Numerical solution of differential problems with constraints and applications

我研究的总体目标是为应用中出现的涉及微分方程（DEs）的模型开发高效可靠的计算方法和软件。重点是受约束的微分方程，例如在图形、图像处理和虚拟现实模拟中出现的问题，以及涉及微分方程和优化的问题，例如在分布参数估计中出现的问题。我也对时间依赖性de的保守离散化感兴趣。虽然我的研究重点是在应用领域之间的知识和专业知识的转移，但重点将放在这个框架内的特定应用上：-涉及不连续的大规模分布参数估计问题的算法和软件-分段光滑表面，水平集和接口的重建，以及大型稀疏问题。-图形应用的科学计算方法，例如布料模拟和图像处理。-偏微分方程双曲型系统的紧凑、保守方法，以及时间反转的应用。

The general objective of my research is to develop efficient and reliable computational methods and software for models involving differential equations (DEs) that arise in applications. The focus is on constrained DEs, such as those arising in graphics, image processing and virtual reality simulations, and on problems involving DEs and optimization, such as those arising in distributed parameter estimation. I am also interested in conservative discretizations for time-dependent DEs. While my research focuses on the transfer of knowledge and expertise among areas of application, emphasis will be placed within this framework on particular applications: - Algorithms and software for large scale distributed parameter estimation problems involving discontinuities -- reconstruction of piecewise smooth surfaces, level sets and interfaces, and large sparse problems. - Methods of scientific computing for graphics applications, e.g. cloth simulation and image processing. - Compact, conservative methods for hyperbolic systems of partial differential equations, and time reversal applications.