GRK 1754: Optimisation and Numerical Analysis for Partial Differential Equations with Non-smooth Structures

GRK 1754：非光滑结构偏微分方程的优化和数值分析

• 批准号: 188264188
• 金额: --
• 依托单位: Technische Universität München (TUM)
• 依托单位国家: 德国
• 项目类别: International Research Training Groups
• 财政年份: 2012
• 资助国家: 德国
• 起止时间: 2011-12-31 至 2020-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/188264188?language=en
• 关键词: GRK; 1754; Optimisation; Numerical; Analysis

Many application problems coming from physics, chemistry, biology or engineering sciences are described by mathematical models involving partial differential equations (PDEs). Often such problems involve different kinds of non-smooth structures (singularities, interfaces, inequality constraints etc.). The mathematical treatment of the corresponding PDE-based models is crucial for the efficient solution of practical problems. There is a significant demand for highly qualified junior scientists with postgraduate education and experience in this area, in academia as well as in industry and commerce. The International Research Training Group intends to meet this demand. The major goals of the Research Training Group are: (1) transfer of cutting-edge research topics to the education of doctoral students, (2) development and investigation of novel methods in numerical treatment and optimisation for problems involving PDEs and possessing non-smooth structures. The Research Training Group is a joint project of the four universities Technische Universität München, Universität der Bundeswehr München, Karl-Franzens-Universität Graz and Technische Universität Graz. The institutions in Munich and Graz contribute to the joint research programme through their internationally visible scientific strengths in applied mathematics: the TU München has long-range experience in the analytical and numerical treatment of non-linear phenomena, whereas the institutes in Graz contribute their expertise in optimisation, variational calculus and numerical analysis. The combination of the expertise will result in high synergy effects, which shall be highlighted and exploited by this International Research Training Group. Methodological approaches ranging from adaptivity and non-smooth optimisation to the treatment of interfaces and shapes will enter in the research and study programme of the International Research Training Group.

许多物理、化学、生物或工程科学中的应用问题都是由涉及偏微分方程的数学模型来描述的。这些问题通常涉及不同种类的非光滑结构（奇点、界面、不等式约束等）。相应的基于偏微分方程的模型的数学处理是至关重要的有效解决实际问题。在学术界以及工业和商业界，对具有研究生教育和这一领域经验的高素质青年科学家的需求很大。国际研究训练集团打算满足这一需求。研究培训组的主要目标是：（1）将尖端研究课题转移到博士生教育中，（2）开发和研究涉及偏微分方程和具有非光滑结构的问题的数值处理和优化的新方法。研究培训小组是慕尼黑工业大学、慕尼黑联邦国防军大学、卡尔-弗朗茨-格拉兹大学和格拉兹工业大学这四所大学的联合项目。慕尼黑和格拉兹的机构通过其在应用数学方面的国际知名科学实力为联合研究计划做出了贡献：慕尼黑工业大学在非线性现象的分析和数值处理方面拥有长期经验，而格拉兹的研究所则贡献了他们在优化，变分法和数值分析方面的专业知识。这些专门知识的结合将产生高度的协同效应，这一点将得到国际研究培训小组的重视和利用。从适应性和非光滑优化到界面和形状处理的方法学方法将进入国际研究培训小组的研究和学习方案。