Wavenumber-Explicit hp-FEM Analysis for Maxwell’s Equations with Impedance Boundary Conditions
The time-harmonic Maxwell equations at high wavenumber k in domains with an analytic boundary and impedance boundary conditions are considered. A wavenumber-explicit stability and regularity theory is developed that decomposes the solution into a part with finite Sobolev regularity that is controlle...
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| Veröffentlicht in: | Foundations of computational mathematics 2024, Vol.24 (6), p.1871-1939 |
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| container_end_page | 1939 |
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| container_issue | 6 |
| container_start_page | 1871 |
| container_title | Foundations of computational mathematics |
| container_volume | 24 |
| creator | Melenk, J. M. Sauter, S. A. |
| description | The time-harmonic Maxwell equations at high wavenumber
k
in domains with an analytic boundary and impedance boundary conditions are considered. A wavenumber-explicit stability and regularity theory is developed that decomposes the solution into a part with finite Sobolev regularity that is controlled uniformly in
k
and an analytic part. Using this regularity, quasi-optimality of the Galerkin discretization based on Nédélec elements of order
p
on a mesh with mesh size
h
is shown under the
k
-explicit scale resolution condition that (a)
kh
/
p
is sufficient small and (b)
p
/
ln
k
is bounded from below. |
| doi_str_mv | 10.1007/s10208-023-09626-7 |
| format | Article |
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k
in domains with an analytic boundary and impedance boundary conditions are considered. A wavenumber-explicit stability and regularity theory is developed that decomposes the solution into a part with finite Sobolev regularity that is controlled uniformly in
k
and an analytic part. Using this regularity, quasi-optimality of the Galerkin discretization based on Nédélec elements of order
p
on a mesh with mesh size
h
is shown under the
k
-explicit scale resolution condition that (a)
kh
/
p
is sufficient small and (b)
p
/
ln
k
is bounded from below.</description><identifier>ISSN: 1615-3375</identifier><identifier>EISSN: 1615-3383</identifier><identifier>DOI: 10.1007/s10208-023-09626-7</identifier><identifier>PMID: 39649677</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Applications of Mathematics ; Boundary conditions ; Computer Science ; Economics ; Finite element method ; Impedance ; Linear and Multilinear Algebras ; Math Applications in Computer Science ; Mathematics ; Mathematics and Statistics ; Matrix Theory ; Maxwell's equations ; Numerical Analysis ; Regularity ; Wavelengths</subject><ispartof>Foundations of computational mathematics, 2024, Vol.24 (6), p.1871-1939</ispartof><rights>The Author(s) 2023</rights><rights>The Author(s) 2023.</rights><rights>Copyright Springer Nature B.V. 2024</rights><rights>The Author(s) 2023 2023</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c475t-5698851e19ae074f268e3c2ce69fbbcb32ce1a17cb47b55c9f9b73a1ecb4ff5c3</citedby><cites>FETCH-LOGICAL-c475t-5698851e19ae074f268e3c2ce69fbbcb32ce1a17cb47b55c9f9b73a1ecb4ff5c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10208-023-09626-7$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10208-023-09626-7$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>230,314,776,780,881,27901,27902,41464,42533,51294</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/39649677$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Melenk, J. M.</creatorcontrib><creatorcontrib>Sauter, S. A.</creatorcontrib><title>Wavenumber-Explicit hp-FEM Analysis for Maxwell’s Equations with Impedance Boundary Conditions</title><title>Foundations of computational mathematics</title><addtitle>Found Comput Math</addtitle><addtitle>Found Comut Math</addtitle><description>The time-harmonic Maxwell equations at high wavenumber
k
in domains with an analytic boundary and impedance boundary conditions are considered. A wavenumber-explicit stability and regularity theory is developed that decomposes the solution into a part with finite Sobolev regularity that is controlled uniformly in
k
and an analytic part. Using this regularity, quasi-optimality of the Galerkin discretization based on Nédélec elements of order
p
on a mesh with mesh size
h
is shown under the
k
-explicit scale resolution condition that (a)
kh
/
p
is sufficient small and (b)
p
/
ln
k
is bounded from below.</description><subject>Applications of Mathematics</subject><subject>Boundary conditions</subject><subject>Computer Science</subject><subject>Economics</subject><subject>Finite element method</subject><subject>Impedance</subject><subject>Linear and Multilinear Algebras</subject><subject>Math Applications in Computer Science</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Matrix Theory</subject><subject>Maxwell's equations</subject><subject>Numerical Analysis</subject><subject>Regularity</subject><subject>Wavelengths</subject><issn>1615-3375</issn><issn>1615-3383</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9kctu1DAUhi0EoqXwAiyQJTZsDHYc2_EKldEUKrViA2JpHM9Jx1Vip3bSy47X6Ov1SXBnynBZsPKRz3f-c_kResnoW0apepcZrWhDaMUJ1bKSRD1C-0wyQThv-ONdrMQeepbzOaVMaFY_RXtcy1pLpfbR92_2EsI8tJDI8nrsvfMTXo_kaHmKD4Ptb7LPuIsJn9rrK-j7ux-3GS8vZjv5GDK-8tMaHw8jrGxwgD_EOaxsusGLGFZ-gzxHTzrbZ3jx8B6gr0fLL4tP5OTzx-PF4QlxtRITEVI3jWDAtAWq6q6SDXBXOZC6a1vX8hIyy5Rra9UK4XSnW8Utg_LRdcLxA_R-qzvO7QArB2FKtjdj8kMZyETrzd-Z4NfmLF4aVq7UsIYXhTcPCilezJAnM_jsys42QJyz4ayWkgpa6YK-_gc9j3Mq59pQjEoh5T1VbSmXYs4Jut00jJp7B83WQVMcNBsHjSpFr_7cY1fyy7IC8C2QSyqcQfrd-z-yPwGEEKmP</recordid><startdate>2024</startdate><enddate>2024</enddate><creator>Melenk, J. M.</creator><creator>Sauter, S. A.</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>NPM</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>7X8</scope><scope>5PM</scope></search><sort><creationdate>2024</creationdate><title>Wavenumber-Explicit hp-FEM Analysis for Maxwell’s Equations with Impedance Boundary Conditions</title><author>Melenk, J. M. ; Sauter, S. A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c475t-5698851e19ae074f268e3c2ce69fbbcb32ce1a17cb47b55c9f9b73a1ecb4ff5c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Applications of Mathematics</topic><topic>Boundary conditions</topic><topic>Computer Science</topic><topic>Economics</topic><topic>Finite element method</topic><topic>Impedance</topic><topic>Linear and Multilinear Algebras</topic><topic>Math Applications in Computer Science</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Matrix Theory</topic><topic>Maxwell's equations</topic><topic>Numerical Analysis</topic><topic>Regularity</topic><topic>Wavelengths</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Melenk, J. M.</creatorcontrib><creatorcontrib>Sauter, S. A.</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>PubMed</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>MEDLINE - Academic</collection><collection>PubMed Central (Full Participant titles)</collection><jtitle>Foundations of computational mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Melenk, J. M.</au><au>Sauter, S. A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Wavenumber-Explicit hp-FEM Analysis for Maxwell’s Equations with Impedance Boundary Conditions</atitle><jtitle>Foundations of computational mathematics</jtitle><stitle>Found Comput Math</stitle><addtitle>Found Comut Math</addtitle><date>2024</date><risdate>2024</risdate><volume>24</volume><issue>6</issue><spage>1871</spage><epage>1939</epage><pages>1871-1939</pages><issn>1615-3375</issn><eissn>1615-3383</eissn><abstract>The time-harmonic Maxwell equations at high wavenumber
k
in domains with an analytic boundary and impedance boundary conditions are considered. A wavenumber-explicit stability and regularity theory is developed that decomposes the solution into a part with finite Sobolev regularity that is controlled uniformly in
k
and an analytic part. Using this regularity, quasi-optimality of the Galerkin discretization based on Nédélec elements of order
p
on a mesh with mesh size
h
is shown under the
k
-explicit scale resolution condition that (a)
kh
/
p
is sufficient small and (b)
p
/
ln
k
is bounded from below.</abstract><cop>New York</cop><pub>Springer US</pub><pmid>39649677</pmid><doi>10.1007/s10208-023-09626-7</doi><tpages>69</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | Applications of Mathematics Boundary conditions Computer Science Economics Finite element method Impedance Linear and Multilinear Algebras Math Applications in Computer Science Mathematics Mathematics and Statistics Matrix Theory Maxwell's equations Numerical Analysis Regularity Wavelengths |
| title | Wavenumber-Explicit hp-FEM Analysis for Maxwell’s Equations with Impedance Boundary Conditions |
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