Quadrature-rule type approximations to the quasicontinuum method for long-range interatomic interactions
A quadrature-rule type method is presented to approximate the quasicontinuum method for atomistic mechanics. For both the short-range and long-range interaction cases, the complexity of this method depends on the number of representative particles but not on the total number of particles. Simple ana...
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| Veröffentlicht in: | Computer methods in applied mechanics and engineering 2010-01, Vol.199 (9), p.648-659 |
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| container_title | Computer methods in applied mechanics and engineering |
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| creator | Zhang, Yanzhi Gunzburger, Max |
| description | A quadrature-rule type method is presented to approximate the quasicontinuum method for atomistic mechanics. For both the short-range and long-range interaction cases, the complexity of this method depends on the number of representative particles but not on the total number of particles. Simple analysis and numerical experiments are provided to illustrate the accuracy and performance of the method. It is shown that, for the same accuracy, the quadrature-rule type method is much less costly than the quasicontinuum method. |
| doi_str_mv | 10.1016/j.cma.2009.10.015 |
| format | Article |
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It is shown that, for the same accuracy, the quadrature-rule type method is much less costly than the quasicontinuum method.</description><identifier>ISSN: 0045-7825</identifier><identifier>EISSN: 1879-2138</identifier><identifier>DOI: 10.1016/j.cma.2009.10.015</identifier><identifier>CODEN: CMMECC</identifier><language>eng</language><publisher>Kidlington: Elsevier B.V</publisher><subject>Atomistic models ; Computational techniques ; Coulomb potential ; Exact sciences and technology ; Fundamental areas of phenomenology (including applications) ; Long-range interactions ; Mathematical methods in physics ; Physics ; Quadrature-rule type approximation ; Quasicontinuum method ; Solid mechanics ; Structural and continuum mechanics</subject><ispartof>Computer methods in applied mechanics and engineering, 2010-01, Vol.199 (9), p.648-659</ispartof><rights>2009 Elsevier B.V.</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c359t-c8e7ccaae7f29afe1af91e2253648129b046a06656f2230af0a7a0c1b977ee253</citedby><cites>FETCH-LOGICAL-c359t-c8e7ccaae7f29afe1af91e2253648129b046a06656f2230af0a7a0c1b977ee253</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0045782509003600$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=22536638$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Zhang, Yanzhi</creatorcontrib><creatorcontrib>Gunzburger, Max</creatorcontrib><title>Quadrature-rule type approximations to the quasicontinuum method for long-range interatomic interactions</title><title>Computer methods in applied mechanics and engineering</title><description>A quadrature-rule type method is presented to approximate the quasicontinuum method for atomistic mechanics. 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It is shown that, for the same accuracy, the quadrature-rule type method is much less costly than the quasicontinuum method.</description><subject>Atomistic models</subject><subject>Computational techniques</subject><subject>Coulomb potential</subject><subject>Exact sciences and technology</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>Long-range interactions</subject><subject>Mathematical methods in physics</subject><subject>Physics</subject><subject>Quadrature-rule type approximation</subject><subject>Quasicontinuum method</subject><subject>Solid mechanics</subject><subject>Structural and continuum mechanics</subject><issn>0045-7825</issn><issn>1879-2138</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLAzEUhYMoWKs_wF024mpqknlkBldSfIEggq7DbXrTpsxM2iQj9t-bPnBpNje5fPfknkPINWcTznh1t5roDiaCsSa9J4yXJ2TEa9lkguf1KRkxVpSZrEV5Ti5CWLF0ai5GZPkxwNxDHDxmfmiRxu0aKazX3v3YDqJ1faDR0bhEuhkgWO36aPth6GiHcenm1DhPW9cvMg_9AqntIyY911l9vOu9yCU5M9AGvDrWMfl6evycvmRv78-v04e3TOdlEzNdo9QaAKURDRjkYBqOQpR5VaSFmxkrKmBVVVZGiJyBYSCBaT5rpERM2JjcHnSTg82AIarOBo1tCz26IShZ5AVjsmoSyQ-k9i4Ej0atfbLst4oztQtVrVQKVe1C3bVSqGnm5qgOQUNrkmdtw9_gfs8qrxN3f-AwWf226FXQFnuNc-tRRzV39p9ffgFi5o8R</recordid><startdate>20100101</startdate><enddate>20100101</enddate><creator>Zhang, Yanzhi</creator><creator>Gunzburger, Max</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>IQODW</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></search><sort><creationdate>20100101</creationdate><title>Quadrature-rule type approximations to the quasicontinuum method for long-range interatomic interactions</title><author>Zhang, Yanzhi ; Gunzburger, Max</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c359t-c8e7ccaae7f29afe1af91e2253648129b046a06656f2230af0a7a0c1b977ee253</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Atomistic models</topic><topic>Computational techniques</topic><topic>Coulomb potential</topic><topic>Exact sciences and technology</topic><topic>Fundamental areas of phenomenology (including applications)</topic><topic>Long-range interactions</topic><topic>Mathematical methods in physics</topic><topic>Physics</topic><topic>Quadrature-rule type approximation</topic><topic>Quasicontinuum method</topic><topic>Solid mechanics</topic><topic>Structural and continuum mechanics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhang, Yanzhi</creatorcontrib><creatorcontrib>Gunzburger, Max</creatorcontrib><collection>Pascal-Francis</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><jtitle>Computer methods in applied mechanics and engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zhang, Yanzhi</au><au>Gunzburger, Max</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Quadrature-rule type approximations to the quasicontinuum method for long-range interatomic interactions</atitle><jtitle>Computer methods in applied mechanics and engineering</jtitle><date>2010-01-01</date><risdate>2010</risdate><volume>199</volume><issue>9</issue><spage>648</spage><epage>659</epage><pages>648-659</pages><issn>0045-7825</issn><eissn>1879-2138</eissn><coden>CMMECC</coden><abstract>A quadrature-rule type method is presented to approximate the quasicontinuum method for atomistic mechanics. 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| ispartof | Computer methods in applied mechanics and engineering, 2010-01, Vol.199 (9), p.648-659 |
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| language | eng |
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| source | Elsevier ScienceDirect Journals |
| subjects | Atomistic models Computational techniques Coulomb potential Exact sciences and technology Fundamental areas of phenomenology (including applications) Long-range interactions Mathematical methods in physics Physics Quadrature-rule type approximation Quasicontinuum method Solid mechanics Structural and continuum mechanics |
| title | Quadrature-rule type approximations to the quasicontinuum method for long-range interatomic interactions |
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