Acta Numerica最新文献_第5页

Numerical methods for nonlocal and fractional models 非局部和分数模型的数值方法

IF 14.2 1区数学

Acta Numerica Pub Date : 2020-02-01 DOI: 10.2172/1598758

M. D'Elia, Q. Du, Christian A. Glusa, M. Gunzburger, Xiaochuan Tian, Zhi Zhou

{"title":"Numerical methods for nonlocal and fractional models","authors":"M. D'Elia, Q. Du, Christian A. Glusa, M. Gunzburger, Xiaochuan Tian, Zhi Zhou","doi":"10.2172/1598758","DOIUrl":"https://doi.org/10.2172/1598758","url":null,"abstract":"Partial differential equations (PDEs) are used with huge success to model phenomena across all scientific and engineering disciplines. However, across an equally wide swath, there exist situations in which PDEs fail to adequately model observed phenomena, or are not the best available model for that purpose. On the other hand, in many situations, nonlocal models that account for interaction occurring at a distance have been shown to more faithfully and effectively model observed phenomena that involve possible singularities and other anomalies. In this article we consider a generic nonlocal model, beginning with a short review of its definition, the properties of its solution, its mathematical analysis and of specific concrete examples. We then provide extensive discussions about numerical methods, including finite element, finite difference and spectral methods, for determining approximate solutions of the nonlocal models considered. In that discussion, we pay particular attention to a special class of nonlocal models that are the most widely studied in the literature, namely those involving fractional derivatives. The article ends with brief considerations of several modelling and algorithmic extensions, which serve to show the wide applicability of nonlocal modelling.","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"29 1","pages":"1 - 124"},"PeriodicalIF":14.2,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44856694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 117

Computing quantum dynamics in the semiclassical regime 半经典区域中的量子动力学计算

IF 14.2 1区数学

Acta Numerica Pub Date : 2020-02-01 DOI: 10.1017/S0962492920000033

C. Lasser, C. Lubich

引用次数: 58

Approximation algorithms in combinatorial scientific computing 组合科学计算中的近似算法

IF 14.2 1区数学

Acta Numerica Pub Date : 2019-05-01 DOI: 10.1017/S0962492919000035

A. Pothen, S. Ferdous, F. Manne

引用次数: 16

ANU volume 28 Cover and Front matter 澳大利亚国立大学第28卷封面和封面

IF 14.2 1区数学

Acta Numerica Pub Date : 2019-05-01 DOI: 10.1017/s0962492919000072

引用次数: 0

Numerical analysis of hemivariational inequalities in contact mechanics 接触力学中半变分不等式的数值分析

IF 14.2 1区数学

Acta Numerica Pub Date : 2019-05-01 DOI: 10.1017/S0962492919000023

W. Han, M. Sofonea

{"title":"Numerical analysis of hemivariational inequalities in contact mechanics","authors":"W. Han, M. Sofonea","doi":"10.1017/S0962492919000023","DOIUrl":"https://doi.org/10.1017/S0962492919000023","url":null,"abstract":"Contact phenomena arise in a variety of industrial process and engineering applications. For this reason, contact mechanics has attracted substantial attention from research communities. Mathematical problems from contact mechanics have been studied extensively for over half a century. Effort was initially focused on variational inequality formulations, and in the past ten years considerable effort has been devoted to contact problems in the form of hemivariational inequalities. This article surveys recent development in studies of hemivariational inequalities arising in contact mechanics. We focus on contact problems with elastic and viscoelastic materials, in the framework of linearized strain theory, with a particular emphasis on their numerical analysis. We begin by introducing three representative mathematical models which describe the contact between a deformable body in contact with a foundation, in static, history-dependent and dynamic cases. In weak formulations, the models we consider lead to various forms of hemivariational inequalities in which the unknown is either the displacement or the velocity field. Based on these examples, we introduce and study three abstract hemivariational inequalities for which we present existence and uniqueness results, together with convergence analysis and error estimates for numerical solutions. The results on the abstract hemivariational inequalities are general and can be applied to the study of a variety of problems in contact mechanics; in particular, they are applied to the three representative mathematical models. We present numerical simulation results giving numerical evidence on the theoretically predicted optimal convergence order; we also provide mechanical interpretations of simulation results.","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"28 1","pages":"175 - 286"},"PeriodicalIF":14.2,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0962492919000023","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46932286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 81

ANU volume 28 Cover and Back matter 澳大利亚国立大学第28卷封面和封底

IF 14.2 1区数学

Acta Numerica Pub Date : 2019-05-01 DOI: 10.1017/s0962492919000084

引用次数: 0

Solving inverse problems using data-driven models 使用数据驱动模型求解逆问题

IF 14.2 1区数学

Acta Numerica Pub Date : 2019-05-01 DOI: 10.1017/S0962492919000059

S. Arridge, P. Maass, O. Öktem, C. Schönlieb

引用次数: 415

Numerical methods for Kohn–Sham density functional theory Kohn-Sham密度泛函理论的数值方法

IF 14.2 1区数学

Acta Numerica Pub Date : 2019-05-01 DOI: 10.1017/S0962492919000047

Lin Lin, Jianfeng Lu, Lexing Ying

引用次数: 24

Derivative-free optimization methods 无导数优化方法

IF 14.2 1区数学

Acta Numerica Pub Date : 2019-04-25 DOI: 10.1017/S0962492919000060

Jeffrey Larson, M. Menickelly, Stefan M. Wild

{"title":"Derivative-free optimization methods","authors":"Jeffrey Larson, M. Menickelly, Stefan M. Wild","doi":"10.1017/S0962492919000060","DOIUrl":"https://doi.org/10.1017/S0962492919000060","url":null,"abstract":"In many optimization problems arising from scientific, engineering and artificial intelligence applications, objective and constraint functions are available only as the output of a black-box or simulation oracle that does not provide derivative information. Such settings necessitate the use of methods for derivative-free, or zeroth-order, optimization. We provide a review and perspectives on developments in these methods, with an emphasis on highlighting recent developments and on unifying treatment of such problems in the non-linear optimization and machine learning literature. We categorize methods based on assumed properties of the black-box functions, as well as features of the methods. We first overview the primary setting of deterministic methods applied to unconstrained, non-convex optimization problems where the objective function is defined by a deterministic black-box oracle. We then discuss developments in randomized methods, methods that assume some additional structure about the objective (including convexity, separability and general non-smooth compositions), methods for problems where the output of the black-box oracle is stochastic, and methods for handling different types of constraints.","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"28 1","pages":"287 - 404"},"PeriodicalIF":14.2,"publicationDate":"2019-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0962492919000060","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42600201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 80

Data assimilation: The Schrödinger perspective 数据同化:Schrödinger视角

IF 14.2 1区数学

Acta Numerica Pub Date : 2018-07-22 DOI: 10.1017/S0962492919000011

S. Reich

引用次数: 50