2019/10/24 by Joshua Hanophy, Hanophy, Joshua, Ben S. Southworth +7 · 1 citation
Computer Science · Engineering · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.1910.11463
openalex publication_date 2019/10/24 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
The computational kernel in solving the SN transport equations is the\nparallel sweep, which corresponds to directly inverting a block lower\ntriangular linear system that arises in discretizations of the linear transport\nequation. Existing parallel sweep algorithms are fairly efficient on structured\ngrids, but still have polynomial scaling, P1/d for d dimensions and P\nprocessors. Moreover, an efficient scalable parallel sweep algorithm for use on\ngeneral unstructured meshes remains elusive. Recently, a classical algebraic\nmultigrid (AMG) method based on approximate ideal restriction (AIR) was\ndeveloped for nonsymmetric matrices and shown to be an effective solver for\nlinear transport. Motivated by the superior scalability of AMG methods\n(logarithmic in P) as well as the simplicity with which AMG methods can be\nused in most situations, including on arbitrary unstructured meshes, this paper\ninvestigates the use of parallel AIR (pAIR) for solving the SN transport\nequations with source iteration in place of parallel sweeps. Results presented\nin this paper show that pAIR is a robust and scalable solver. Although sweeps\nare still shown to be much faster than pAIR on a structured mesh of a unit\ncube, pAIR is shown to perform similarly on both a structured and unstructured\nmesh, and offers a new, simple, black box alternative to parallel transport\nsweeps.\n