IMA Journal of Numerical Analysis最新文献_第2页

Minimal residual discretization of a class of fully nonlinear elliptic PDE 一类完全非线性椭圆偏微分方程的最小残差离散化

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-08-28 DOI: 10.1093/imanum/draf075

Dietmar Gallistl, Ngoc Tien Tran

引用次数: 0

Wavelet compressed, modified Hilbert transform in the space–time discretization of the heat equation 小波压缩后，修正希尔伯特变换在时空离散化中的热方程

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-08-21 DOI: 10.1093/imanum/draf061

Helmut Harbrecht, Christoph Schwab, Marco Zank

{"title":"Wavelet compressed, modified Hilbert transform in the space–time discretization of the heat equation","authors":"Helmut Harbrecht, Christoph Schwab, Marco Zank","doi":"10.1093/imanum/draf061","DOIUrl":"https://doi.org/10.1093/imanum/draf061","url":null,"abstract":"On a finite time interval $(0,T)$ we consider the multiresolution Galerkin discretization of a modified Hilbert transform ${mathscr{H}}_{T}$ that arises in the space–time Galerkin discretization of the linear diffusion equation. To this end, we design spline-wavelet systems in $(0,T)$ consisting of piecewise polynomials of degree $geq 1$ with sufficiently many vanishing moments that constitute Riesz bases in the Sobolev spaces $ H^{s}_{0,}(0,T)$ and $H^{s}_{,0}(0,T)$. These bases provide stable multilevel splittings of the temporal discretization spaces into ‘increment’ or ‘detail’ spaces. Furthermore, they allow to optimally compress the nonlocal integrodifferential operators that appear in stable space–time variational formulations of initial-boundary value problems, such as the heat equation and the acoustic wave equation. We then obtain sparse space–time tensor-product spaces via algebraic tensor-products of the temporal multilevel discretizations with standard, hierarchic finite element spaces in the spatial domain (with standard Lagrangian FE bases). Hence, the construction of multiresolutions in the spatial domain is not necessary. An efficient multilevel preconditioner is proposed that solves the linear system of equations resulting from the sparse space–time Galerkin discretization with essentially linear complexity (in work and memory). A substantial reduction in the number of the degrees of freedom and CPU time (compared with time-marching discretizations) is demonstrated in numerical experiments.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"7 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144900123","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

Maximum bound principle and original energy dissipation of arbitrarily high-order ETD Runge–Kutta schemes for Allen–Cahn equations Allen-Cahn方程任意高阶ETD龙格-库塔格式的最大界原理和原始能量耗散

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-08-12 DOI: 10.1093/imanum/draf069

Chaoyu Quan, Xiaoming Wang, Pinzhong Zheng, Zhi Zhou

{"title":"Maximum bound principle and original energy dissipation of arbitrarily high-order ETD Runge–Kutta schemes for Allen–Cahn equations","authors":"Chaoyu Quan, Xiaoming Wang, Pinzhong Zheng, Zhi Zhou","doi":"10.1093/imanum/draf069","DOIUrl":"https://doi.org/10.1093/imanum/draf069","url":null,"abstract":"The energy dissipation law and the maximum bound principle are two fundamental physical properties of the Allen–Cahn equations. While many existing time-stepping methods are known to preserve the energy dissipation law most of them apply to a modified form of energy. In this work we show that, when the nonlinear term of the Allen–Cahn equation is Lipschitz continuous, a class of arbitrarily high-order exponential time differencing Runge–Kutta schemes with the linear stabilization technique preserves the original energy dissipation property under some step-size constraint. To ensure the Lipschitz condition on the nonlinear term we introduce a rescaling post-processing technique, which guarantees that the numerical solution unconditionally satisfies the maximum bound principle. As a result, our proposed schemes simultaneously maintain both the original energy dissipation law and the maximum bound principle while achieving arbitrarily high-order accuracy. We also establish the optimal error estimate for the proposed schemes. Numerical experiments fully confirm the convergence rates, the preservation of the maximum bound principle and the original energy dissipation property, as well as the high efficiency of the high-order schemes for long-time simulations.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"40 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144850646","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

Upper bounds of higher-order derivatives for Wachspress coordinates on polytopes 多面体上wachpress坐标的高阶导数的上界

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-08-02 DOI: 10.1093/imanum/draf063

Pengjie Tian, Yanqiu Wang

引用次数: 0

Low-cost second-order time-stepping methods for natural convection problem with variable density 变密度自然对流问题的低成本二阶时间步进方法

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-08-02 DOI: 10.1093/imanum/draf057

Jilian Wu, Ning Li, Xinlong Feng, Leilei Wei

引用次数: 0

Long-term behaviour of symmetric partitioned linear multistep methods. I: global error and conservation of invariants 对称分段线性多步方法的长期行为。I：全局误差和不变量的守恒

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-07-24 DOI: 10.1093/imanum/draf062

Begoña Cano, Ángel Durán, Melquiades Rodríguez

引用次数: 0

Convergence and near-optimal sampling for multivariate function approximations in irregular domains via Vandermonde with Arnoldi 基于Vandermonde和Arnoldi的不规则域多元函数逼近的收敛性和近最优抽样

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-07-22 DOI: 10.1093/imanum/draf055

Wenqi Zhu, Yuji Nakatsukasa

{"title":"Convergence and near-optimal sampling for multivariate function approximations in irregular domains via Vandermonde with Arnoldi","authors":"Wenqi Zhu, Yuji Nakatsukasa","doi":"10.1093/imanum/draf055","DOIUrl":"https://doi.org/10.1093/imanum/draf055","url":null,"abstract":"Vandermonde matrices are usually exponentially ill-conditioned and often result in unstable approximations. In this paper we introduce and analyse the multivariate Vandermonde with Arnoldi (V+A) method, which is based on least-squares approximation together with a Stieltjes orthogonalization process, for approximating continuous, multivariate functions on $d$-dimensional irregular domains. The V+A method addresses the ill-conditioning of the Vandermonde approximation by creating a set of discrete orthogonal bases with respect to a discrete measure. The V+A method is simple and general, relying only on the domain’s sample points. This paper analyses the sample complexity of the least-squares approximation that uses the V+A method. We show that, for a large class of domains, this approximation gives a well-conditioned and near-optimal $N$-dimensional least-squares approximation using $M={cal O}(N^{2})$ equispaced sample points or $M={cal O}(N^{2}log N)$ random sample points, independently of $d$. We provide a comprehensive analysis of the error estimates and the rate of convergence of the least-squares approximation that uses the V+A method. Based on the multivariate V+A techniques we propose a new variant of the weighted V+A least-squares algorithm that uses only $M={cal O}(Nlog N)$ sample points to achieve a near-optimal approximation. Our initial numerical results validate that the V+A least-squares approximation method provides well-conditioned and near-optimal approximations for multivariate functions on (irregular) domains. Additionally, the (weighted) least-squares approximation that uses the V+A method performs competitively with state-of-the-art orthogonalization techniques and can serve as a practical tool for selecting near-optimal distributions of sample points in irregular domains.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"25 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144684797","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

Numerical analysis of lowest-order finite volume methods for a class of Stokes variational inequality problem 一类Stokes变分不等式问题的最低阶有限体积法数值分析

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-07-21 DOI: 10.1093/imanum/draf056

Feifei Jing, Takahito Kashiwabara, Wenjing Yan

引用次数: 0

A conditional gradient homotopy method with applications to semidefinite programming 一个条件梯度同伦方法在半定规划中的应用

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-07-20 DOI: 10.1093/imanum/draf059

Pavel Dvurechensky, Gabriele Iommazzo, Shimrit Shtern, Mathias Staudigl

引用次数: 0

Approximation in Hilbert spaces of the Gaussian and related analytic kernels 希尔伯特空间中高斯核及相关解析核的近似