Pub Date : 2020-10-12DOI: 10.1515/9783110497397-010
{"title":"10 Simulations III: goal-oriented error control for a phase-field slit and time control for a screw","authors":"","doi":"10.1515/9783110497397-010","DOIUrl":"https://doi.org/10.1515/9783110497397-010","url":null,"abstract":"","PeriodicalId":221433,"journal":{"name":"Multiphysics Phase-Field Fracture","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123943560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-12DOI: 10.1515/9783110497397-202
{"title":"Classes and schools related to this monograph","authors":"","doi":"10.1515/9783110497397-202","DOIUrl":"https://doi.org/10.1515/9783110497397-202","url":null,"abstract":"","PeriodicalId":221433,"journal":{"name":"Multiphysics Phase-Field Fracture","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130312528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-12DOI: 10.1515/9783110497397-201
U. Langer
Finishing this book was a challenging exercise!1 Let me start differently than usual. First of all, I wish to thank De Gruyter and notably Nadja Schedensack as well as the managing editor of this book series, Ulrich Langer, for this opportunity and their endless patience and professional cooperation. When I proposed the concept in April 2016, I had a tranquille2 life as a Post doc at the Radon Institute of Computational and Applied Mathematics (RICAM) in Linz, Austria. Originally, this monograph was envisaged as part of the habilitation procedure as final qualification for a university career. I am sure that I would have achieved the goal of completing this book if I had stayed longer at RICAM. Suddenly, however (luckily as I can say today!), I was overtaken by events: I got an offer as maître de conférences from École Polytechnique in Palaiseau (near Paris), France, and soon after a (permanent) professorship position at the Leibniz University Hannover inGermany. Iwas incredibly lucky to get involved in somany activities since then. I neverwanted tomiss all of these activities. But there is one task I did not pursue as I should have: this book! In Spring 2020, I found the most valuable treasure of our times in my profession: time! Time for both my children3 and this book.4 I shall now briefly introduce the main topic, which is to discuss recent developments in mathematical modeling, design of algorithms, and numerical simulations in multiphysics variational phase-field fracture propagation. Variational modeling of fracture has been influential in several communities since 1998 when the first paper by Gilles Francfort and Jean-Jacques Marigo appeared. The simplified prototype structure of a phase-fieldmodel for fracture propagation is: Find vector-valued displacements u : B→ Rd and a scalar-valued, smoothed, indicator function φ : B→ R such that
完成这本书是一个具有挑战性的练习!让我以不同的方式开始。首先，我要感谢De Gruyter，特别是Nadja Schedensack以及本丛书的总编辑Ulrich Langer，感谢他们给我这次机会，感谢他们的耐心和专业合作。当我在2016年4月提出这个概念时，我在奥地利林茨的氡计算与应用数学研究所(RICAM)过着平静的博士后生活。最初，这本专著被设想为适应程序的一部分，作为大学生涯的最终资格。我相信，如果我在RICAM待久一点，我就能完成这本书的目标。然而，突然之间(我今天可以说很幸运!)，我被一些事件击倒了:我得到了法国Palaiseau(巴黎附近)École Polytechnique的offer，成为了职业生涯硕士(tre de confrences)，不久之后，我又得到了德国汉诺威莱布尼茨大学(Leibniz University Hannover)的(永久)教授职位。从那以后，我非常幸运地参加了许多活动。我不想错过所有这些活动。但有一件事我没有按我应该做的去做:这本书!在2020年的春天，我发现了我们这个时代最宝贵的财富:时间!有时间给我的孩子和这本书现在我将简要介绍主要主题，即讨论在多物理场变分相场裂缝扩展的数学建模、算法设计和数值模拟方面的最新进展。自1998年Gilles Francfort和Jean-Jacques Marigo发表第一篇论文以来，裂缝变分模型在几个领域产生了影响。裂缝扩展相场模型的简化原型结构为:求向量值位移u: B→Rd和一个标量值的光滑指示函数φ: B→R，使
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Pub Date : 2020-10-12DOI: 10.1515/9783110497397-007
{"title":"7 Numerical modeling part II: linearizations, nonlinear solvers, and linear solution","authors":"","doi":"10.1515/9783110497397-007","DOIUrl":"https://doi.org/10.1515/9783110497397-007","url":null,"abstract":"","PeriodicalId":221433,"journal":{"name":"Multiphysics Phase-Field Fracture","volume":"117 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117240955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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