IMA Journal of Numerical Analysis最新文献_第8页

Complexity guarantees for nonconvex Newton-MR under inexact Hessian information 非精确Hessian信息下非凸Newton-MR的复杂度保证

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-03-05 DOI: 10.1093/imanum/drae110

Alexander Lim, Fred Roosta

引用次数: 0

Parametric finite element approximation of two-phase Navier–Stokes flow with viscoelasticity 黏弹性两相Navier-Stokes流的参数有限元逼近

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-02-24 DOI: 10.1093/imanum/drae103

Harald Garcke, Robert Nürnberg, Dennis Trautwein

{"title":"Parametric finite element approximation of two-phase Navier–Stokes flow with viscoelasticity","authors":"Harald Garcke, Robert Nürnberg, Dennis Trautwein","doi":"10.1093/imanum/drae103","DOIUrl":"https://doi.org/10.1093/imanum/drae103","url":null,"abstract":"In this work we present a parametric finite element approximation of two-phase Navier–Stokes flow with viscoelasticity. The free boundary problem is given by the viscoelastic Navier–Stokes equations in the two fluid phases, connected by jump conditions across the interface. The elasticity in the fluids is characterized using the Oldroyd-B model with possible stress diffusion. The model was originally introduced to approximate fluid-structure interaction problems between an incompressible Newtonian fluid and a hyperelastic neo-Hookean solid, which are possible limit cases of the model. We approximate a variational formulation of the model with an unfitted finite element method that uses piecewise linear parametric finite elements. The two-phase Navier–Stokes–Oldroyd-B system in the bulk regions is discretized in a way that guarantees unconditional solvability and stability for the coupled bulk–interface system. Good volume conservation properties for the two phases are observed in the case where the pressure approximation space is enriched with the help of an extended finite element method function. We show the applicability of our method with some numerical results.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"9 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143485893","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

Smoothed circulant embedding with applications to multilevel Monte Carlo methods for PDEs with random coefficients 光滑循环嵌入及其在带随机系数偏微分方程的多层蒙特卡罗方法中的应用

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-02-22 DOI: 10.1093/imanum/drae102

Anastasia Istratuca, Aretha L Teckentrup

引用次数: 0

Efficient low rank matrix recovery with flexible group sparse regularization 基于柔性群稀疏正则化的高效低秩矩阵恢复

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-01-30 DOI: 10.1093/imanum/drae099

Quan Yu, Minru Bai, Xinzhen Zhang

{"title":"Efficient low rank matrix recovery with flexible group sparse regularization","authors":"Quan Yu, Minru Bai, Xinzhen Zhang","doi":"10.1093/imanum/drae099","DOIUrl":"https://doi.org/10.1093/imanum/drae099","url":null,"abstract":"In this paper, we present a novel approach to the low rank matrix recovery (LRMR) problem by casting it as a group sparsity problem. Specifically, we propose a flexible group sparse regularizer (FLGSR) that can group any number of matrix columns as a unit, whereas existing methods group each column as a unit. We prove the equivalence between the matrix rank and the FLGSR under some mild conditions, and show that the LRMR problem with either of them has the same global minimizers. We also establish the equivalence between the relaxed and the penalty formulations of the LRMR problem with FLGSR. We then propose an inexact restarted augmented Lagrangian method, which solves each subproblem by an extrapolated linearized alternating minimization method. We analyse the convergence of our method. Remarkably, our method linearizes each group of the variable separately and uses the information of the previous groups to solve the current group within the same iteration step. This strategy enables our algorithm to achieve fast convergence and high performance, which are further improved by the restart technique. Finally, we conduct numerical experiments on both grayscale images and high altitude aerial images to confirm the superiority of the proposed FLGSR and algorithm.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"96 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071528","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

Compound Poisson particle approximation for McKean–Vlasov SDEs McKean-Vlasov SDEs的复合泊松粒子近似

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-01-23 DOI: 10.1093/imanum/drae095

Xicheng Zhang

{"title":"Compound Poisson particle approximation for McKean–Vlasov SDEs","authors":"Xicheng Zhang","doi":"10.1093/imanum/drae095","DOIUrl":"https://doi.org/10.1093/imanum/drae095","url":null,"abstract":"We present a comprehensive discretization scheme for linear and nonlinear stochastic differential equations (SDEs) driven by either Brownian motions or $alpha $-stable processes. Our approach utilizes compound Poisson particle approximations, allowing for simultaneous discretization of both the time and space variables in McKean–Vlasov SDEs. Notably, the approximation processes can be represented as a Markov chain with values on a lattice. Importantly, we demonstrate the propagation of chaos under relatively mild assumptions on the coefficients, including those with polynomial growth. This result establishes the convergence of the particle approximations towards the true solutions of the McKean–Vlasov SDEs. By only imposing moment conditions on the intensity measure of compound Poisson processes our approximation exhibits universality. In the case of ordinary differential equations (ODEs) we investigate scenarios where the drift term satisfies the one-sided Lipschitz assumption. We prove the optimal convergence rate for Filippov solutions in this setting. Additionally, we establish a functional central limit theorem for the approximation of ODEs and show the convergence of invariant measures for linear SDEs. As a practical application we construct a compound Poisson approximation for two-dimensional Navier–Stokes equations on the torus and demonstrate the optimal convergence rate.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"38 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143020598","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

Gauss quadrature rules for integrals involving weight functions with variable exponents and an application to weakly singular Volterra integral equations 变指数权函数积分的高斯积分规则及其在弱奇异Volterra积分方程中的应用

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-01-23 DOI: 10.1093/imanum/drae088

Chafik Allouch, Gradimir V Milovanović

引用次数: 0

Numerical analysis of a spherical harmonic discontinuous Galerkin method for scaled radiative transfer equations with isotropic scattering 具有各向同性散射的尺度辐射传递方程的球谐不连续伽辽金方法的数值分析

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-01-23 DOI: 10.1093/imanum/drae096

Qiwei Sheng, Cory D Hauck, Yulong Xing

{"title":"Numerical analysis of a spherical harmonic discontinuous Galerkin method for scaled radiative transfer equations with isotropic scattering","authors":"Qiwei Sheng, Cory D Hauck, Yulong Xing","doi":"10.1093/imanum/drae096","DOIUrl":"https://doi.org/10.1093/imanum/drae096","url":null,"abstract":"In highly diffusion regimes when the mean free path $varepsilon $ tends to zero, the radiative transfer equation has an asymptotic behavior which is governed by a diffusion equation and the corresponding boundary condition. Generally, a numerical scheme for solving this problem has the truncation error containing an $varepsilon ^{-1}$ contribution that leads to a nonuniform convergence for small $varepsilon $. Such phenomenons require high resolutions of discretizations, which degrades the performance of the numerical scheme in the diffusion limit. In this paper, we first provide a priori estimates for the scaled spherical harmonic ($P_{N}$) radiative transfer equation. Then we present an error analysis for the spherical harmonic discontinuous Galerkin (DG) method of the scaled radiative transfer equation showing that, under some additional assumptions, its solutions converge uniformly in $varepsilon $ to the solution of the scaled radiative transfer equation. We further present an optimal convergence result for the DG method with the upwind flux on Cartesian grids. Error estimates of $left (1+mathcal{O}(varepsilon )right )h^{k+1}$ (where $h$ is the maximum element length) are obtained when tensor product polynomials of degree at most $k$ are used.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"104 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143020599","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 fast algorithm for smooth convex minimization problems and its application to inverse source problems 光滑凸极小化问题的快速算法及其在逆源问题中的应用

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-01-21 DOI: 10.1093/imanum/drae091

Pham Quy Muoi, Vo Quang Duy, Chau Vinh Khanh, Nguyen Trung Thành

引用次数: 0

Polynomial quasi-Trefftz DG for PDEs with smooth coefficients: elliptic problems 光滑系数偏微分方程的多项式拟trefftz DG：椭圆型问题

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-01-19 DOI: 10.1093/imanum/drae094

Lise-Marie Imbert-Gérard, Andrea Moiola, Chiara Perinati, Paul Stocker

{"title":"Polynomial quasi-Trefftz DG for PDEs with smooth coefficients: elliptic problems","authors":"Lise-Marie Imbert-Gérard, Andrea Moiola, Chiara Perinati, Paul Stocker","doi":"10.1093/imanum/drae094","DOIUrl":"https://doi.org/10.1093/imanum/drae094","url":null,"abstract":"Trefftz schemes are high-order Galerkin methods whose discrete spaces are made of elementwise exact solutions of the underlying partial differential equation (PDE). Trefftz basis functions can be easily computed for many PDEs that are linear, homogeneous and have piecewise-constant coefficients. However, if the equation has variable coefficients, exact solutions are generally unavailable. Quasi-Trefftz methods overcome this limitation relying on elementwise ‘approximate solutions’ of the PDE, in the sense of Taylor polynomials. We define polynomial quasi-Trefftz spaces for general linear PDEs with smooth coefficients and source term, describe their approximation properties and, under a nondegeneracy condition, provide a simple algorithm to compute a basis. We then focus on a quasi-Trefftz DG method for variable-coefficient elliptic diffusion–advection–reaction problems, showing stability and high-order convergence of the scheme. The main advantage over standard DG schemes is the higher accuracy for comparable numbers of degrees of freedom. For nonhomogeneous problems with piecewise-smooth source term we propose to construct a local quasi-Trefftz particular solution and then solve for the difference. Numerical experiments in two and three space dimensions show the excellent properties of the method both in diffusion-dominated and advection-dominated problems.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"5 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990075","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

Discontinuous Galerkin discretization of coupled poroelasticity–elasticity problems 耦合孔弹-弹性问题的不连续Galerkin离散化

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2024-12-28 DOI: 10.1093/imanum/drae093

Paola F Antonietti, Michele Botti, Ilario Mazzieri

引用次数: 0