Design Considerations for a Flexible Multigrid Preconditioning Library

Abstract

MueLu is a library within the Trilinos software project [An overview of Trilinos, Technical Report SAND2003-2927, Sandia National Laboratories, 2003] and provides a framework for parallel multigrid preconditioning methods for large sparse linear systems. While providing efficient implementations of modern multigrid methods based on smoothed aggregation and energy minimization concepts, MueLu is designed to be customized and extended. This article gives an overview of design considerations for the MueLu package: user interfaces, internal design, data management, usage of modern software constructs, leveraging Trilinos capabilities, linear algebra operations and advanced application. J. Gaidamour et al. / Design considerations for a flexible multigrid preconditioning library // Linear problem RCP< Tpetra::CrsMatrix<double> > A = ...; // Scalar matrix // MueLu operator. Default view is 'point' (1x1 block) RCP< MueLu::Operator > Op = rcp (new CrsOperator(A)); // Create a 2x2 block representation of the matrix Op.CreateConstBlkView("2x2", 2, 2); // The 2x2 can be used everywhere by default by using: // Op.SetDefaultView('2x2'); // Alternatively, it can be done on a case by case basis: // Multigrid hierarchy Hierarchy H(Op); // The 2x2 block view is used during the aggregation andSaPFactory aggregationFact = rcp(new UCAggregationFactory()); tentativePFact = rcp(new TentativePFactory(aggregationFact)); prolongationFact = rcp(new SaPFactory(tentativePFact)); prolongationFact->SetDiagonalView("2x2"); prolongationFact->SetView("2x2");

Towards Extreme-Scale Simulations for Low Mach Fluids with Second-Generation Trilinos

“…Solves for all equations other than the pressure Poisson equation (PPE) were preconditioned using Ifpack2's symmetric Gauss-Seidel preconditioner. For the PPE, Nalu used MueLu's [13] algebraic multigrid preconditioner with If-pack2's Chebyshev smoother on all levels except for the coarsest, which used the SuperLU direct solver through the Amesos2 interface [11]. To improve efficiency of the multigrid preconditioner, MueLu rebalances its coarser levels using Zoltan2's multijagged algorithm [18].…”

Tolerating Silent Data Corruption in Opaque Preconditioners

“…This matters because preconditioners are often orders of magnitude more complex than the iterative solvers that utilize them, in terms of both algorithms and lines of code. For example, one can express CG in a dozen lines of code, but the algebraic multigrid implementation MueLu [7] we use in this work includes over half a million lines of code from several Trilinos packages, as of the 11.8 Trilinos release, not counting thirdparty sparse direct factorization libraries for coarse-grid solves.…”