GRK 1128: Analysis, Numerics, and Optimisation of Multiphase Problems

GRK 1128：多相问题的分析、数值和优化

• 批准号: 462999
• 金额: --
• 依托单位: Humboldt-Universität zu Berlin
• 依托单位国家: 德国
• 项目类别: Research Training Groups
• 财政年份: 2005
• 资助国家: 德国
• 起止时间: 2004-12-31 至 2008-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/462999?language=en
• 关键词: GRK; 1128; Analysis; Numerics; Optimisation

Systems with multiple phases arise in various scientific fields. Their mathematical modelling, analysis, numerical treatment, and optimisation requires novel approaches to deal for example with nonlocal effects or varying scales. The aim of the Research Training Group is to enhance and to disseminate the understanding of morphological changes during phase transformations, coarsening of grain structures in crystals, epitactial growth of thin metallic films, multiphase equilibria of mixed fluids, subsonic/supersonic flight transitions in aerodynamics, and other multiphase phenomena.The Research Training Group focuses on the development and teaching of mathematical techniques and algorithms for the treatment of nonlinear partial differential equations and inequalities arising in multiple phase problems. Doctoral candidates are expected to have a strong background in applied mathematics though they may have graduated in engineering or sciences. The programme is attracting a significant number of international fellows to Berlin and is therefore conducted in English.The department of mathematics of Humboldt University maintains a strong tradition in the fundamental mathematics of partial differential equations (PDE). The recent appointment of three chairs has complemented this strength in the key areas of applied analysis, numerics of PDEs, and nonlinear optimisation. Several adjunct professors and some other senior scientists from Weierstrass Institute for Applied Analysis and Stochastics (WIAS) in Berlin complete the research expertise on multiphase problems. There is also cooperation with other universities and research laboratories and scientific institutions in the Berlin area.

多相系统出现在各个科学领域。他们的数学建模，分析，数值处理和优化需要新的方法来处理，例如与非局部效应或不同的尺度。研究培训小组的目的是加强和传播对相变过程中形态变化的理解，晶体中晶粒结构的粗化，薄金属膜的外延生长，混合流体的多相平衡，空气动力学中的亚音速/超音速飞行过渡，和其他多相现象。研究培训组的重点是数学技术和算法的开发和教学，处理非线性偏微分方程和多相问题中产生的不等式。博士候选人预计将有一个强大的应用数学背景，虽然他们可能已经毕业于工程或科学。该方案吸引了相当数量的国际研究员到柏林，因此以英语进行。洪堡大学数学系在偏微分方程（PDE）的基础数学方面保持着悠久的传统。最近任命的三把椅子补充了这一优势，在关键领域的应用分析，偏微分方程的数值，和非线性优化。来自柏林维尔斯特拉斯应用分析和随机研究所（WIAS）的几位兼职教授和其他一些资深科学家完成了多相问题的研究专长。此外，还与柏林地区的其他大学、研究实验室和科研机构开展合作。