MueLu User's Guide

Berger-Vergiat, Luc; Glusa, Christian; Hu, Jonathan J.; Siefert, Christopher; Tuminaro, Raymond S.; Matthias, Mayr; Prokopenko, Andrey; Tobias, Wiesner

doi:10.2172/1491860

Cited by 33 publications

(33 citation statements)

References 6 publications

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“…The block smoothing methods and their cheap variants are available in the Xpetra package of the Trilinos project. 83 For further details on the implementation, we refer to the MueLu user's guide 82 and the MueLu and Xpetra websites, 84,92 respectively.…”

Section: Cheap Variants Of Block Smoothersmentioning

confidence: 99%

“…The coarsening strategy outlined in Algorithm 1 as well as all other AMG components of the presented saddle-point preconditioner for contact problems have been implemented in MueLu, 82 the next-generation multigrid package within the Trilinos project. 83 For further details on the implementation, we refer to the MueLu user's guide 82 and the MueLu website. 84…”

Section: Return Aggregates For Lagrange Multipliers Returnmentioning

confidence: 99%

“…83 The implementation of the multigrid algorithms is based on Trilinos' MueLu package. 82,95 In particular, all block smoothers from Section 5 as well as the contact specific aggregation strategy for the Lagrange multiplier unknowns as described in Section 4 are readily available in MueLu.…”

Section: Numerical Examplesmentioning

confidence: 99%

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Algebraic multigrid methods for saddle point systems arising from mortar contact formulations

Wiesner¹,

Mayr

Popp

et al. 2021

Numerical Meth Engineering

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In this article, a fully aggregation-based algebraic multigrid strategy is developed for nonlinear contact problems of saddle point type using a mortar finite element approach. While the idea of extending multigrid methods to saddle point systems can already be found, for example, in the context of Stokes and Oseen equations in literature, the main contributions of this work are (i) the development and open-source implementation of an interface aggregation strategy specifically suited for generating Lagrange multiplier aggregates that are required for coupling structural equilibrium equations with contact constraints and (ii) a review of saddle point smoothers in the context of constrained interface problems. The new interface aggregation strategy perfectly fits into an aggregation-based multigrid framework and can easily be combined with segregated transfer operators, which allow to preserve the saddle point structure on the coarse levels. Further analysis provides insight into saddle point smoothers applied to contact problems, while numerical experiments illustrate the robustness of the new method.We have implemented the proposed algorithm within the MueLu package of the open-source Trilinos project. Numerical examples demonstrate the robustness of the proposed method in complex dynamic contact problems as well as its scalability up to 23.9 million unknowns on 480 MPI ranks.

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Section: Cheap Variants Of Block Smoothersmentioning

confidence: 99%

Section: Return Aggregates For Lagrange Multipliers Returnmentioning

confidence: 99%

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Algebraic multigrid methods for saddle point systems arising from mortar contact formulations

Wiesner¹,

Mayr

Popp

et al. 2021

Numerical Meth Engineering

Self Cite

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“…To achieve this in EMPIRE-PIC we use the traditional Krylov iterative methods provided by the Belos Trilinos package [8]. The MueLu Trilinos package is used in conjunction with Belos to provide an Algebraic Multigrid (AMG) preconditioner [10]. The Belos and MueLu packages both make full use of MPI and Kokkos in order to achieve performance both on a single node and at scale.…”

Section: Field Solvermentioning

confidence: 99%

EMPIRE-PIC: A Performance Portable Unstructured Particle-in-Cell Code

sci¹

2021

CICP

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In this paper we introduce EMPIRE-PIC, a finite element method particlein-cell (FEM-PIC) application developed at Sandia National Laboratories. The code has been developed in C++ using the Trilinos library and the Kokkos Performance Portability Framework to enable running on multiple modern compute architectures while only requiring maintenance of a single codebase. EMPIRE-PIC is capable of solving both electrostatic and electromagnetic problems in two-and three-dimensions to second-order accuracy in space and time. In this paper we validate the code against three benchmark problems -a simple electron orbit, an electrostatic Langmuir wave, and a transverse electromagnetic wave propagating through a plasma. We demonstrate the performance of EMPIRE-PIC on four different architectures: Intel Haswell CPUs, Intel's Xeon Phi Knights Landing, ARM Thunder-X2 CPUs, and NVIDIA Tesla V100 GPUs attached to IBM POWER9 processors. This analysis demonstrates scalability of the code up to more than two thousand GPUs, and greater than one hundred thousand CPUs.

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“…Starting from the ideas in [6], an extension to the monolithic coupling of an arbitrary number of fields is detailed in [17]. An open-source implementation by Wiesner et al [18] makes such block AMG preconditioners available via the MueLu package [19,20] of the Trilinos library. 1 Heil [7] and Heil et al [4] use block-triangular approximations to the full Jacobian as preconditioner.…”

Section: Introductionmentioning

confidence: 99%

A hybrid interface preconditioner for monolithic fluid–structure interaction solvers

Mayr

Noll

Gee

2020

Adv. Model. and Simul. in Eng. Sci.

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We propose a hybrid interface preconditioner for the monolithic solution of surface-coupled problems. Powerful preconditioning techniques are crucial when it comes to solving large monolithic systems of linear equations efficiently, especially when arising from coupled multi-physics problems like in fluid–structure interaction. Existing physics-based block preconditioners have proven to be efficient, but their error assessment reveals an accumulation of the error at the coupling surface. We address this issue by combining them with an additional additive Schwarz preconditioner, whose subdomains span across the interface on purpose. By performing cheap but accurate subdomain solves that do not depend on the separation of physical fields, this error accumulation can be reduced effectively. Numerical experiments compare the performance of the hybrid preconditioner to existing approaches, demonstrate the increased efficiency, and study its parallel performance.

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MueLu User's Guide

Cited by 33 publications

References 6 publications

Algebraic multigrid methods for saddle point systems arising from mortar contact formulations

Algebraic multigrid methods for saddle point systems arising from mortar contact formulations

EMPIRE-PIC: A Performance Portable Unstructured Particle-in-Cell Code

A hybrid interface preconditioner for monolithic fluid–structure interaction solvers

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