An extreme-scale implicit solver for complex PDEs

Rudi, Johann; Malossi, A. Cristiano I.; Isaac, Tobin; Stadler, Georg; Gurnis, Michael; Staar, Peter; Ineichen, Yves; Bekas, Costas; Curioni, A.; Ghattas, Omar

doi:10.1145/2807591.2807675

Cited by 103 publications

(32 citation statements)

References 29 publications

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“…This greatly increases model run time and therefore it is important to implement a more efficient nonlinear solving strategy than the Picard iterations currently used by ASPECT. The more sophisticated Newton solver (see for example Popov and Sobolev, 2008;May et al, 2015;Rudi et al, 2015;Kaus et al, 2016;Wilson et al, 2017) will help achieve faster convergence. Convergence behavior has also been suggested to improve from including elasticity (Kaus, 2010), but especially dynamic pressure-dependent plasticity remains difficult to converge for both Picard iterations and Newton solvers (Spiegelman et al, 2016).…”

Section: Discussionmentioning

confidence: 99%

Nonlinear viscoplasticity in ASPECT: benchmarking and applications to subduction

et al. 2018

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Abstract. ASPECT (Advanced Solver for Problems in Earth's ConvecTion) is a massively parallel finite element code originally designed for modeling thermal convection in the mantle with a Newtonian rheology. The code is characterized by modern numerical methods, high-performance parallelism and extensibility. This last characteristic is illustrated in this work: we have extended the use of ASPECT from global thermal convection modeling to upper-mantle-scale applications of subduction.Subduction modeling generally requires the tracking of multiple materials with different properties and with nonlinear viscous and viscoplastic rheologies. To this end, we implemented a frictional plasticity criterion that is combined with a viscous diffusion and dislocation creep rheology. Because ASPECT uses compositional fields to represent different materials, all material parameters are made dependent on a user-specified number of fields.The goal of this paper is primarily to describe and verify our implementations of complex, multi-material rheology by reproducing the results of four well-known two-dimensional benchmarks: the indentor benchmark, the brick experiment, the sandbox experiment and the slab detachment benchmark. Furthermore, we aim to provide hands-on examples for prospective users by demonstrating the use of multi-material viscoplasticity with three-dimensional, thermomechanical models of oceanic subduction, putting ASPECT on the map as a community code for high-resolution, nonlinear rheology subduction modeling.

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Section: Discussionmentioning

confidence: 99%

Nonlinear viscoplasticity in ASPECT: benchmarking and applications to subduction

et al. 2018

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“…Multigrid is known for its mesh-independent convergence and optimal complexity in the number of unknowns Hackbusch (1985); Brandt and Diskin (1994). Therefore, parallel multigrid is of a special interest for large scale high-performance computations, Gmeiner et al (2016); Notay and Napov (2015); Sundar et al (2012); Rudi et al (2015). The mesh hierarchy T introduced in Section 2.1 is used to construct a geometric multigrid solver with its coarsest level for = 0 and finest level for = L. In order to solve the algebraic equation A L u L = f L associated with the finest mesh, we apply multigrid V-cycles; see, e.g, (Hackbusch, 1985, Algorithm (2.5.4)).…”

Section: Solver Setupmentioning

confidence: 99%

Adaptive control in roll-forward recovery for extreme scale multigrid

Huber

Rüde

Wohlmuth

2018

The International Journal of High Performance Computing Applica

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With the increasing number of compute components, failures in future exa-scale computer systems are expected to become more frequent. This motivates the study of novel resilience techniques. Here, we extend a recently proposed algorithm-based recovery method for multigrid iterations by introducing an adaptive control. After a fault, the healthy part of the system continues the iterative solution process, while the solution in the faulty domain is re-constructed by an asynchronous on-line recovery. The computations in both the faulty and healthy subdomains must be coordinated in a sensitive way, in particular, both under and over-solving must be avoided. Both of these waste computational resources and will therefore increase the overall time-to-solution. To control the local recovery and guarantee an optimal re-coupling, we introduce a stopping criterion based on a mathematical error estimator. It involves hierarchical weighted sums of residuals within the context of uniformly refined meshes and is well-suited in the context of parallel high-performance computing. The re-coupling process is steered by local contributions of the error estimator. We propose and compare two criteria which differ in their weights. Failure scenarios when solving up to 6.9 · 10 11 unknowns on more than 245 766 parallel processes will be reported on a state-of-the-art peta-scale supercomputer demonstrating the robustness of the method.

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“…For example, in [16], an Earth's mantle convection flow solver based on highorder continuous/discontinuous finite elements with octree-based adaptive mesh refinement and coarsening (AMR/C) is reported to scale up to 1.5 million processor cores such strategy. The referred paper won the prestigious Gordon Bell prize in 2015.…”

Section: Introductionmentioning

confidence: 99%

A scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problem

Côrtes

Dalcín

Sarmiento

et al. 2017

Computer Methods in Applied Mechanics and Engineering

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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractThe recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity-pressure pairs for viscous incompressible flows that are at the same time inf − sup stable and pointwise divergence-free. When applied to the discretized Stokes problem, these spaces generate a symmetric and indefinite saddle-point linear system. The iterative method of choice to solve such system is the Generalized Minimum Residual Method. This method lacks robustness, and one remedy is to use preconditioners. For linear systems of saddle-point type, a large family of preconditioners can be obtained by using a block factorization of the system. In this paper, we show how the nesting of "black-box" solvers and preconditioners can be put together in a block triangular strategy to build a scalable block preconditioner for the Stokes system discretized by divergence-conforming B-splines. Besides the known cavity flow problem, we used for benchmark flows defined on complex geometries: an eccentric annulus and hollow torus of an eccentric annular cross-section.

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An extreme-scale implicit solver for complex PDEs

Cited by 103 publications

References 29 publications

Nonlinear viscoplasticity in ASPECT: benchmarking and applications to subduction

Nonlinear viscoplasticity in ASPECT: benchmarking and applications to subduction

Adaptive control in roll-forward recovery for extreme scale multigrid

A scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problem

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