Volume 19, Issue 6
A Class of New Parallel Hybrid Algebraic Multilevel Iterations

Zhong Zhi Bai

DOI:

J. Comp. Math., 19 (2001), pp. 651-672

Published online: 2001-12

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  • Abstract

For the large sparse system of linear equations with symmetric positive definite block coefficient matrix resulted from suitable finite element discretization of the second-order self-adjoint elliptic boundary value problem, by making use of the algebraic multilevel iteration technique and the blocked preconditioning strategy, we construct preconditioning matrices having parallel computing function for the coefficient matrix and set up a class of parallel hybrid algebraic multilevel iteration methods for solving this kind of system of linear equations. Theoretical analyses show that, besides much suitable for implementing on the high-speed parallel multiprocessor systems, these new methods are optimal-order methods. That is to say, their convergence rates are independent of both the sizes and the levels of the constructed matrix sequence, and the computational workloads are bounded by linear functions in the order number of the considered system of linear equations, respectively.

  • Keywords

Elliptic boundary value problem System of linear equations Symmetric positive definite

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@Article{JCM-19-651, author = {}, title = {A Class of New Parallel Hybrid Algebraic Multilevel Iterations}, journal = {Journal of Computational Mathematics}, year = {2001}, volume = {19}, number = {6}, pages = {651--672}, abstract = { For the large sparse system of linear equations with symmetric positive definite block coefficient matrix resulted from suitable finite element discretization of the second-order self-adjoint elliptic boundary value problem, by making use of the algebraic multilevel iteration technique and the blocked preconditioning strategy, we construct preconditioning matrices having parallel computing function for the coefficient matrix and set up a class of parallel hybrid algebraic multilevel iteration methods for solving this kind of system of linear equations. Theoretical analyses show that, besides much suitable for implementing on the high-speed parallel multiprocessor systems, these new methods are optimal-order methods. That is to say, their convergence rates are independent of both the sizes and the levels of the constructed matrix sequence, and the computational workloads are bounded by linear functions in the order number of the considered system of linear equations, respectively. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9017.html} }
TY - JOUR T1 - A Class of New Parallel Hybrid Algebraic Multilevel Iterations JO - Journal of Computational Mathematics VL - 6 SP - 651 EP - 672 PY - 2001 DA - 2001/12 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9017.html KW - Elliptic boundary value problem KW - System of linear equations KW - Symmetric positive definite AB - For the large sparse system of linear equations with symmetric positive definite block coefficient matrix resulted from suitable finite element discretization of the second-order self-adjoint elliptic boundary value problem, by making use of the algebraic multilevel iteration technique and the blocked preconditioning strategy, we construct preconditioning matrices having parallel computing function for the coefficient matrix and set up a class of parallel hybrid algebraic multilevel iteration methods for solving this kind of system of linear equations. Theoretical analyses show that, besides much suitable for implementing on the high-speed parallel multiprocessor systems, these new methods are optimal-order methods. That is to say, their convergence rates are independent of both the sizes and the levels of the constructed matrix sequence, and the computational workloads are bounded by linear functions in the order number of the considered system of linear equations, respectively.
Zhong Zhi Bai. (1970). A Class of New Parallel Hybrid Algebraic Multilevel Iterations. Journal of Computational Mathematics. 19 (6). 651-672. doi:
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