Variable Preconditioning of Krylov Subspace Methods for Hierarchical Matrices With Adaptive Cross Approximation

• Published in: IEEE transactions on magnetics Vol. 52; no. 3; pp. 1 - 4
• Main Authors: Ida, Akihiro, Iwashita, Takeshi, Mifune, Takeshi, Takahashi, Yasuhito
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Approximation; Approximation algorithms; Approximation methods; Conductors; Convergence; Electrostatic fields; Electrostatic processes; Iterative algorithms; Linear systems; Magnetism; Mathematical analysis; Mathematical models; Matrix decomposition; Numerical analysis; Preconditioning; Sparse matrices; Subspace methods; Approximation algorithms; linear systems; electrostatic processes; numerical analysis; iterative algorithms
• ISSN: 0018-9464; 1941-0069
• DOI: 10.1109/TMAG.2015.2464104

This paper discusses Krylov subspace methods to solve a linear system whose coefficient matrix is represented by a hierarchical matrix. We propose a preconditioning technique using a part of the original hierarchical matrix to accelerate the convergence of the Krylov subspace methods. The proposed preconditioning technique is based on the assumption that the submatrices on the original hierarchical matrix are approximated using the adaptive cross approximation or variants thereof. The performance of Krylov subspace methods with the proposed preconditioning technique is examined through numerical experiments on an electrostatic field analysis.