Algebraic Multigrid For Discrete Differential Forms

Discrete dierential forms arise in scientic disciplines ranging from computational electromagnetics to computer graphics. Examples include stable discretizations of the eddy-current problem, topological methods for sensor network coverage, visualization of complex ows, surface parameterization, and the design of vector elds on meshes. In this thesis we describe e cient and scalable numerical solvers for discrete k-form problems. Our approach is based on the principles of algebraic multigrid (AMG) which is designed to solve large-scale linear systems with optimal, or near-optimal e ciency. Since the k-form problems to be solved are arbitrarily large, the need for scalable numerical solvers is clear