Title: Fast Algebraic Multigrid Solvers for the Maxwell's Equations

Speaker: Chris Siefert, 1416, Scalable Algorithms, SNL/NM, Candidate for SMTS in Computational Shock & Multiphysics, 1431          

Date/Time: Monday, April 28, 2008, 9:00 – 10:00 am

Location: CSRI Building/Room 90 (Sandia NM)

Brief Abstract: With the rise in popularity of compatible finite element, finite difference and finite volume discretizations for the time domain eddy current equations, there has been a corresponding need for fast solvers of the resulting linear algebraic systems.  However, the traits that make compatible discretizations a preferred choice for the Maxwell's equations also render these linear systems essentially intractable by truly black-box techniques.  We propose a new algebraic reformulation of the discrete eddy current equations along with a new algebraic multigrid technique (AMG) for this reformulated problem.  The reformulation process takes advantage of a discrete Hodge decomposition to replace the discrete eddy current equations by an equivalent 2x2 block linear system.

While this new AMG technique requires somewhat specialized treatment on the finest mesh, the coarser meshes can be handled using standard methods for Laplace-type problems, allowing for code reuse. Our new AMG method is applicable to a wide range of compatible methods on structured and unstructured grids. We illustrate the new technique, using edge elements, in the context of smoothed aggregation AMG.  We will demonstrate the weak scalability of our method to over 20,000 processors on Red Storm.  An implementation of this method was released in Trilinos 8.0.

CSRI POC: Randall Summers, (505) 844-6296