Numerical solution of differential problems with constraints and applications

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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.