A high-order discontinuous Galerkin method for level set problems on polygonal meshes
We propose and analyze discontinuous Galerkin schemes for solving level set equations on polygonal meshes. For linear equations, we assume that the velocity is given only on the cell surface. Velocity inside mesh cells is approximated using virtual element projectors on polynomial spaces. For nonlin...
Gespeichert in:
| Veröffentlicht in: | Journal of computational physics 2019-11, Vol.397 (C), p.108834, Article 108834 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | C |
| container_start_page | 108834 |
| container_title | Journal of computational physics |
| container_volume | 397 |
| creator | Lipnikov, Konstantin Morgan, Nathaniel |
| description | We propose and analyze discontinuous Galerkin schemes for solving level set equations on polygonal meshes. For linear equations, we assume that the velocity is given only on the cell surface. Velocity inside mesh cells is approximated using virtual element projectors on polynomial spaces. For nonlinear equations, we use the Taylor expansion to approximate the normalized solution gradient. We analyze the new schemes for a set of typical level set problems using square and polygonal meshes. The numerical results indicate great potential for using polygonal meshes in applications.
•High-order DG schemes for level set equations on polygonal meshes.•New algorithms for velocity reconstruction inside mesh cells from boundary data.•Using Taylor expansion to calculate the normalized solution gradient. |
| doi_str_mv | 10.1016/j.jcp.2019.07.033 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_osti_</sourceid><recordid>TN_cdi_osti_scitechconnect_1557748</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0021999119305182</els_id><sourcerecordid>2303821217</sourcerecordid><originalsourceid>FETCH-LOGICAL-c395t-8e14f098a8cfa69c88b491d2c58f664d0654f4fcd03c1677c7eaf3c30c52a97a3</originalsourceid><addsrcrecordid>eNp9kD1PwzAURS0EEuXjB7BZMCc8x0lsiwkhKEhILHS2XOeZOKRxsVMk_j2uysz0lnOf7j2EXDEoGbD2digHuy0rYKoEUQLnR2TBQEFRCdYekwVAxQqlFDslZykNACCbWi7I6p72_qMvQuww0s4nG6bZT7uwS3RpRoyffqIbnPvQURciHfEbR5pwptsY1iNuEg0T3Ybx5yNMZsxo6jFdkBNnxoSXf_ecrJ4e3x-ei9e35cvD_WthuWrmQiKrHShppHWmVVbKda1YV9lGuratO2ib2tXOdsAta4WwAo3jloNtKqOE4efk-vA3pNnrZP2Mts8LJrSzZk0jRC0zdHOAcuOvHaZZD2EXc9mkKw5cVqxiIlPsQNkYUoro9Db6jYk_moHeK9aDzor1XrEGobPinLk7ZDBv_PYY9xVwstj5uG_QBf9P-hejTIP3</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2303821217</pqid></control><display><type>article</type><title>A high-order discontinuous Galerkin method for level set problems on polygonal meshes</title><source>Elsevier ScienceDirect Journals</source><creator>Lipnikov, Konstantin ; Morgan, Nathaniel</creator><creatorcontrib>Lipnikov, Konstantin ; Morgan, Nathaniel ; Los Alamos National Lab. (LANL), Los Alamos, NM (United States)</creatorcontrib><description>We propose and analyze discontinuous Galerkin schemes for solving level set equations on polygonal meshes. For linear equations, we assume that the velocity is given only on the cell surface. Velocity inside mesh cells is approximated using virtual element projectors on polynomial spaces. For nonlinear equations, we use the Taylor expansion to approximate the normalized solution gradient. We analyze the new schemes for a set of typical level set problems using square and polygonal meshes. The numerical results indicate great potential for using polygonal meshes in applications.
•High-order DG schemes for level set equations on polygonal meshes.•New algorithms for velocity reconstruction inside mesh cells from boundary data.•Using Taylor expansion to calculate the normalized solution gradient.</description><identifier>ISSN: 0021-9991</identifier><identifier>EISSN: 1090-2716</identifier><identifier>DOI: 10.1016/j.jcp.2019.07.033</identifier><language>eng</language><publisher>Cambridge: Elsevier Inc</publisher><subject>Computational physics ; Discontinuous Galerkin ; Galerkin method ; High-order ; Level set ; Linear equations ; Mathematical analysis ; MATHEMATICS AND COMPUTING ; Nonlinear equations ; Polygonal mesh ; Polygons ; Polynomials ; Projectors ; Taylor series ; Virtual element projectors</subject><ispartof>Journal of computational physics, 2019-11, Vol.397 (C), p.108834, Article 108834</ispartof><rights>2019 Elsevier Inc.</rights><rights>Copyright Elsevier Science Ltd. Nov 15, 2019</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c395t-8e14f098a8cfa69c88b491d2c58f664d0654f4fcd03c1677c7eaf3c30c52a97a3</citedby><cites>FETCH-LOGICAL-c395t-8e14f098a8cfa69c88b491d2c58f664d0654f4fcd03c1677c7eaf3c30c52a97a3</cites><orcidid>0000-0002-7611-8449 ; 0000000214754626 ; 0000000276118449</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.jcp.2019.07.033$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>230,314,777,781,882,3537,27905,27906,45976</link.rule.ids><backlink>$$Uhttps://www.osti.gov/servlets/purl/1557748$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Lipnikov, Konstantin</creatorcontrib><creatorcontrib>Morgan, Nathaniel</creatorcontrib><creatorcontrib>Los Alamos National Lab. (LANL), Los Alamos, NM (United States)</creatorcontrib><title>A high-order discontinuous Galerkin method for level set problems on polygonal meshes</title><title>Journal of computational physics</title><description>We propose and analyze discontinuous Galerkin schemes for solving level set equations on polygonal meshes. For linear equations, we assume that the velocity is given only on the cell surface. Velocity inside mesh cells is approximated using virtual element projectors on polynomial spaces. For nonlinear equations, we use the Taylor expansion to approximate the normalized solution gradient. We analyze the new schemes for a set of typical level set problems using square and polygonal meshes. The numerical results indicate great potential for using polygonal meshes in applications.
•High-order DG schemes for level set equations on polygonal meshes.•New algorithms for velocity reconstruction inside mesh cells from boundary data.•Using Taylor expansion to calculate the normalized solution gradient.</description><subject>Computational physics</subject><subject>Discontinuous Galerkin</subject><subject>Galerkin method</subject><subject>High-order</subject><subject>Level set</subject><subject>Linear equations</subject><subject>Mathematical analysis</subject><subject>MATHEMATICS AND COMPUTING</subject><subject>Nonlinear equations</subject><subject>Polygonal mesh</subject><subject>Polygons</subject><subject>Polynomials</subject><subject>Projectors</subject><subject>Taylor series</subject><subject>Virtual element projectors</subject><issn>0021-9991</issn><issn>1090-2716</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp9kD1PwzAURS0EEuXjB7BZMCc8x0lsiwkhKEhILHS2XOeZOKRxsVMk_j2uysz0lnOf7j2EXDEoGbD2digHuy0rYKoEUQLnR2TBQEFRCdYekwVAxQqlFDslZykNACCbWi7I6p72_qMvQuww0s4nG6bZT7uwS3RpRoyffqIbnPvQURciHfEbR5pwptsY1iNuEg0T3Ybx5yNMZsxo6jFdkBNnxoSXf_ecrJ4e3x-ei9e35cvD_WthuWrmQiKrHShppHWmVVbKda1YV9lGuratO2ib2tXOdsAta4WwAo3jloNtKqOE4efk-vA3pNnrZP2Mts8LJrSzZk0jRC0zdHOAcuOvHaZZD2EXc9mkKw5cVqxiIlPsQNkYUoro9Db6jYk_moHeK9aDzor1XrEGobPinLk7ZDBv_PYY9xVwstj5uG_QBf9P-hejTIP3</recordid><startdate>20191115</startdate><enddate>20191115</enddate><creator>Lipnikov, Konstantin</creator><creator>Morgan, Nathaniel</creator><general>Elsevier Inc</general><general>Elsevier Science Ltd</general><general>Elsevier</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>7U5</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>OIOZB</scope><scope>OTOTI</scope><orcidid>https://orcid.org/0000-0002-7611-8449</orcidid><orcidid>https://orcid.org/0000000214754626</orcidid><orcidid>https://orcid.org/0000000276118449</orcidid></search><sort><creationdate>20191115</creationdate><title>A high-order discontinuous Galerkin method for level set problems on polygonal meshes</title><author>Lipnikov, Konstantin ; Morgan, Nathaniel</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c395t-8e14f098a8cfa69c88b491d2c58f664d0654f4fcd03c1677c7eaf3c30c52a97a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Computational physics</topic><topic>Discontinuous Galerkin</topic><topic>Galerkin method</topic><topic>High-order</topic><topic>Level set</topic><topic>Linear equations</topic><topic>Mathematical analysis</topic><topic>MATHEMATICS AND COMPUTING</topic><topic>Nonlinear equations</topic><topic>Polygonal mesh</topic><topic>Polygons</topic><topic>Polynomials</topic><topic>Projectors</topic><topic>Taylor series</topic><topic>Virtual element projectors</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lipnikov, Konstantin</creatorcontrib><creatorcontrib>Morgan, Nathaniel</creatorcontrib><creatorcontrib>Los Alamos National Lab. (LANL), Los Alamos, NM (United States)</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</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>OSTI.GOV - Hybrid</collection><collection>OSTI.GOV</collection><jtitle>Journal of computational physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lipnikov, Konstantin</au><au>Morgan, Nathaniel</au><aucorp>Los Alamos National Lab. (LANL), Los Alamos, NM (United States)</aucorp><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A high-order discontinuous Galerkin method for level set problems on polygonal meshes</atitle><jtitle>Journal of computational physics</jtitle><date>2019-11-15</date><risdate>2019</risdate><volume>397</volume><issue>C</issue><spage>108834</spage><pages>108834-</pages><artnum>108834</artnum><issn>0021-9991</issn><eissn>1090-2716</eissn><abstract>We propose and analyze discontinuous Galerkin schemes for solving level set equations on polygonal meshes. For linear equations, we assume that the velocity is given only on the cell surface. Velocity inside mesh cells is approximated using virtual element projectors on polynomial spaces. For nonlinear equations, we use the Taylor expansion to approximate the normalized solution gradient. We analyze the new schemes for a set of typical level set problems using square and polygonal meshes. The numerical results indicate great potential for using polygonal meshes in applications.
•High-order DG schemes for level set equations on polygonal meshes.•New algorithms for velocity reconstruction inside mesh cells from boundary data.•Using Taylor expansion to calculate the normalized solution gradient.</abstract><cop>Cambridge</cop><pub>Elsevier Inc</pub><doi>10.1016/j.jcp.2019.07.033</doi><orcidid>https://orcid.org/0000-0002-7611-8449</orcidid><orcidid>https://orcid.org/0000000214754626</orcidid><orcidid>https://orcid.org/0000000276118449</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0021-9991 |
| ispartof | Journal of computational physics, 2019-11, Vol.397 (C), p.108834, Article 108834 |
| issn | 0021-9991 1090-2716 |
| language | eng |
| recordid | cdi_osti_scitechconnect_1557748 |
| source | Elsevier ScienceDirect Journals |
| subjects | Computational physics Discontinuous Galerkin Galerkin method High-order Level set Linear equations Mathematical analysis MATHEMATICS AND COMPUTING Nonlinear equations Polygonal mesh Polygons Polynomials Projectors Taylor series Virtual element projectors |
| title | A high-order discontinuous Galerkin method for level set problems on polygonal meshes |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-19T15%3A57%3A35IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_osti_&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20high-order%20discontinuous%20Galerkin%20method%20for%20level%20set%20problems%20on%20polygonal%20meshes&rft.jtitle=Journal%20of%20computational%20physics&rft.au=Lipnikov,%20Konstantin&rft.aucorp=Los%20Alamos%20National%20Lab.%20(LANL),%20Los%20Alamos,%20NM%20(United%20States)&rft.date=2019-11-15&rft.volume=397&rft.issue=C&rft.spage=108834&rft.pages=108834-&rft.artnum=108834&rft.issn=0021-9991&rft.eissn=1090-2716&rft_id=info:doi/10.1016/j.jcp.2019.07.033&rft_dat=%3Cproquest_osti_%3E2303821217%3C/proquest_osti_%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2303821217&rft_id=info:pmid/&rft_els_id=S0021999119305182&rfr_iscdi=true |