Mathematics Colloquia and Seminars

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In this talk, we will present recent work on developing a geometry-based, principled approach to computational modeling. We will show that the use of discrete differential forms (along with their associated mixed finite elements) often resolves the apparent mismatch between differential and discrete modeling, and that variational definitions of continuous notions are computationally beneficial for a wide range of applications. An emphasis on the importance of preserving key differential geometric structures (such as symmetries and invariants) in the discrete setting will be a recurring theme throughout the talk, and examples ranging from processing of scanned geometry to simulation of incompressible fluids will be used to illustrate numerical benefits.