IMA Journal of Numerical Analysis最新文献

Mean square temporal error estimates for the two-dimensional stochastic Navier–Stokes equations with transport noise 含输运噪声的二维随机Navier-Stokes方程的均方时间误差估计

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-06-13 DOI: 10.1093/imanum/draf042

D Breit, T C Moyo, A Prohl, J Wichmann

引用次数: 0

Consistency and stability of boundary conditions for a two-velocities lattice Boltzmann scheme 双速度晶格Boltzmann格式边界条件的一致性和稳定性

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-06-12 DOI: 10.1093/imanum/draf039

Thomas Bellotti

引用次数: 0

A new framework for the construction and analysis of exponential wave integrators for the Zakharov system Zakharov系统指数波积分器的构造与分析的新框架

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-06-11 DOI: 10.1093/imanum/draf016

Jiyong Li, Bin Wang

引用次数: 0

Perturbation estimates for order-one strong approximations of SDEs without globally monotone coefficients 无全局单调系数的SDEs的一阶强近似的微扰估计

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-06-09 DOI: 10.1093/imanum/draf034

Lei Dai, Xiaojie Wang

{"title":"Perturbation estimates for order-one strong approximations of SDEs without globally monotone coefficients","authors":"Lei Dai, Xiaojie Wang","doi":"10.1093/imanum/draf034","DOIUrl":"https://doi.org/10.1093/imanum/draf034","url":null,"abstract":"To obtain strong convergence rates of numerical schemes, an overwhelming majority of existing works impose a global monotonicity condition on coefficients of stochastic differential equations (SDEs). Nevertheless, there are still many SDEs from applications that do not have globally monotone coefficients. As a recent breakthrough, the authors of (Hutzenthaler and Jentzen 2020, Ann. Prob., 48, 53–93) originally presented a perturbation theory for SDEs, which is crucial to recovering strong convergence rates of numerical schemes in a non-globally monotone setting. However, only a convergence rate of order $1/2$ was obtained there for time-stepping schemes such as a stopped increment-tamed Euler–Maruyama (SITEM) method. An interesting question arises, also raised by the aforementioned work, as to whether a higher convergence rate than $1/2$ can be obtained when higher order schemes are used. The present work attempts to give a positive answer to this question. To this end, we develop some new perturbation estimates that are able to reveal the order-one strong convergence of numerical methods. As the first application of the newly developed estimates, we identify the expected order-one pathwise uniformly strong convergence of the SITEM method for additive noise driven SDEs and multiplicative noise driven second-order SDEs with non-globally monotone coefficients. As the other application, we propose and analyze a positivity preserving explicit Milstein-type method for Lotka–Volterra competition model driven by multi-dimensional noise, with a pathwise uniformly strong convergence rate of order one recovered under mild assumptions. These obtained results are completely new and significantly improve the existing theory. Numerical experiments are also provided to confirm the theoretical findings.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"26 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144252258","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

Efficient solution of ill-posed integral equations through averaging 不适定积分方程的平均有效解

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-06-06 DOI: 10.1093/imanum/draf038

Michael Griebel, Tim Jahn

引用次数: 0

Learning a Gaussian mixture for sparsity regularization in inverse problems 学习高斯混合稀疏正则化反问题

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-06-06 DOI: 10.1093/imanum/draf037

Giovanni S Alberti, Luca Ratti, Matteo Santacesaria, Silvia Sciutto

{"title":"Learning a Gaussian mixture for sparsity regularization in inverse problems","authors":"Giovanni S Alberti, Luca Ratti, Matteo Santacesaria, Silvia Sciutto","doi":"10.1093/imanum/draf037","DOIUrl":"https://doi.org/10.1093/imanum/draf037","url":null,"abstract":"In inverse problems it is widely recognized that the incorporation of a sparsity prior yields a regularization effect on the solution. This approach is grounded on the a priori assumption that the unknown can be appropriately represented in a basis with a limited number of significant components while most coefficients are close to zero. This occurrence is frequently observed in real-world scenarios, such as with piecewise smooth signals. In this study we propose a probabilistic sparsity prior formulated as a mixture of degenerate Gaussians, capable of modelling sparsity with respect to a generic basis. Under this premise we design a neural network that can be interpreted as the Bayes estimator for linear inverse problems. Additionally, we put forth both a supervised and an unsupervised training strategy to estimate the parameters of this network. To evaluate the effectiveness of our approach we conduct a numerical comparison with commonly employed sparsity-promoting regularization techniques, namely Least Absolute Shrinkage and Selection Operator (LASSO), group LASSO, iterative hard thresholding and sparse coding/dictionary learning. Notably, our reconstructions consistently exhibit lower mean square error values across all one-dimensional datasets utilized for the comparisons, even in cases where the datasets significantly deviate from a Gaussian mixture model.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"39 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144228439","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

On the convergence of classical and multilevel variants of the Uzawa and Arrow–Hurwicz algorithms related to the LBB condition 关于与LBB条件相关的Uzawa和Arrow-Hurwicz算法的经典和多层变体的收敛性

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-06-05 DOI: 10.1093/imanum/draf040

Lori Badea

{"title":"On the convergence of classical and multilevel variants of the Uzawa and Arrow–Hurwicz algorithms related to the LBB condition","authors":"Lori Badea","doi":"10.1093/imanum/draf040","DOIUrl":"https://doi.org/10.1093/imanum/draf040","url":null,"abstract":"In this paper we propose a systematic study of classical and multilevel variants of the Uzawa and Arrow–Hurwicz methods. The multilevel methods are obtained from the classical ones by the introduction of multilevel inner iterations to calculate the solution of the first equation instead of its exact calculation as in the classical Uzawa or Arrow–Hurwicz methods. In our study, an essential role is played by the LBB condition. For classical and multilevel variants of the Uzawa and Arrow–Hurwicz algorithms, we prove theorems which give the convergence conditions of the methods and explicit formulas of the convergence rates. On the basis of these results we compare the convergence conditions and the convergence rates of the classical methods with those of their corresponding ones in the multilevel methods. Concerning the Uzawa methods, we prove that, the limit of the convergence condition and the convergence rate of the multilevel method, when the number of the inner iterations tends to infinity, coincide with those of the classical one. Also, from the dependence of the convergence rate on the number of inner iterations of the multilevel method, we conclude that, the multilevel method with a small number of inner iterations converges better than the classical one. For the Arrow–Hurwicz methods we found that for a large number of inner iterations of the multilevel algorithm, the convergence condition of the multilevel method coincides with that of the classical method and the convergence rate of the multilevel method is equal to or smaller than that of the classical method. Finally, the behavior of the introduced methods is investigated by numerical experiments carried out for the driven-cavity Stokes problem and they confirm the theoretical results.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"7 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144228464","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

Unique continuation for the wave equation based on a discontinuous Galerkin time discretization 基于不连续伽辽金时间离散的波动方程的唯一延拓

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-05-30 DOI: 10.1093/imanum/draf036

Erik Burman, Janosch Preuss

引用次数: 0

Computation of Miura surfaces with gradient Dirichlet boundary conditions 梯度Dirichlet边界条件下Miura曲面的计算

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-05-28 DOI: 10.1093/imanum/draf033

Frédéric Marazzato

引用次数: 0

A second-order accurate, positivity-preserving numerical scheme for the Poisson–Nernst–Planck–Navier–Stokes system 泊松-能斯特-普朗克-纳维-斯托克斯系统的二阶精确保正数值格式

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-05-28 DOI: 10.1093/imanum/draf027

Yuzhe Qin, Cheng Wang

{"title":"A second-order accurate, positivity-preserving numerical scheme for the Poisson–Nernst–Planck–Navier–Stokes system","authors":"Yuzhe Qin, Cheng Wang","doi":"10.1093/imanum/draf027","DOIUrl":"https://doi.org/10.1093/imanum/draf027","url":null,"abstract":"In this paper we propose and analyse a second-order accurate (in both time and space) numerical scheme for the Poisson–Nernst–Planck–Navier–Stokes system, which describes the ion electro-diffusion in fluids. In particular, the Poisson–Nernst–Planck (PNP) equation is reformulated as a nonconstant mobility gradient flow in the energetic variational approach. The marker and cell finite difference method is chosen as the spatial discretization, which facilitates the analysis for the fluid part. In the temporal discretization the mobility function is computed by a second-order extrapolation formula for the sake of unique solvability analysis, while a modified Crank–Nicolson approximation is applied to the singular logarithmic nonlinear term. Nonlinear artificial regularization terms are added in the chemical potential part, so that the positivity-preserving property could be theoretically proved. Meanwhile, a second-order accurate, semi-implicit approximation is applied to the convective term in the PNP evolutionary equation, and the fluid momentum equation is similarly computed. In addition, an optimal rate convergence analysis is provided, based on the higher order asymptotic expansion for the numerical solution, and the rough and refined error estimate techniques. The following combined theoretical properties have been established for the second-order accurate numerical method: (i) second-order accuracy, (ii) unique solvability and positivity, (iii) total energy stability and (iv) optimal rate convergence. A few numerical results are displayed to validate the theoretical analysis.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"244 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144165275","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