Parameter identification in models with sharp phase transitions

具有急剧相变的模型中的参数识别

• 批准号: 313878693
• 负责人: Professor Dr. Christian Clason
• 金额: --
• 依托单位: Arbeitsgruppe Nichtlineare Optimierung
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/313878693?language=en
• 关键词: Parameter; identification; models; sharp; phase

The aim of this project is the analysis of and development of algorithms for parameter identification problems where the solution of the forward problem exhibits multiple structurally different phases. Such problems occur in climatology (cloud nucleation, glacial melting), material science (crystal growth, steel annealing) and mechanics (contact, defect mechanics) and can be modeled as variational inequalities or partial differential equations involving non-smooth nonlinearities. A common feature of such models is that the solution operator is nonlinear and non-differentiable, making classical analytical and numerical approaches that rely on local linearization inapplicable. Our goal is therefore to derive error estimates and to develop new iterative algorithms for parameter estimation problems for a class of partial differential equations involving non-smooth but Lipschitz continuous and directionally differentiable nonlinearities such as those appearing in the two-phase Stefan problem.

该项目的目的是分析和开发参数识别问题的算法，其中正问题的解决方案具有多个结构不同的阶段。这些问题出现在气候学（云成核，冰川融化），材料科学（晶体生长，钢退火）和力学（接触，缺陷力学），可以建模为变分不等式或偏微分方程，涉及非光滑非线性。这种模型的一个共同特点是，解决方案运营商是非线性和不可微的，使经典的分析和数值方法，依赖于局部线性化不适用。因此，我们的目标是获得误差估计和开发新的迭代算法的一类偏微分方程的参数估计问题，涉及非光滑，但Lipschitz连续和方向可微的非线性，如那些出现在两相Stefan问题。