IMA Journal of Numerical Analysis最新文献

Employing nonresonant step sizes for time integration of highly oscillatory nonlinear Dirac equations 采用非谐振步长对高振荡非线性狄拉克方程进行时间积分

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-10-08 DOI: 10.1093/imanum/draf085

Tobias Jahnke, Michael Kirn

引用次数: 0

Maximal regularity of evolving FEMs for parabolic equations on an evolving surface 演化曲面上抛物型方程演化有限元的极大正则性

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-10-02 DOI: 10.1093/imanum/draf082

Genming Bai, Balázs Kovács, Buyang Li

引用次数: 0

Variationally correct neural residual regression for parametric PDEs: on the viability of controlled accuracy 参数偏微分方程的变差校正神经残差回归：关于控制精度的可行性

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-10-02 DOI: 10.1093/imanum/draf073

Markus Bachmayr, Wolfgang Dahmen, Mathias Oster

{"title":"Variationally correct neural residual regression for parametric PDEs: on the viability of controlled accuracy","authors":"Markus Bachmayr, Wolfgang Dahmen, Mathias Oster","doi":"10.1093/imanum/draf073","DOIUrl":"https://doi.org/10.1093/imanum/draf073","url":null,"abstract":"This paper is about learning the parameter-to-solution map for systems of partial differential equations (PDEs) that depend on a potentially large number of parameters covering all PDE types for which a stable variational formulation (SVF) can be found. A central constituent is the notion of variationally correct residual loss function, meaning that its value is always uniformly proportional to the squared solution error in the norm determined by the SVF, hence facilitating rigorous a posteriori accuracy control. It is based on a single variational problem, associated with the family of parameter-dependent fibre problems, employing the notion of direct integrals of Hilbert spaces. Since in its original form the loss function is given as a dual test norm of the residual; a central objective is to develop equivalent computable expressions. The first critical role is played by hybrid hypothesis classes, whose elements are piecewise polynomial in (low-dimensional) spatio-temporal variables with parameter-dependent coefficients that can be represented, for example, by neural networks. Second, working with first-order SVFs we distinguish two scenarios: (i) the test space can be chosen as an $L_{2}$-space (such as for elliptic or parabolic problems) so that residuals can be evaluated directly as elements of $L_{2}$; (ii) when trial and test spaces for the fibre problems depend on the parameters (as for transport equations) we use ultra-weak formulations. In combination with discontinuous Petrov–Galerkin concepts the hybrid format is then instrumental to arrive at variationally correct computable residual loss functions. Our findings are illustrated by numerical experiments representing (i) and (ii), namely elliptic boundary value problems with piecewise constant diffusion coefficients and pure transport equations with parameter-dependent convection fields.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"3 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145209783","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

Combined DG–CG finite element method for the Westervelt equation Westervelt方程的组合DG-CG有限元法

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-09-28 DOI: 10.1093/imanum/draf080

Sergio Gómez, Vanja Nikolić

引用次数: 0

Asymptotic-preserving finite difference method for partially dissipative hyperbolic systems 部分耗散双曲型系统的渐近保持有限差分法

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-09-24 DOI: 10.1093/imanum/draf066

Timothée Crin-Barat, Dragoș Manea

{"title":"Asymptotic-preserving finite difference method for partially dissipative hyperbolic systems","authors":"Timothée Crin-Barat, Dragoș Manea","doi":"10.1093/imanum/draf066","DOIUrl":"https://doi.org/10.1093/imanum/draf066","url":null,"abstract":"We analyse the preservation of asymptotic properties of partially dissipative hyperbolic systems when switching to a fully discrete setting. We prove that one of the simplest consistent and unconditionally stable numerical methods—the implicit central finite-difference scheme—preserves both the large time asymptotic behaviour and the parabolic relaxation limit of one-dimensional partially dissipative hyperbolic systems that satisfy the Kalman rank condition. The large time asymptotic-preserving property is achieved by conceiving time-weighted perturbed energy functionals in the spirit of the hypocoercivity theory. For the relaxation-preserving property, drawing inspiration from the observation that, in the continuous case, solutions are shown to exhibit distinct behaviour in low and high frequencies we introduce a novel discrete Littlewood–Paley decomposition tailored to the central finite-difference scheme. This allows us to prove Bernstein-type estimates for discrete differential operators and leads to new diffusive limit results such as the strong convergence of the discrete linearized compressible Euler system with damping towards the discrete heat equation, uniformly with respect to the spatial mesh parameter.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"1 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145133442","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 bundle-trust method via gradient sampling technique for nonsmooth optimization using exact and inexact gradients 一种基于梯度抽样技术的基于精确和非精确梯度的非光滑优化束信任方法

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-09-18 DOI: 10.1093/imanum/draf087

Morteza Maleknia, Majid Soleimani-damaneh

{"title":"A bundle-trust method via gradient sampling technique for nonsmooth optimization using exact and inexact gradients","authors":"Morteza Maleknia, Majid Soleimani-damaneh","doi":"10.1093/imanum/draf087","DOIUrl":"https://doi.org/10.1093/imanum/draf087","url":null,"abstract":"Based on the proximal bundle and gradient sampling (GS) methods, we develop a robust algorithm for minimizing the locally Lipschitz function $f:mathbb{R}^{n}to mathbb{R}$. As an interesting feature of the proposed method, thanks to the GS technique, we sample a set of differentiable auxiliary points from the vicinity of the current point to construct an initial piecewise linear model for the objective function. If necessary, inspired by bundle methods, we iteratively enrich the set of sampled points by using a single nonredundant auxiliary point suggested by a modified variant of Mifflin’s line search. However, we may terminate the enrichment process without achieving a descent step, which is different from classic bundle methods. Indeed, the proposed enrichment process only accepts those auxiliary points having a small gradient locality measure, which significantly improves the efficiency of the method in practice. In theory, our method keeps iterations where the objective function is differentiable, and consequently, it works only with the gradient vectors of the objective function. In contrast with existing GS methods, the radius of the sampling region is not monotone. More precisely, by proposing a nonmonotone proximity parameter based on the radius of the sampling region, we add some valuable features of the trust region philosophy to our algorithm. The convergence analysis of the proposed method is comprehensively studied using exact and inexact gradients. By means of various academic and semi-academic test problems, we demonstrate the reliability and efficiency of the proposed method in practice.1","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"5 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145093586","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

An ODE characterization of multi-marginal optimal transport with pairwise cost functions 具有成对代价函数的多边际最优运输的ODE表征

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-09-06 DOI: 10.1093/imanum/draf067

Luca Nenna, Brendan Pass

引用次数: 0

Deep-layer limit and stability analysis of the basic forward–backward-splitting induced network (I): feed-forward systems 基本前-后分裂诱导网络的深层极限与稳定性分析（一）：前馈系统

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-08-30 DOI: 10.1093/imanum/draf068

Xuan Lin, Chunlin Wu

{"title":"Deep-layer limit and stability analysis of the basic forward–backward-splitting induced network (I): feed-forward systems","authors":"Xuan Lin, Chunlin Wu","doi":"10.1093/imanum/draf068","DOIUrl":"https://doi.org/10.1093/imanum/draf068","url":null,"abstract":"Forward-backward splitting (FBS) is one of the most fundamental and efficient optimization algorithms in linear inverse problems like sparse recovery and image reconstruction, and has recently been unrolled to construct several deep neural networks with dramatic performance advantages over conventional methods. This circumstance motivates us to consider some theoretical aspects of the basic FBS-induced network. Here, ‘basic’ means that the neural network is unrolled from the original FBS algorithm with direct parameter relaxation. In this paper we report the first part of our study, i.e., deep-layer limit behavior and stability of feed-forward systems. We formulate the finite layer network as a difference inclusion and model the related deep-layer limit system as a differential inclusion. We mainly analyze the uniform convergence properties from the state of the finite layer network to that of the related deep-layer limit system, as well as their forward stability. Our analysis procedure can be simplified to analyze the LISTA- and ALISTA-like networks. A numerical example is implemented to illustrate the convergence results and perturbation stability. As a side product of this study, some corollaries in the case of pointwise sampling and Lipschitz continuity assumptions provide convergence results in the context of numerical ordinary differential inclusion.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"130 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144919399","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

Velocity-vorticity-pressure mixed formulation for the Kelvin–Voigt–Brinkman–Forchheimer equations Kelvin-Voigt-Brinkman-Forchheimer方程的速度-涡度-压力混合公式

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-08-30 DOI: 10.1093/imanum/draf072

Sergio Caucao, Ivan Yotov

{"title":"Velocity-vorticity-pressure mixed formulation for the Kelvin–Voigt–Brinkman–Forchheimer equations","authors":"Sergio Caucao, Ivan Yotov","doi":"10.1093/imanum/draf072","DOIUrl":"https://doi.org/10.1093/imanum/draf072","url":null,"abstract":"In this paper, we propose and analyze a mixed formulation for the Kelvin–Voigt–Brinkman–Forchheimer equations for unsteady viscoelastic flows in porous media. Besides the velocity and pressure, our approach introduces the vorticity as a further unknown. Consequently, we obtain a three-field mixed variational formulation, where the aforementioned variables are the main unknowns of the system. We establish the existence and uniqueness of a solution for the weak formulation, and derive the corresponding stability bounds, employing a fixed-point strategy, along with monotone operators theory and Schauder theorem. Afterwards, we introduce a semidiscrete continuous-in-time approximation based on stable Stokes elements for the velocity and pressure, and continuous or discontinuous piecewise polynomial spaces for the vorticity. Additionally, employing backward Euler time discretization, we introduce a fully discrete finite element scheme. We prove well-posedness, derive stability bounds and establish the corresponding error estimates for both schemes. We provide several numerical results verifying the theoretical rates of convergence and illustrating the performance and flexibility of the method for a range of domain configurations and model parameters.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"38 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144919237","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

Optimal convergence in finite element semidiscrete error analysis of the Doyle–Fuller–Newman model beyond one dimension with a novel projection operator 一种新的投影算子在一维以外的Doyle-Fuller-Newman模型有限元半离散误差分析中的最优收敛性

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-08-29 DOI: 10.1093/imanum/draf065

Shu Xu, Liqun Cao

引用次数: 0