Block recursive LU preconditioners for the thermally coupled incompressible inductionless MHD problem

Badia, Santiago; Martı́n, Alberto F.; Planas, Ramón

doi:10.1016/j.jcp.2014.06.028

Cited by 42 publications

(36 citation statements)

References 35 publications

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“…For the 2D case, the fluid movement in the cavity is induced by the imposed boundary condition u = u 0 on the boundary y = 1 ( figure 6.3). The constant background magnetic field is B 0 = (0, 1) T . The velocity field perturbs to the magnetic fields, and the Lorentz force acts on the fluid and changes the motion of the fluid flow.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Robust preconditioners for incompressible MHD models

et al. 2016

Journal of Computational Physics

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ABSTRACT. In this paper, we develop two classes of robust preconditioners for the structurepreserving discretization of the incompressible magnetohydrodynamics (MHD) system. By studying the well-posedness of the discrete system, we design block preconditioners for them and carry out rigorous analysis on their performance. We prove that such preconditioners are robust with respect to most physical and discretization parameters. In our proof, we improve the existing estimates of the block triangular preconditioners for saddle point problems by removing the scaling parameters, which are usually difficult to choose in practice. This new technique is not only applicable to the MHD system, but also to other problems. Moreover, we prove that Krylov iterative methods with our preconditioners preserve the divergence-free condition exactly, which complements the structure-preserving discretization. Another feature is that we can directly generalize this technique to other discretizations of the MHD system. We also present preliminary numerical results to support the theoretical results and demonstrate the robustness of the proposed preconditioners.

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Section: Numerical Experimentsmentioning

confidence: 99%

Robust preconditioners for incompressible MHD models

et al. 2016

Journal of Computational Physics

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“…In conclusion, the SIMPLE iteration (17) transforms the saddled point system (14) into an almost standard FSI equation that can be solved with available techniques plus a small Schur complement equation that can be attacked with a direct solver.…”

Section: Handling Of the Volumetric Constraintsmentioning

confidence: 99%

“…Through such a model, it is possible to simulate both exhalation as well as inhalation.However, coupled models are particularly challenging in a computational point of view. The strong coupling between the underlying physical fields requires monolithic solution schemes [11,12], which are usually more robust and efficient than partitioned methods [13] as it is observed in several applications including bio-mechanics [14][15][16][17][18][19]. Per contra, the monolithic approach results in a large and complex system of linear equations in which all the physical fields are tied together.…”

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confidence: 99%

Efficient solvers for coupled models in respiratory mechanics

Verdugo

Roth

Yoshihara

et al. 2016

Numer Methods Biomed Eng

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We present efficient preconditioners for one of the most physiologically relevant pulmonary models currently available. Our underlying motivation is to enable the efficient simulation of such a lung model on high-performance computing platforms in order to assess mechanical ventilation strategies and contributing to design more protective patient-specific ventilation treatments. The system of linear equations to be solved using the proposed preconditioners is essentially the monolithic system arising in fluid-structure interaction (FSI) extended by additional algebraic constraints. The introduction of these constraints leads to a saddle point problem that cannot be solved with usual FSI preconditioners available in the literature. The key ingredient in this work is to use the idea of the semi-implicit method for pressure-linked equations (SIMPLE) for getting rid of the saddle point structure, resulting in a standard FSI problem that can be treated with available techniques. The numerical examples show that the resulting preconditioners approach the optimal performance of multigrid methods, even though the lung model is a complex multiphysics problem. Moreover, the preconditioners are robust enough to deal with physiologically relevant simulations involving complex real-world patient-specific lung geometries. The same approach is applicable to other challenging biomedical applications where coupling between flow and tissue deformations is modeled with additional algebraic constraints. Copyright © 2016 John Wiley & Sons, Ltd.

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“…The proposed implementation of inexact BDDC methods has been coded in FEMPAR, a massively parallel finite element solver devoted to the LES simulation of incompressible turbulent flows and MHD on unstructured meshes (see [22,23,24,25]). In these problems, the typical approach is to consider a pressure segregation technique (see [26,27]), which leads to a momentum equation that is usually integrated explicitly and a pressure Poisson solver, the bottleneck of these simulations.…”

Section: Motivationmentioning

confidence: 99%

On the scalability of inexact balancing domain decomposition by constraints with overlapped coarse/fine corrections

2015

Self Cite

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In this work, we analyze the scalability of inexact two-level Balancing Domain Decomposition by Constraints (BDDC) preconditioners for Krylov subspace iterative solvers, when using a highly scalable asynchronous parallel implementation where fine and coarse correction computations are overlapped in time. This way, the coarse-grid problem can be fully overlapped by fine-grid computations (which are embarrassingly parallel) in a wide range of cases. Further, we consider inexact solvers to reduce the computational cost/complexity and memory consumption of coarse and local problems and boost the scalability of the solver. Out of our numerical experimentation, we conclude that the BDDC preconditioner is quite insensitive to inexact solvers. In particular, one cycle of algebraic multigrid (AMG) is enough to attain algorithmic scalability. Further, the clear reduction of computing time and memory requirements of inexact solvers compared to sparse direct ones makes possible to scale far beyond state-of-the-art BDDC implementations. Excellent weak scalability results have been obtained with the proposed inexact/overlapped implementation of the two-level BDDC preconditioner, up to 93,312 cores and 20 billion unknowns on JUQUEEN. Further, we have also applied the proposed setting to unstructured meshes and partitions for the pressure Poisson solver in the backward-facing step benchmark domain.

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Block recursive LU preconditioners for the thermally coupled incompressible inductionless MHD problem

Cited by 42 publications

References 35 publications

Robust preconditioners for incompressible MHD models

Robust preconditioners for incompressible MHD models

Efficient solvers for coupled models in respiratory mechanics

On the scalability of inexact balancing domain decomposition by constraints with overlapped coarse/fine corrections

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