dc.contributor.author | Khoromskij, Boris | |
dc.contributor.author | Repin, Sergey | |
dc.date.accessioned | 2017-07-31T09:48:27Z | |
dc.date.available | 2018-06-17T21:35:27Z | |
dc.date.issued | 2017 | |
dc.identifier.citation | Khoromskij, B., & Repin, S. (2017). Rank Structured Approximation Method for Quasi-Periodic Elliptic Problems. <i>Computational Methods in Applied Mathematics</i>, <i>17</i>(3), 457-477. <a href="https://doi.org/10.1515/cmam-2017-0014" target="_blank">https://doi.org/10.1515/cmam-2017-0014</a> | |
dc.identifier.other | CONVID_27081071 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/54949 | |
dc.description.abstract | We consider an iteration method for solving an elliptic type boundary value problem Au=f, where a positive definite operator A is generated by a quasi-periodic structure with rapidly changing coefficients (a typical period is characterized by a small parameter ϵ). The method is based on using a simpler operator A0 (inversion of A0 is much simpler than inversion of A), which can be viewed as a preconditioner for A. We prove contraction of the iteration method and establish explicit estimates of the contraction factor q. Certainly the value of q depends on the difference between A and A0. For typical quasi-periodic structures, we establish simple relations that suggest an optimal A0 (in a selected set of “simple” structures) and compute the corresponding contraction factor. Further, this allows us to deduce fully computable two-sided a posteriori estimates able to control numerical solutions on any iteration. The method is especially efficient if the coefficients of A admit low-rank representations and if algebraic operations are performed in tensor structured formats. Under moderate assumptions the storage and solution complexity of our approach depends only weakly (merely linear-logarithmically) on the frequency parameter 1/ϵ. | |
dc.language.iso | eng | |
dc.publisher | de Gruyter | |
dc.relation.ispartofseries | Computational Methods in Applied Mathematics | |
dc.subject.other | elliptic problems with periodic and quasi-periodic coefficients | |
dc.subject.other | precondition methods | |
dc.subject.other | tensor type methods | |
dc.subject.other | guaranteed error bounds | |
dc.title | Rank Structured Approximation Method for Quasi-Periodic Elliptic Problems | |
dc.type | research article | |
dc.identifier.urn | URN:NBN:fi:jyu-201707183314 | |
dc.contributor.laitos | Informaatioteknologian tiedekunta | fi |
dc.contributor.laitos | Faculty of Information Technology | en |
dc.contributor.oppiaine | Tietotekniikka | fi |
dc.contributor.oppiaine | Mathematical Information Technology | en |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | |
dc.date.updated | 2017-07-18T12:15:05Z | |
dc.type.coar | http://purl.org/coar/resource_type/c_2df8fbb1 | |
dc.description.reviewstatus | peerReviewed | |
dc.format.pagerange | 457-477 | |
dc.relation.issn | 1609-4840 | |
dc.relation.numberinseries | 3 | |
dc.relation.volume | 17 | |
dc.type.version | publishedVersion | |
dc.rights.copyright | © 2017 Walter de Gruyter GmbH, Berlin/Boston. Published in this repository with the kind permission of the publisher. | |
dc.rights.accesslevel | openAccess | fi |
dc.type.publication | article | |
dc.relation.doi | 10.1515/cmam-2017-0014 | |
dc.type.okm | A1 | |