Parallel Matrix-free polynomial preconditioners with application to flow simulations in discrete fracture networks

@article{Bergamaschi2022ParallelMP,
  title={Parallel Matrix-free polynomial preconditioners with application to flow simulations in discrete fracture networks},
  author={Luca Bergamaschi and Massimiliano Ferronato and Giovanni Isotton and Carlo Janna and {\'A}ngeles Mart{\'i}nez},
  journal={ArXiv},
  year={2022},
  volume={abs/2208.01339}
}
. We develop a robust matrix-free, communication avoiding parallel, high-degree polynomial preconditioner for the Conjugate Gradient method for large and sparse symmetric positive definite linear systems.We discuss the selection of a scaling parameter aimed at avoiding unwanted clustering of eigenvalues of the preconditioned matrices at the extrema of the spectrum. We use this preconditioned framework to solve a 3 × 3 block system arising in the simulation of fluid flow in large-size discrete… 

References

SHOWING 1-10 OF 33 REFERENCES

Numerical investigation on a block preconditioning strategy to improve the computational efficiency of DFN models

This work focuses on accelerating the iterative solution of the system with matrix K by introducing effective block preconditioning techniques and solving inexactly the projected matrix by either an explicit or a matrix-free approach.

A Survey of Low-Rank Updates of Preconditioners for Sequences of Symmetric Linear Systems

This paper will analyze a number of techniques of updating a given initial preconditioner by a low-rank matrix with the aim of improving the clustering of eigenvalues around 1, in order to speed-up the convergence of the Preconditioned Conjugate Gradient (PCG) method.

Polynomial Preconditioned GMRES in Trilinos: Practical Considerations for High-Performance Computing

The GMRES polynomial is implemented as a preconditioner in the software library Trilinos and it is demonstrated that it is stable and effective for parallel computing.

Polynomial Preconditioned Arnoldi with Stability Control

Polynomial preconditioning can improve the convergence of the Arnoldi method for computing eigenvalues. Such preconditioning significantly reduces the cost of orthogonalization; for difficult

A Class of Spectral Two-Level Preconditioners

This paper proposes a class of preconditioners both for unsymmetric and for symmetric linear systems that can also be adapted for asymmetric positive definite problems and shows the advantages of the preconditionsers for solving dense linear systems arising in electromagnetism applications.

Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method

A variant of the AINV factorized sparse approximate inverse algorithm which is applicable to any symmetric positive definite matrix and the new preconditioner is breakdown-free and results in a reliable solver for highly ill-conditioned linear systems.

Parallel Newton-Chebyshev Polynomial Preconditioners for the Conjugate Gradient method

This note exploits polynomial preconditioners for the Conjugate Gradient method to solve large symmetric positive definite linear systems in a parallel environment and proposes a simple modification of one parameter which avoids clustering of extremal eigenvalues in order to speed up convergence.

Using Chebyshev polynomials and approximate inverse triangular factorizations for preconditioning the conjugate gradient method

The use of polynomial preconditioning based on Chebyshev polynomials makes it possible to considerably reduce the amount of scalar product operations (at the cost of an insignificant increase in the total number of arithmetic operations).

Approximate inverse-based block preconditioners in poroelasticity

This work investigates the use of approximate inverse-based techniques to decouple the native system of equations and obtain explicit sparse approximations of the Schur complements related to the physics-based partitioning of the unknowns by field type.