Preconditioning Techniques in Krylov Subspace Methods

Zina Jabbar Najm

doi:10.47134/ppm.v2i4.2054

Authors

Zina Jabbar Najm University of Mohaghegh Ardabili

DOI:

https://doi.org/10.47134/ppm.v2i4.2054

Keywords:

Krylov Methods, Preconditioning, Conjugate Gradient, Artificial Intelligence

Abstract

This study discusses preconditioning approaches to address large, sparse linear systems as well as Krylov subspace methods. Among others, computational fluid dynamics, structural analysis, and electromagnetic simulations use Krylov methods like the Conjugate Gradient (CG) and Generalized Minimal Residual (GMRES). These techniques use iterative approximations that approach to the solution by projecting the problem onto a Krylov subspace. The efficiency of Krylov methods is greatly influenced by the selection of preconditions, which help the system's conditioning and so accelerate convergence. Jacobi Preconditioning, Incomplete LU Decomposition (ILU), and Multigrid Preconditioning are examples of preconditioning techniques. Though it has advantages, preconditioning has disadvantages including choosing the proper conditions and controlling memory and costing calculations. Further investigated were possible changes including adaptive and nonlinear preconditioning as well as the integration of Artificial Intelligence

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