The Department of Applied Mathematics weekly seminar is given by scholars and researchers working in applied mathematics, broadly interpreted.
Title: Transforming meshes, or, algebraic topology for fun and profit
Abstract: Generating meshes is one of the key ingredients in solving partial differential equations on irregular domains using the finite element or finite volume method. All algorithms for generating, optimizing, and simplifying unstructured meshes are based on applying a sequence of elementary topological transformations. The vocabulary of available transformations dictates how well the algorithm works. In most meshing tools, however, this vocabulary is quite limited because implementing and debugging the transformations is... not enjoyable, in any respect. In this talk, I'll describe a heartbreakingly elegant* way to implement these transformation kernels. The method uses some ideas from algebraic topology but the only prerequisite is linear algebra.
*Rotten fruit will be provided for the audience in the event that the method should prove insufficiently elegant.