I am Kai Kang, a Computer Science junior at Carnegie Mellon University, with a minor in Mathematics. I am using this webpage for my senior thesis project Efficient Poisson Equation Solver with Professor Keenan Crane.
Much like the FFT in traditional signal processing, the Poisson equation is the central tool used across a wide variety of digital geometry processing algorithms, where one wishes to manipulate three-dimensional surfaces. The goal of this project is to develop fast, scalable tools for solving the Poisson equation on triangulated surfaces by (i) surveying existing best practices, (ii) specializing general-purpose algorithms to the special case of mesh geometry, and (iii) adapting solvers to a context where scalability is needed (e.g., massive data sets and distributed platforms). The initial steps will be :
(i) to implement fundamental geometry processing algorithms using algebraic multigrid (http://pyamg.org) and
(ii) analyze how general-purpose matrix reordering schemes (e.g., http://glaros.dtc.umn.edu/gkhome/views/metis) behave on mesh data sets.
The deliverable will be an easy-to-use package for solving Poisson equations that provides users with several different solvers, with the goal of improving on the state of the art. This work has the potential for broad impact in any area that depends on geometric data processing.
Link to detailed proposal here
Link to Gitbook Here