A comparative study of scalable multilevel preconditioners for cardiac mechanics

@article{Barnafi2022ACS,
  title={A comparative study of scalable multilevel preconditioners for cardiac mechanics},
  author={Nicolas A. Barnafi and Luca F. Pavarino and Simone Scacchi},
  journal={ArXiv},
  year={2022},
  volume={abs/2208.06191}
}
In this work, we provide a performance comparison between the Balancing Domain Decomposition by Constraints (BDDC) and the Algebraic Multigrid (AMG) preconditioners for cardiac mechanics on both structured and unstructured finite element meshes. The mechanical behavior of myocardium can be described by the equations of three-dimensional finite elasticity, which are discretized by finite elements in space and yield the solution of a large scale nonlinear algebraic system. This problem is solved by… 

References

SHOWING 1-10 OF 51 REFERENCES

A Numerical Study of Scalable Cardiac Electro-Mechanical Solvers on HPC Architectures

The results of several 3D parallel simulations show the scalability of both linear and non-linear solvers and their application to the study of both physiological excitation-contraction cardiac dynamics and re-entrant waves in the presence of different mechano-electrical feedbacks.

A highly parallel implicit domain decomposition method for the simulation of the left ventricle on unstructured meshes

A fully implicit overlapping domain decomposition method on unstructured meshes for the discretized system and shows numerically that the algorithm is highly parallel and robust with respect to the material parameters, the large deformation, the fiber reinforcement, and the geometry of the patient-specific left ventricle.

A robust adaptive algebraic multigrid linear solver for structural mechanics

An Algebraic Multigrid Method for Linear Elasticity

An algebraic multigrid (AMG) method for the efficient solution of linear block-systems stemming from a discretization of a system of partial differential equations (PDEs) is presented and it is shown that the method provides fast convergence for a large variety of discretized elasticity problems.

An Optimal Domain Decomposition Preconditioner for the Finite Element Solution of Linear Elasticity Problems

It is proven that the condition number of the resulting system does not grow as the substructures are made smaller and the mesh is refined, and this result holds for two and three dimensions.

Evaluation of three unstructured multigrid methods on 3D finite element problems in solid mechanics

This paper investigates three unstructured multigrid methods that show promise for challenging problems in 3D elasticity: non‐nested geometric multigrids, smoothed aggregation, and plain aggregation algebraicMultigrid.

Verification of cardiac mechanics software: benchmark problems and solutions for testing active and passive material behaviour

  • S. LandV. Gurev S. Niederer
  • Biology
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2015
These benchmark problems test the ability to accurately simulate pressure-type forces that depend on the deformed objects geometry, anisotropic and spatially varying material properties similar to those seen in the left ventricle and active contractile forces.
...