No Cover Image

Conference Paper/Proceeding/Abstract 700 views 28 downloads

Completeness Characterization of Type-I Box Splines

Nelly Villamizar Orcid Logo, Angelos Mantzaflaris, Bert Jüttler

Geometric Challenges in Isogeometric Analysis. Springer INdAM Series, Volume: 49, Pages: 279 - 304

Swansea University Author: Nelly Villamizar Orcid Logo

Check full text

DOI (Published version): 10.1007/978-3-030-92313-6_12

Abstract

We present a completeness characterization of box splines on three-directionaltriangulations, also called Type-I box spline spaces, based on edge-contact smoothness properties.For any given Type-I box spline, of specific maximum degree and order of globalsmoothness, our results allow to identify the...

Full description

Published in: Geometric Challenges in Isogeometric Analysis. Springer INdAM Series
ISBN: 9783030923129 9783030923136
ISSN: 2281-518X 2281-5198
Published: Cham Springer International Publishing 2022
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa56991
first_indexed 2021-05-31T22:26:18Z
last_indexed 2024-11-14T12:11:03Z
id cronfa56991
recordtype SURis
fullrecord <?xml version="1.0"?><rfc1807><datestamp>2024-07-29T15:38:58.0902314</datestamp><bib-version>v2</bib-version><id>56991</id><entry>2021-05-31</entry><title>Completeness Characterization of Type-I Box Splines</title><swanseaauthors><author><sid>41572bcee47da6ba274ecd1828fbfef4</sid><ORCID>0000-0002-8741-7225</ORCID><firstname>Nelly</firstname><surname>Villamizar</surname><name>Nelly Villamizar</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2021-05-31</date><deptcode>MACS</deptcode><abstract>We present a completeness characterization of box splines on three-directionaltriangulations, also called Type-I box spline spaces, based on edge-contact smoothness properties.For any given Type-I box spline, of specific maximum degree and order of globalsmoothness, our results allow to identify the local linear subspace of polynomials spanned by the box spline translates. We use the global super-smoothness properties of box splines as well as the additional super-smoothness conditions at edges to characterize the spline space spanned by the box spline translates. Subsequently, we prove the completeness of this space space with respect to the local polynomial space induced by the box spline translates. The completeness property allows the construction of hierarchical spaces spanned by the translatesof box splines for any polynomial degree on multilevel Type-I grids. We provide a basis for these hierarchical box spline spaces under explicit geometric conditions of the domain.</abstract><type>Conference Paper/Proceeding/Abstract</type><journal>Geometric Challenges in Isogeometric Analysis. Springer INdAM Series</journal><volume>49</volume><journalNumber/><paginationStart>279</paginationStart><paginationEnd>304</paginationEnd><publisher>Springer International Publishing</publisher><placeOfPublication>Cham</placeOfPublication><isbnPrint>9783030923129</isbnPrint><isbnElectronic>9783030923136</isbnElectronic><issnPrint>2281-518X</issnPrint><issnElectronic>2281-5198</issnElectronic><keywords/><publishedDay>9</publishedDay><publishedMonth>8</publishedMonth><publishedYear>2022</publishedYear><publishedDate>2022-08-09</publishedDate><doi>10.1007/978-3-030-92313-6_12</doi><url/><notes/><college>COLLEGE NANME</college><department>Mathematics and Computer Science School</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>MACS</DepartmentCode><institution>Swansea University</institution><apcterm/><funders/><projectreference>EP/V012835/1, The Alliance Hubert Curien Programme reference: 515492678</projectreference><lastEdited>2024-07-29T15:38:58.0902314</lastEdited><Created>2021-05-31T23:21:25.7583325</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Mathematics and Computer Science - Mathematics</level></path><authors><author><firstname>Nelly</firstname><surname>Villamizar</surname><orcid>0000-0002-8741-7225</orcid><order>1</order></author><author><firstname>Angelos</firstname><surname>Mantzaflaris</surname><order>2</order></author><author><firstname>Bert</firstname><surname>J&#xFC;ttler</surname><order>3</order></author></authors><documents><document><filename>56991__20034__d50d688bcab24dd9acc97b9819bb39d3.pdf</filename><originalFilename>Villamizar_Mantzaflaris_Juettler_2021.pdf</originalFilename><uploaded>2021-05-31T23:25:24.3291566</uploaded><type>Output</type><contentLength>633850</contentLength><contentType>application/pdf</contentType><version>Accepted Manuscript</version><cronfaStatus>true</cronfaStatus><embargoDate>2023-08-09T00:00:00.0000000</embargoDate><copyrightCorrect>true</copyrightCorrect><language>eng</language></document></documents><OutputDurs/></rfc1807>
spelling 2024-07-29T15:38:58.0902314 v2 56991 2021-05-31 Completeness Characterization of Type-I Box Splines 41572bcee47da6ba274ecd1828fbfef4 0000-0002-8741-7225 Nelly Villamizar Nelly Villamizar true false 2021-05-31 MACS We present a completeness characterization of box splines on three-directionaltriangulations, also called Type-I box spline spaces, based on edge-contact smoothness properties.For any given Type-I box spline, of specific maximum degree and order of globalsmoothness, our results allow to identify the local linear subspace of polynomials spanned by the box spline translates. We use the global super-smoothness properties of box splines as well as the additional super-smoothness conditions at edges to characterize the spline space spanned by the box spline translates. Subsequently, we prove the completeness of this space space with respect to the local polynomial space induced by the box spline translates. The completeness property allows the construction of hierarchical spaces spanned by the translatesof box splines for any polynomial degree on multilevel Type-I grids. We provide a basis for these hierarchical box spline spaces under explicit geometric conditions of the domain. Conference Paper/Proceeding/Abstract Geometric Challenges in Isogeometric Analysis. Springer INdAM Series 49 279 304 Springer International Publishing Cham 9783030923129 9783030923136 2281-518X 2281-5198 9 8 2022 2022-08-09 10.1007/978-3-030-92313-6_12 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University EP/V012835/1, The Alliance Hubert Curien Programme reference: 515492678 2024-07-29T15:38:58.0902314 2021-05-31T23:21:25.7583325 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Nelly Villamizar 0000-0002-8741-7225 1 Angelos Mantzaflaris 2 Bert Jüttler 3 56991__20034__d50d688bcab24dd9acc97b9819bb39d3.pdf Villamizar_Mantzaflaris_Juettler_2021.pdf 2021-05-31T23:25:24.3291566 Output 633850 application/pdf Accepted Manuscript true 2023-08-09T00:00:00.0000000 true eng
title Completeness Characterization of Type-I Box Splines
spellingShingle Completeness Characterization of Type-I Box Splines
Nelly Villamizar
title_short Completeness Characterization of Type-I Box Splines
title_full Completeness Characterization of Type-I Box Splines
title_fullStr Completeness Characterization of Type-I Box Splines
title_full_unstemmed Completeness Characterization of Type-I Box Splines
title_sort Completeness Characterization of Type-I Box Splines
author_id_str_mv 41572bcee47da6ba274ecd1828fbfef4
author_id_fullname_str_mv 41572bcee47da6ba274ecd1828fbfef4_***_Nelly Villamizar
author Nelly Villamizar
author2 Nelly Villamizar
Angelos Mantzaflaris
Bert Jüttler
format Conference Paper/Proceeding/Abstract
container_title Geometric Challenges in Isogeometric Analysis. Springer INdAM Series
container_volume 49
container_start_page 279
publishDate 2022
institution Swansea University
isbn 9783030923129
9783030923136
issn 2281-518X
2281-5198
doi_str_mv 10.1007/978-3-030-92313-6_12
publisher Springer International Publishing
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description We present a completeness characterization of box splines on three-directionaltriangulations, also called Type-I box spline spaces, based on edge-contact smoothness properties.For any given Type-I box spline, of specific maximum degree and order of globalsmoothness, our results allow to identify the local linear subspace of polynomials spanned by the box spline translates. We use the global super-smoothness properties of box splines as well as the additional super-smoothness conditions at edges to characterize the spline space spanned by the box spline translates. Subsequently, we prove the completeness of this space space with respect to the local polynomial space induced by the box spline translates. The completeness property allows the construction of hierarchical spaces spanned by the translatesof box splines for any polynomial degree on multilevel Type-I grids. We provide a basis for these hierarchical box spline spaces under explicit geometric conditions of the domain.
published_date 2022-08-09T08:02:04Z
_version_ 1821391742274895872
score 11.04748

Similar Items