A Class of Symmetric Factored Approximate Inverses and Hybrid Two-Level Solver

Panagiotis E. Kyziropoulos; Christos K. Filelis-Papadopoulos; George A. Gravvanis

doi:10.1142/S0219876218500500

A Class of Symmetric Factored Approximate Inverses and Hybrid Two-Level Solver

Panagiotis E. Kyziropoulos
, Christos K. Filelis-Papadopoulos
, George A. Gravvanis

Democritus University of Thrace

Research output: Contribution to journal › Article › peer-review

Abstract

A new class of symmetric factored approximate inverses is proposed and used in conjunction with the Preconditioned Conjugate Gradient method for solving sparse symmetric linear systems. Additionally, a new hybrid two-level solver is proposed utilizing a block independent set reordering, in order to create the two level hierarchy. The Schur complement is formed explicitly by inverting the blocks created by reordering. Then, the preconditioned conjugate gradient method is used in conjunction with the symmetric factored approximate inverse to solve the reduced order linear system. Furthermore, numerical results on the performance and convergence behavior for solving various model problems are presented.

Original language	English
Article number	1850050
Journal	International Journal of Computational Methods
Volume	15
Issue number	6
DOIs	https://doi.org/10.1142/S0219876218500500
Publication status	Published - 1 Sep 2018
Externally published	Yes

Keywords

Multilevel algorithms
Preconditioned conjugate gradient
Symmetric factored approximate sparse inverses
Two level algebraic symmetric factored approximate inverse solver

Access to Document

10.1142/S0219876218500500

Cite this

@article{bbc3561059f44aaf87b241b3f53731df,

title = "A Class of Symmetric Factored Approximate Inverses and Hybrid Two-Level Solver",

abstract = "A new class of symmetric factored approximate inverses is proposed and used in conjunction with the Preconditioned Conjugate Gradient method for solving sparse symmetric linear systems. Additionally, a new hybrid two-level solver is proposed utilizing a block independent set reordering, in order to create the two level hierarchy. The Schur complement is formed explicitly by inverting the blocks created by reordering. Then, the preconditioned conjugate gradient method is used in conjunction with the symmetric factored approximate inverse to solve the reduced order linear system. Furthermore, numerical results on the performance and convergence behavior for solving various model problems are presented.",

keywords = "Multilevel algorithms, Preconditioned conjugate gradient, Symmetric factored approximate sparse inverses, Two level algebraic symmetric factored approximate inverse solver",

author = "Kyziropoulos, \{Panagiotis E.\} and Filelis-Papadopoulos, \{Christos K.\} and Gravvanis, \{George A.\}",

note = "Publisher Copyright: {\textcopyright} 2018 World Scientific Publishing Company.",

year = "2018",

month = sep,

day = "1",

doi = "10.1142/S0219876218500500",

language = "English",

volume = "15",

journal = "International Journal of Computational Methods",

issn = "0219-8762",

publisher = "World Scientific",

number = "6",

}

TY - JOUR

T1 - A Class of Symmetric Factored Approximate Inverses and Hybrid Two-Level Solver

AU - Kyziropoulos, Panagiotis E.

AU - Filelis-Papadopoulos, Christos K.

AU - Gravvanis, George A.

PY - 2018/9/1

Y1 - 2018/9/1

N2 - A new class of symmetric factored approximate inverses is proposed and used in conjunction with the Preconditioned Conjugate Gradient method for solving sparse symmetric linear systems. Additionally, a new hybrid two-level solver is proposed utilizing a block independent set reordering, in order to create the two level hierarchy. The Schur complement is formed explicitly by inverting the blocks created by reordering. Then, the preconditioned conjugate gradient method is used in conjunction with the symmetric factored approximate inverse to solve the reduced order linear system. Furthermore, numerical results on the performance and convergence behavior for solving various model problems are presented.

AB - A new class of symmetric factored approximate inverses is proposed and used in conjunction with the Preconditioned Conjugate Gradient method for solving sparse symmetric linear systems. Additionally, a new hybrid two-level solver is proposed utilizing a block independent set reordering, in order to create the two level hierarchy. The Schur complement is formed explicitly by inverting the blocks created by reordering. Then, the preconditioned conjugate gradient method is used in conjunction with the symmetric factored approximate inverse to solve the reduced order linear system. Furthermore, numerical results on the performance and convergence behavior for solving various model problems are presented.

KW - Multilevel algorithms

KW - Preconditioned conjugate gradient

KW - Symmetric factored approximate sparse inverses

KW - Two level algebraic symmetric factored approximate inverse solver

UR - https://www.scopus.com/pages/publications/85052879442

U2 - 10.1142/S0219876218500500

DO - 10.1142/S0219876218500500

M3 - Article

AN - SCOPUS:85052879442

SN - 0219-8762

VL - 15

JO - International Journal of Computational Methods

JF - International Journal of Computational Methods

IS - 6

M1 - 1850050

ER -

A Class of Symmetric Factored Approximate Inverses and Hybrid Two-Level Solver

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this