Numerical simulation of surface reconstruction, inverse problems and differential equations in applications

表面重构、反问题和微分方程的数值模拟应用

基本信息

批准号：
4306-2011
负责人：
Ascher, Uri
金额：
$ 2.4万
依托单位：
University of British Columbia
依托单位国家：
加拿大
项目类别：
Discovery Grants Program - Individual
财政年份：
2015
资助国家：
加拿大
起止时间：
2015-01-01 至 2016-12-31
项目状态：
已结题

来源：
https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=568349
关键词：
Numerical simulation surface reconstruction inverse

项目摘要

The general objective of my research is to develop efficient and reliable computational methods and software for models involving surface reconstruction, inverse problems and differential equations (DEs). The focus is on methods for constrained DEs and optimization problems, such as those arising in 3D digital geometry, image processing, virtual reality simulations and distributed parameter estimation. I am also interested in conservative methods for time-dependent deterministic and stochastic 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 instances. 1. Algorithms and software for large scale distributed parameter estimation problems involving discontinuities: reconstructing piecewise smooth surfaces, handling interfaces, level set methods and solving large inverse problems. 2. Scientific computing for graphics and image processing applications: surface reconstruction from point cloud sets, sparse solution methods, cloth simulation, space-time reconstruction, discrete dynamics in image processing, and constrained flexible-body mechanical system simulations in robotics and virtual reality. 3. Numerical methods in sensorimotor applications: control and inverse problems in computed myography and saccadic eye movement. 4. Compact, conservative methods for hyperbolic systems of PDEs: non-integrable problems and data assimilation.

我的研究的一般目标是为涉及表面重建，反问题和微分方程（DES）的模型开发高效可靠的计算方法和软件。重点是用于约束DES和优化问题的方法，例如在3D数字几何，图像处理，虚拟现实模拟和分布式参数估计中产生的方法。我也对时间依赖性的确定性和随机性DES的保守方法感兴趣。尽管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，但将重点放在特定情况下。 1。用于大规模分布的参数估计问题的算法和软件涉及不连续性：重建分段平滑表面，处理接口，级别设置方法并解决大问题。 2。用于图形和图像处理应用程序的科学计算：从点云集，稀疏解决方案方法，布仿真，时空重建，图像处理中的离散动态以及机器人和虚拟现实中的柔性机械系统模拟受约束的柔性机械系统模拟。 3。感觉运动应用中的数值方法：计算的myagraghy和saccadic眼运动中的控制和反问题。 4。PDE双曲线系统的紧凑，保守方法：不可综合的问题和数据同化。