Parallel Multigrid Acceleration for the Finite-Element Gaussian Belief Propagation Algorithm

• Published in: IEEE transactions on magnetics Vol. 50; no. 2; pp. 581 - 584
• Main Authors: El-Kurdi, Yousef, Gross, Warren J., Giannacopoulos, Dennis
• Format: Journal Article Conference Proceeding
• Language: English
• Published: New York, NY IEEE 01.02.2014; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Belief propagation; Convergence; Cross-disciplinary physics: materials science; rheology; Exact sciences and technology; FEMs; Finite element analysis; Gaussian belief propagation (GaBP); Graphical models; Libraries; Magnetism; Materials science; multigrid; Other topics in materials science; Physics; Sparse matrices; Vectors; Finite element method; Modelling; FEMs; Gaussian belief propagation (GaBP); multigrid; Magnetic properties
• ISSN: 0018-9464; 1941-0069
• DOI: 10.1109/TMAG.2013.2284483

We introduce a novel parallel multigrid algorithm, referred to as the finite-element multigrid Gaussian belief propagation (FMGaBP), to accelerate the convergence of the recently introduced finite-element Gaussian belief propagation solver. The FMGaBP algorithm processes the FEM computation in a fully distributed and parallel manner, with stencil-like element-by-element operations, demonstrating high parallel efficiency. The results for both sequential as well as parallel message scheduling versions of FMGaBP demonstrate high convergence rates independent of the scale of discretization on the finest mesh. In comparison with the multigrid preconditioned conjugate gradient (MG-PCG) solver, the FMGaBP algorithm demonstrates considerable iteration reductions as tested by Laplace benchmark problems. In addition, the parallel implementation of FMGaBP shows a speedup of 2.9 times over the parallel implementation of MG-PCG using eight CPU cores.