Comparison of three accelerated FFT-based schemes for computing the mechanical response of composite materials
SUMMARYSince the early 1990s when an iterative method based on Fourier transforms was introduced to compute the mechanical properties of heterogeneous materials, several algorithms have been proposed to increase the convergence rate of the initial scheme. This paper is devoted to the comparison of t...
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| Veröffentlicht in: | International journal for numerical methods in engineering 2014-03, Vol.97 (13), p.960-985 |
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| container_title | International journal for numerical methods in engineering |
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| creator | Moulinec, H. Silva, F. |
| description | SUMMARYSince the early 1990s when an iterative method based on Fourier transforms was introduced to compute the mechanical properties of heterogeneous materials, several algorithms have been proposed to increase the convergence rate of the initial scheme. This paper is devoted to the comparison of three of these accelerated schemes. It shows that two of them are special cases of the third, corresponding to particular choices of parameters of the method. An upper bound of the spectral radius of the schemes is determined, from which sufficient conditions of convergence of the schemes are derived. Conditions are found for minimizing this upper bound. In particular, the accelerated scheme, which minimizes this upper bound, is exhibited. The paper discusses the choice of the convergence test used in the schemes. Copyright © 2013 John Wiley & Sons, Ltd. |
| doi_str_mv | 10.1002/nme.4614 |
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This paper is devoted to the comparison of three of these accelerated schemes. It shows that two of them are special cases of the third, corresponding to particular choices of parameters of the method. An upper bound of the spectral radius of the schemes is determined, from which sufficient conditions of convergence of the schemes are derived. Conditions are found for minimizing this upper bound. In particular, the accelerated scheme, which minimizes this upper bound, is exhibited. The paper discusses the choice of the convergence test used in the schemes. 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J. Numer. Meth. Engng</addtitle><description>SUMMARYSince the early 1990s when an iterative method based on Fourier transforms was introduced to compute the mechanical properties of heterogeneous materials, several algorithms have been proposed to increase the convergence rate of the initial scheme. This paper is devoted to the comparison of three of these accelerated schemes. It shows that two of them are special cases of the third, corresponding to particular choices of parameters of the method. An upper bound of the spectral radius of the schemes is determined, from which sufficient conditions of convergence of the schemes are derived. Conditions are found for minimizing this upper bound. In particular, the accelerated scheme, which minimizes this upper bound, is exhibited. The paper discusses the choice of the convergence test used in the schemes. Copyright © 2013 John Wiley & Sons, Ltd.</description><subject>Algorithms</subject><subject>Composite materials</subject><subject>Convergence</subject><subject>Engineering Sciences</subject><subject>Fourier transforms</subject><subject>heterogeneous media</subject><subject>Mathematical models</subject><subject>Mechanical properties</subject><subject>Mechanics</subject><subject>micromechanics</subject><subject>Numerical analysis</subject><subject>Physics</subject><subject>Solid mechanics</subject><subject>Spectra</subject><subject>Upper bounds</subject><issn>0029-5981</issn><issn>1097-0207</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNqN0UFLHDEUB_BQFLpqoR9hwEt7GH3JJJPkKIvriqteLEIvIZu-6UZnJttk1tZvb4YVRaHg6YXk9_4keYR8pXBEAdhx3-ERryn_RCYUtCyBgdwhk3ykS6EV_Uz2UroDoFRANSH9NHRrG30KfRGaYlhFxMI6hy1GO-CvYja7KZc25VVyK-wwFU2Ihctdm8H3v3MHFh26le29s20RMa1Dn3AMG1FIfsggR0Vv23RAdptc8Mtz3Sc_Zqc303m5uD47n54sSicqykvlAGshHZMMmoo7jrVsnKsaEFwxC8sl55papRA0ZWxpFdeqRp3btHOMV_vk-zZ3ZVuzjr6z8dEE6838ZGHGPQCpJCj9QLP9trXrGP5sMA2m8yl_QGt7DJtkqBSVoJSLD1DBQNe14CzTw3f0Lmxinx-dFVCV4wBeA10MKUVsXi5LwYzzNHmeZpxnpuWW_vUtPv7XmavL07fepwH_vXgb700tKynM7dWZmc5u5xeXP7VZVE_ROK67</recordid><startdate>20140330</startdate><enddate>20140330</enddate><creator>Moulinec, H.</creator><creator>Silva, F.</creator><general>Blackwell Publishing Ltd</general><general>Wiley Subscription Services, Inc</general><general>Wiley</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>7SR</scope><scope>JG9</scope><scope>1XC</scope><scope>VOOES</scope><orcidid>https://orcid.org/0000-0001-8178-7308</orcidid></search><sort><creationdate>20140330</creationdate><title>Comparison of three accelerated FFT-based schemes for computing the mechanical response of composite materials</title><author>Moulinec, H. ; Silva, F.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c5314-8c0e657c2720f34c4e67fcc3f05482a0bb4491a88e09122ba84986e9c0e9cc243</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Algorithms</topic><topic>Composite materials</topic><topic>Convergence</topic><topic>Engineering Sciences</topic><topic>Fourier transforms</topic><topic>heterogeneous media</topic><topic>Mathematical models</topic><topic>Mechanical properties</topic><topic>Mechanics</topic><topic>micromechanics</topic><topic>Numerical analysis</topic><topic>Physics</topic><topic>Solid mechanics</topic><topic>Spectra</topic><topic>Upper bounds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Moulinec, H.</creatorcontrib><creatorcontrib>Silva, F.</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Engineered Materials Abstracts</collection><collection>Materials Research Database</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>International journal for numerical methods in engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Moulinec, H.</au><au>Silva, F.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Comparison of three accelerated FFT-based schemes for computing the mechanical response of composite materials</atitle><jtitle>International journal for numerical methods in engineering</jtitle><addtitle>Int. 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| language | eng |
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| source | Wiley Online Library Journals Frontfile Complete |
| subjects | Algorithms Composite materials Convergence Engineering Sciences Fourier transforms heterogeneous media Mathematical models Mechanical properties Mechanics micromechanics Numerical analysis Physics Solid mechanics Spectra Upper bounds |
| title | Comparison of three accelerated FFT-based schemes for computing the mechanical response of composite materials |
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