发布求助
文献互助 智能选刊 最新文献

IMA Journal of Numerical Analysis最新文献

筛选
英文 中文
Full operator preconditioning and the accuracy of solving linear systems 全算子预处理与线性系统求解精度
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2024-01-25 DOI: 10.1093/imanum/drad104
Stephan Mohr, Yuji Nakatsukasa, Carolina Urzúa-Torres
{"title":"Full operator preconditioning and the accuracy of solving linear systems","authors":"Stephan Mohr, Yuji Nakatsukasa, Carolina Urzúa-Torres","doi":"10.1093/imanum/drad104","DOIUrl":"https://doi.org/10.1093/imanum/drad104","url":null,"abstract":"Unless special conditions apply, the attempt to solve ill-conditioned systems of linear equations with standard numerical methods leads to uncontrollably high numerical error and often slow convergence of an iterative solver. In many cases, such systems arise from the discretization of operator equations with a large number of discrete variables and the ill-conditioning is tackled by means of preconditioning. A key observation in this paper is the sometimes overlooked fact that while traditional preconditioning effectively accelerates convergence of iterative methods, it generally does not improve the accuracy of the solution. Nonetheless, it is sometimes possible to overcome this barrier: accuracy can be improved significantly if the equation is transformed before discretization, a process we refer to as full operator preconditioning (FOP). We highlight that this principle is already used in various areas, including second kind integral equations and Olver–Townsend’s spectral method. We formulate a sufficient condition under which high accuracy can be obtained by FOP. We illustrate this for a fourth order differential equation which is discretized using finite elements.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"40 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139568274","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
Well-posedness and error estimates for coupled systems of nonlocal conservation laws 非局部守恒定律耦合系统的好拟性和误差估计
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2024-01-20 DOI: 10.1093/imanum/drad101
Aekta Aggarwal, Helge Holden, Ganesh Vaidya
{"title":"Well-posedness and error estimates for coupled systems of nonlocal conservation laws","authors":"Aekta Aggarwal, Helge Holden, Ganesh Vaidya","doi":"10.1093/imanum/drad101","DOIUrl":"https://doi.org/10.1093/imanum/drad101","url":null,"abstract":"This article deals with the error estimates for numerical approximations of the entropy solutions of coupled systems of nonlocal hyperbolic conservation laws. The systems can be strongly coupled through the nonlocal coefficient present in the convection term. A fairly general class of fluxes is being considered, where the local part of the flux can be discontinuous at infinitely many points, with possible accumulation points. The aims of the paper are threefold: (1) Establishing existence of entropy solutions with rough local flux for such systems, by deriving a uniform $operatorname {BV}$ bound on the numerical approximations; (2) Deriving a general Kuznetsov-type lemma (and hence uniqueness) for such systems with both smooth and rough local fluxes; (3) Proving the convergence rate of the finite volume approximations to the entropy solutions of the system as $1/2$ and $1/3$, with homogeneous (in any dimension) and rough local parts (in one dimension), respectively. Numerical experiments are included to illustrate the convergence rates.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"15 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139505816","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
Convergence with rates for a Riccati-based discretization of SLQ problems with SPDEs 基于 Riccati 的 SPDE SLQ 问题离散化的收敛率
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2024-01-19 DOI: 10.1093/imanum/drad097
Andreas Prohl, Yanqing Wang
{"title":"Convergence with rates for a Riccati-based discretization of SLQ problems with SPDEs","authors":"Andreas Prohl, Yanqing Wang","doi":"10.1093/imanum/drad097","DOIUrl":"https://doi.org/10.1093/imanum/drad097","url":null,"abstract":"We consider a new discretization in space (parameter $h>0$) and time (parameter $tau>0$) of a stochastic optimal control problem, where a quadratic functional is minimized subject to a linear stochastic heat equation with linear noise. Its construction is based on the perturbation of a generalized difference Riccati equation to approximate the related feedback law. We prove a convergence rate of almost ${mathcal O}(h^{2}+tau )$ for its solution, and conclude from it a rate of almost ${mathcal O}(h^{2}+tau )$ resp. ${mathcal O}(h^{2}+tau ^{1/2})$ for computable approximations of the optimal state and control with additive resp. multiplicative noise.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"7 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139505922","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
Corrigendum to: Adaptive FEM with quasi-optimal overall cost for nonsymmetric linear elliptic PDEs 更正：非对称线性椭圆 PDEs 的自适应有限元与准最优总成本
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2024-01-19 DOI: 10.1093/imanum/drad103
Maximilian Brunner, Michael Innerberger, Ani Miraçi, Dirk Praetorius, Julian Streitberger, Pascal Heid
{"title":"Corrigendum to: Adaptive FEM with quasi-optimal overall cost for nonsymmetric linear elliptic PDEs","authors":"Maximilian Brunner, Michael Innerberger, Ani Miraçi, Dirk Praetorius, Julian Streitberger, Pascal Heid","doi":"10.1093/imanum/drad103","DOIUrl":"https://doi.org/10.1093/imanum/drad103","url":null,"abstract":"Unfortunately, there is a flaw in the numerical analysis of the published version [IMA J. Numer. Anal., DOI:10.1093/imanum/drad039], which is corrected here. Neither the algorithm nor the results are affected, but constants have to be adjusted.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"40 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139505972","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
Gamma-convergent LDG method for large bending deformations of bilayer plates 双层板大弯曲变形的伽马收敛 LDG 方法
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2024-01-19 DOI: 10.1093/imanum/drad100
Andrea Bonito, Ricardo H Nochetto, Shuo Yang
{"title":"Gamma-convergent LDG method for large bending deformations of bilayer plates","authors":"Andrea Bonito, Ricardo H Nochetto, Shuo Yang","doi":"10.1093/imanum/drad100","DOIUrl":"https://doi.org/10.1093/imanum/drad100","url":null,"abstract":"Bilayer plates are slender structures made of two thin layers of different materials. They react to environmental stimuli and undergo large bending deformations with relatively small actuation. The reduced model is a constrained minimization problem for the second fundamental form, with a given spontaneous curvature that encodes material properties, subject to an isometry constraint. We design a local discontinuous Galerkin (LDG) method, which imposes a relaxed discrete isometry constraint and controls deformation gradients at barycenters of elements. We prove $varGamma $-convergence of LDG, design a fully practical gradient flow, which gives rise to a linear scheme at every step, and show energy stability and control of the isometry defect. We extend the $varGamma $-convergence analysis to piecewise quadratic creases. We also illustrate the performance of the LDG method with several insightful simulations of large deformations, one including a curved crease.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"4 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139505921","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
Darcy’s problem coupled with the heat equation under singular forcing: analysis and discretization 奇异强迫下与热方程耦合的达西问题：分析与离散化
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2024-01-11 DOI: 10.1093/imanum/drad094
Alejandro Allendes, Gilberto Campaña, Francisco Fuica, Enrique Otárola
{"title":"Darcy’s problem coupled with the heat equation under singular forcing: analysis and discretization","authors":"Alejandro Allendes, Gilberto Campaña, Francisco Fuica, Enrique Otárola","doi":"10.1093/imanum/drad094","DOIUrl":"https://doi.org/10.1093/imanum/drad094","url":null,"abstract":"We study the existence of solutions for Darcy’s problem coupled with the heat equation under singular forcing; the right-hand side of the heat equation corresponds to a Dirac measure. The model studied involves thermal diffusion and viscosity depending on the temperature. We propose a finite element solution technique and analyze its convergence properties. In the case where thermal diffusion is independent of temperature, we propose an a posteriori error estimator and study its reliability and efficiency properties. We illustrate the theory with numerical examples.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"1 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139431258","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
Compactness estimates for difference schemes for conservation laws with discontinuous flux 非连续通量守恒定律差分方案的紧凑性估计
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2024-01-04 DOI: 10.1093/imanum/drad096
Kenneth H Karlsen, John D Towers
{"title":"Compactness estimates for difference schemes for conservation laws with discontinuous flux","authors":"Kenneth H Karlsen, John D Towers","doi":"10.1093/imanum/drad096","DOIUrl":"https://doi.org/10.1093/imanum/drad096","url":null,"abstract":"We establish quantitative compactness estimates for finite difference schemes used to solve nonlinear conservation laws. These equations involve a flux function $f(k(x,t),u)$, where the coefficient $k(x,t)$ is $BV$-regular and may exhibit discontinuities along curves in the $(x,t)$ plane. Our approach, which is technically elementary, relies on a discrete interaction estimate and one entropy function. While the details are specifically outlined for the Lax-Friedrichs scheme, the same framework can be applied to other difference schemes. Notably, our compactness estimates are new even in the homogeneous case ($kequiv 1$).","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"35 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139101268","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 constraint dissolving approach for nonsmooth optimization over the Stiefel manifold 在 Stiefel 流形上进行非平滑优化的约束消解方法
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2023-12-23 DOI: 10.1093/imanum/drad098
Xiaoyin Hu, Nachuan Xiao, Xin Liu, Kim-Chuan Toh
{"title":"A constraint dissolving approach for nonsmooth optimization over the Stiefel manifold","authors":"Xiaoyin Hu, Nachuan Xiao, Xin Liu, Kim-Chuan Toh","doi":"10.1093/imanum/drad098","DOIUrl":"https://doi.org/10.1093/imanum/drad098","url":null,"abstract":"This paper focuses on the minimization of a possibly nonsmooth objective function over the Stiefel manifold. The existing approaches either lack efficiency or can only tackle prox-friendly objective functions. We propose a constraint dissolving function named NCDF and show that it has the same first-order stationary points and local minimizers as the original problem in a neighborhood of the Stiefel manifold. Furthermore, we show that the Clarke subdifferential of NCDF is easy to achieve from the Clarke subdifferential of the objective function. Therefore, various existing approaches for unconstrained nonsmooth optimization can be directly applied to nonsmooth optimization problems over the Stiefel manifold. We propose a framework for developing subgradient-based methods and establishing their convergence properties based on prior works. Furthermore, based on our proposed framework, we can develop efficient approaches for optimization over the Stiefel manifold. Preliminary numerical experiments further highlight that the proposed constraint dissolving approach yields efficient and direct implementations of various unconstrained approaches to nonsmooth optimization problems over the Stiefel manifold.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"87 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139041468","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 best p-norm approximation of discrete data by polynomials 论多项式对离散数据的最佳 p-norm 近似值
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2023-12-09 DOI: 10.1093/imanum/drad086
Michael S Floater
{"title":"On best p-norm approximation of discrete data by polynomials","authors":"Michael S Floater","doi":"10.1093/imanum/drad086","DOIUrl":"https://doi.org/10.1093/imanum/drad086","url":null,"abstract":"In this note, we derive a solution to the problem of finding a polynomial of degree at most $n$ that best approximates data at $n+2$ points in the $l_{p}$ norm. Analogous to a result of de la Vallée Poussin, one can express the solution as a convex combination of the Lagrange interpolants over subsets of $n+1$ points, and the error oscillates in sign.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"7 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138559326","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
Semilinear optimal control with Dirac measures 具有狄拉克测度的半线性最优控制
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2023-11-29 DOI: 10.1093/imanum/drad091
Enrique Otárola
{"title":"Semilinear optimal control with Dirac measures","authors":"Enrique Otárola","doi":"10.1093/imanum/drad091","DOIUrl":"https://doi.org/10.1093/imanum/drad091","url":null,"abstract":"The purpose of this work is to study an optimal control problem for a semilinear elliptic partial differential equation with a linear combination of Dirac measures as a forcing term; the control variable corresponds to the amplitude of such singular sources. We analyze the existence of optimal solutions and derive first- and, necessary and sufficient, second-order optimality conditions. We develop a solution technique that discretizes the state and adjoint equations with continuous piecewise linear finite elements; the control variable is already discrete. We analyze the convergence properties of discretizations and obtain, in two dimensions, an a priori error estimate for the underlying approximation of an optimal control variable.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"102 30","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138455384","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: 3
首页 上一页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信