Aggregation-based aggressive coarsening with polynomial smoothing

2013/07/24 by James Brannick, Brannick, James
Computer Science · Engineering · Materials Science · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Block Copolymer Self-Assembly #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1307.6305

openalex publication_date 2013/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

This paper develops an algebraic multigrid preconditioner for the graph Laplacian. The proposed approach uses aggressive coarsening based on the aggregation framework in the setup phase and a polynomial smoother with sufficiently large degree within a (nonlinear) Algebraic Multilevel Iteration as a preconditioner to the flexible Conjugate Gradient iteration in the solve phase. We show that by combining these techniques it is possible to design a simple and scalable algorithm. Results of the algorithm applied to graph Laplacian systems arising from the standard linear finite element discretization of the scalar Poisson problem are reported.

Citations

• Polynomial of best uniform approximation to x^-1 and smoothing in\n two-level methods

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