“Algebraic Multigrid for Discrete Differential Forms”
PhD Thesis (UIUCDCS-R-2008-2986), August 2008
Discrete differential forms arise in scientific 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 flows, surface parameterization, and the design of vector fields on meshes. In this thesis we describe efficient 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 efficiency. Since the k-form problems to be solved are arbitrarily large, the need for scalable numerical solvers is clear.