Numerical solution of differential problems with constraints and applications

我的研究的总体目标是开发有效和可靠的计算方法和软件的模型，涉及微分方程（DE）的应用程序中出现的。重点是约束DE，如在图形，图像处理和虚拟现实模拟中出现的问题，并涉及DE和优化，如在分布参数估计中出现的问题。我也对时变微分方程的保守离散化很感兴趣。虽然我的研究重点是知识和专业知识的应用领域之间的转移，重点将放在这个框架内的特定应用：-算法和软件的大规模分布参数估计问题，涉及不连续性-重建分段光滑表面，水平集和接口，和大型稀疏问题。- 用于图形应用的科学计算方法，例如布料模拟和图像处理。- 双曲型偏微分方程组的紧致守恒方法及时间反演应用。

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.