to weakly consistent alternatives. As we show in the context of steady convection-diffusion-reaction (CDR) equations, nonlinear local projection stabilization terms can be included in a way that preserves the coercivity of local bilinear forms. For the corresponding Galerkin-WENO discretization of a CDR problem, we rigorously derive a priori error estimates. Additionally, we demonstrate the stability and accuracy of the proposed method through one- and two-dimensional numerical experiments for hyperbolic conservation laws and systems thereof. The numerical results for representative test problems are superior to those obtained with traditional WENO schemes, particularly in scenarios involving shocks and steep gradients.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"210 ","pages":"Pages 64-81"},"PeriodicalIF":2.2,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143175013","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

Commutator-based operator splitting for linear port-Hamiltonian systems

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-12-16 DOI: 10.1016/j.apnum.2024.12.007

Marius Mönch, Nicole Marheineke

引用次数: 0

The two-grid hybrid high-order method for the nonlinear strongly damped wave equation on polygonal mesh and its reduced-order model

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-12-16 DOI: 10.1016/j.apnum.2024.12.006

Lu Wang, Youjun Tan, Minfu Feng

引用次数: 0