NEW OPTIMIZED ROBIN−ROBIN DOMAIN DECOMPOSITION METHODS USING KRYLOV SOLVERS FOR THE STOKES−DARCY SYSTEM

Yingzhi Liu; Yassine Boubendir; Xiaoming He; Yinnian He

doi:10.1137/21M1417223

NEW OPTIMIZED ROBIN−ROBIN DOMAIN DECOMPOSITION METHODS USING KRYLOV SOLVERS FOR THE STOKES−DARCY SYSTEM

Yingzhi Liu, Yassine Boubendir, Xiaoming He, Yinnian He

Mathematical Sciences

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

9 Scopus citations

Abstract

In this paper, we are interested in the design of optimized Schwarz domain decomposition algorithms to accelerate the Krylov type solution for the Stokes−Darcy system. We use particular solutions of this system on a circular geometry to analyze the iteration operator mode by mode. We introduce a new optimization strategy of the so-called Robin parameters based on a specific linear relation between these parameters, using the min-max and the expectation minimization approaches. Moreover, we use a Krylov solver to deal with the iteration operator and accelerate this new optimized domain decomposition algorithm. Several numerical experiments are provided to validate the effectiveness of this new method.

Original language	English (US)
Journal	SIAM Journal on Scientific Computing
Volume	44
Issue number	4
DOIs	https://doi.org/10.1137/21M1417223
State	Published - 2022

All Science Journal Classification (ASJC) codes

Computational Mathematics
Applied Mathematics

Keywords

Krylov solvers
Robin interface conditions
Stokes−Darcy system
domain decomposition methods
modal analysis
optimized Schwarz methods

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10.1137/21M1417223

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title = "NEW OPTIMIZED ROBIN−ROBIN DOMAIN DECOMPOSITION METHODS USING KRYLOV SOLVERS FOR THE STOKES−DARCY SYSTEM",

abstract = "In this paper, we are interested in the design of optimized Schwarz domain decomposition algorithms to accelerate the Krylov type solution for the Stokes−Darcy system. We use particular solutions of this system on a circular geometry to analyze the iteration operator mode by mode. We introduce a new optimization strategy of the so-called Robin parameters based on a specific linear relation between these parameters, using the min-max and the expectation minimization approaches. Moreover, we use a Krylov solver to deal with the iteration operator and accelerate this new optimized domain decomposition algorithm. Several numerical experiments are provided to validate the effectiveness of this new method.",

keywords = "Krylov solvers, Robin interface conditions, Stokes−Darcy system, domain decomposition methods, modal analysis, optimized Schwarz methods",

author = "Yingzhi Liu and Yassine Boubendir and Xiaoming He and Yinnian He",

note = "Publisher Copyright: {\textcopyright} 2022 Society for Industrial and Applied Mathematics.",

year = "2022",

doi = "10.1137/21M1417223",

language = "English (US)",

volume = "44",

journal = "SIAM Journal on Scientific Computing",

issn = "1064-8275",

publisher = "Society for Industrial and Applied Mathematics Publications",

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T1 - NEW OPTIMIZED ROBIN−ROBIN DOMAIN DECOMPOSITION METHODS USING KRYLOV SOLVERS FOR THE STOKES−DARCY SYSTEM

AU - Liu, Yingzhi

AU - Boubendir, Yassine

AU - He, Xiaoming

AU - He, Yinnian

PY - 2022

Y1 - 2022

N2 - In this paper, we are interested in the design of optimized Schwarz domain decomposition algorithms to accelerate the Krylov type solution for the Stokes−Darcy system. We use particular solutions of this system on a circular geometry to analyze the iteration operator mode by mode. We introduce a new optimization strategy of the so-called Robin parameters based on a specific linear relation between these parameters, using the min-max and the expectation minimization approaches. Moreover, we use a Krylov solver to deal with the iteration operator and accelerate this new optimized domain decomposition algorithm. Several numerical experiments are provided to validate the effectiveness of this new method.

AB - In this paper, we are interested in the design of optimized Schwarz domain decomposition algorithms to accelerate the Krylov type solution for the Stokes−Darcy system. We use particular solutions of this system on a circular geometry to analyze the iteration operator mode by mode. We introduce a new optimization strategy of the so-called Robin parameters based on a specific linear relation between these parameters, using the min-max and the expectation minimization approaches. Moreover, we use a Krylov solver to deal with the iteration operator and accelerate this new optimized domain decomposition algorithm. Several numerical experiments are provided to validate the effectiveness of this new method.

KW - Krylov solvers

KW - Robin interface conditions

KW - Stokes−Darcy system

KW - domain decomposition methods

KW - modal analysis

KW - optimized Schwarz methods

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DO - 10.1137/21M1417223

M3 - Article

AN - SCOPUS:85140078467

SN - 1064-8275

VL - 44

JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

IS - 4

ER -

NEW OPTIMIZED ROBIN−ROBIN DOMAIN DECOMPOSITION METHODS USING KRYLOV SOLVERS FOR THE STOKES−DARCY SYSTEM

Abstract

All Science Journal Classification (ASJC) codes

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