PiTSBiCG: Parallel in time Stable Bi-Conjugate gradient algorithm

Mohamed Kamel Riahi

doi:10.1016/j.apnum.2022.06.004

PiTSBiCG: Parallel in time Stable Bi-Conjugate gradient algorithm

Mohamed Kamel Riahi

Mathematics

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4 Scopus citations

Abstract

This paper presents a new algorithm for the parallel in time (PiT) numerical simulation of time dependent partial/ordinary differential equations. We propose a reliable alternative to the well know parareal in time algorithm, by formulating the parallel in time problem algebraically and solve it using an adapted Bi-Conjugate gradient stabilized method. The proposed Parallel in time Stable Bi-Conjugate algorithm (PiTSBiCG for short) has a great potential to stabilizing the parallel resolution for a variety of problems. In this work, we describe the mathematical approach to the new algorithm and provide numerical evidence that shows its superiority to the standard parareal method.

Original language	British English
Pages (from-to)	225-233
Number of pages	9
Journal	Applied Numerical Mathematics
Volume	181
DOIs	https://doi.org/10.1016/j.apnum.2022.06.004
State	Published - Nov 2022

Keywords

Acceleration
BiCGStab
Krylov methods
Numerical simulation of PDEs
Parallel computing
Parallel in time algorithm
Parareal

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10.1016/j.apnum.2022.06.004

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title = "PiTSBiCG: Parallel in time Stable Bi-Conjugate gradient algorithm",

abstract = "This paper presents a new algorithm for the parallel in time (PiT) numerical simulation of time dependent partial/ordinary differential equations. We propose a reliable alternative to the well know parareal in time algorithm, by formulating the parallel in time problem algebraically and solve it using an adapted Bi-Conjugate gradient stabilized method. The proposed Parallel in time Stable Bi-Conjugate algorithm (PiTSBiCG for short) has a great potential to stabilizing the parallel resolution for a variety of problems. In this work, we describe the mathematical approach to the new algorithm and provide numerical evidence that shows its superiority to the standard parareal method.",

keywords = "Acceleration, BiCGStab, Krylov methods, Numerical simulation of PDEs, Parallel computing, Parallel in time algorithm, Parareal",

author = "Riahi, \{Mohamed Kamel\}",

note = "Funding Information: The author would like to thank the anonymous reviewers for their valuable comments and remarks that helped in producing a better version of the manuscript. Publisher Copyright: {\textcopyright} 2022 The Author",

year = "2022",

month = nov,

doi = "10.1016/j.apnum.2022.06.004",

language = "British English",

volume = "181",

pages = "225--233",

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T2 - Parallel in time Stable Bi-Conjugate gradient algorithm

AU - Riahi, Mohamed Kamel

N1 - Funding Information: The author would like to thank the anonymous reviewers for their valuable comments and remarks that helped in producing a better version of the manuscript. Publisher Copyright: © 2022 The Author

PY - 2022/11

Y1 - 2022/11

N2 - This paper presents a new algorithm for the parallel in time (PiT) numerical simulation of time dependent partial/ordinary differential equations. We propose a reliable alternative to the well know parareal in time algorithm, by formulating the parallel in time problem algebraically and solve it using an adapted Bi-Conjugate gradient stabilized method. The proposed Parallel in time Stable Bi-Conjugate algorithm (PiTSBiCG for short) has a great potential to stabilizing the parallel resolution for a variety of problems. In this work, we describe the mathematical approach to the new algorithm and provide numerical evidence that shows its superiority to the standard parareal method.

AB - This paper presents a new algorithm for the parallel in time (PiT) numerical simulation of time dependent partial/ordinary differential equations. We propose a reliable alternative to the well know parareal in time algorithm, by formulating the parallel in time problem algebraically and solve it using an adapted Bi-Conjugate gradient stabilized method. The proposed Parallel in time Stable Bi-Conjugate algorithm (PiTSBiCG for short) has a great potential to stabilizing the parallel resolution for a variety of problems. In this work, we describe the mathematical approach to the new algorithm and provide numerical evidence that shows its superiority to the standard parareal method.

KW - Acceleration

KW - BiCGStab

KW - Krylov methods

KW - Numerical simulation of PDEs

KW - Parallel computing

KW - Parallel in time algorithm

KW - Parareal

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DO - 10.1016/j.apnum.2022.06.004

M3 - Article

AN - SCOPUS:85132505838

SN - 0168-9274

VL - 181

SP - 225

EP - 233

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

PiTSBiCG: Parallel in time Stable Bi-Conjugate gradient algorithm

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