Collaborative Research-ITR-High Order Partial Differential Equations: Theory, Computational Tools, and Applications in Image Processing, Computer Graphics, Biology, and Fluids

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This project seeks to develop a comprehensive research and education program in the area of computationalmethods and simulations of physical systems described by high order Partial Differential Equations (PDEs). The program will unify algorithmic, visualization, theoretical, and experimental efforts as well as address applications in areas of science and technology, including computer graphics, image processing, biology, and fluids.Intellectual merit of the proposed activityThis project advances knowledge in the area of high order PDEs, with particular emphasis on curved surface data, and produces enabling technology to address fundamental problems in biology, image processing, computer graphics, and fluids in general. The novel science is in the computationaltechniques, experimental research, and diverse applications addressed by a multi-disciplinary team. Thisproject brings together the five fields of computer science, applied mathematics, mechanical engineering, physics, and electrical and computer engineering.Broader impacts of the proposed activityWith the increasing interest in high order PDEs, the computational tools and experience resulting from this project impact beyond the particular applications in this proposal. Students will receive unusually broadinterdisciplinary training and the workshop planned further brings experts from different fields together. New public domain software incorporating the developed algorithms enables researchers from different fields using higher order PDEs to perform state-of-the-art numerical simulations and graphics rendering of their application of interest.Educational initiatives of this research program include: (1) new interdisciplinary training of graduate students and postdocs through co-mentoring by PIs in different fields; (2) new interdisciplinary courses in computer graphics, numerical analysis, and modeling/simulation of physical phenomena described by higher order PDEs; (3) a workshop bringing together for the first time diverse scientific researchers using high order PDEs.