{"id":"https://openalex.org/W2931468134","doi":"https://doi.org/10.1007/s00211-020-01161-9","title":"On superconvergence of Runge\u2013Kutta convolution quadrature for the wave equation","display_name":"On superconvergence of Runge\u2013Kutta convolution quadrature for the wave equation","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W2931468134","doi":"https://doi.org/10.1007/s00211-020-01161-9","mag":"2931468134"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-020-01161-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-020-01161-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-020-01161-9.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"type":"preprint","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00211-020-01161-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058356670","display_name":"Jens Markus Melenk","orcid":"https://orcid.org/0000-0001-9024-6028"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Jens Markus Melenk","raw_affiliation_strings":["Technische Universit\u00e4t Wien, Wiedner Hauptstrasse 8-10, A-1040, Wien, Austria","Technische Universit\u00e4t Wien, Wien, Austria"],"affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Wien, Wiedner Hauptstrasse 8-10, A-1040, Wien, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Technische Universit\u00e4t Wien, Wien, Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051486563","display_name":"Alexander Rieder","orcid":"https://orcid.org/0000-0003-2144-7648"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]},{"id":"https://openalex.org/I4210088715","display_name":"FH Campus Wien","ror":"https://ror.org/003f4pg83","country_code":"AT","type":"education","lineage":["https://openalex.org/I4210088715"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Alexander Rieder","raw_affiliation_strings":["Universit\u00e4t Wien, Oskar-Morgenstern-Platz 1, A-1090, Wien, Austria","Universitat Wien, , Wien, Austria"],"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Wien, Oskar-Morgenstern-Platz 1, A-1090, Wien, Austria","institution_ids":["https://openalex.org/I129774422"]},{"raw_affiliation_string":"Universitat Wien, , Wien, Austria","institution_ids":["https://openalex.org/I4210088715","https://openalex.org/I129774422"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5058356670"],"corresponding_institution_ids":["https://openalex.org/I145847075"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.1476,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.36777363,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"147","issue":"1","first_page":"157","last_page":"188"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/superconvergence","display_name":"Superconvergence","score":0.7046504020690918},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6621443629264832},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6200634837150574},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.5879160761833191},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.567892849445343},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.5136162638664246},{"id":"https://openalex.org/keywords/extrapolation","display_name":"Extrapolation","score":0.4963083863258362},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.46568694710731506},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.4564637243747711},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.43732404708862305},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.43250855803489685},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.41729676723480225},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.40213072299957275},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2196747362613678},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.17375198006629944},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.1210932731628418},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11622953414916992},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.08004313707351685}],"concepts":[{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.7046504020690918},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6621443629264832},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6200634837150574},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.5879160761833191},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.567892849445343},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.5136162638664246},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.4963083863258362},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.46568694710731506},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.4564637243747711},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.43732404708862305},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.43250855803489685},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.41729676723480225},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.40213072299957275},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2196747362613678},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.17375198006629944},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.1210932731628418},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11622953414916992},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.08004313707351685},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00211-020-01161-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-020-01161-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-020-01161-9.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"mag:2931468134","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1904.00847.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1904.00847","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1904.00847","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1007/s00211-020-01161-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-020-01161-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-020-01161-9.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7830124546","display_name":null,"funder_award_id":"SFB F65","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320321691","display_name":"Universit\u00e4t Wien","ror":"https://ror.org/03prydq77"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2931468134.pdf","grobid_xml":"https://content.openalex.org/works/W2931468134.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W1602383637","https://openalex.org/W1604678099","https://openalex.org/W1964625607","https://openalex.org/W1979313496","https://openalex.org/W2002388618","https://openalex.org/W2017611864","https://openalex.org/W2026554262","https://openalex.org/W2038870672","https://openalex.org/W2042462787","https://openalex.org/W2059357993","https://openalex.org/W2073243103","https://openalex.org/W2087828859","https://openalex.org/W2129647233","https://openalex.org/W2135764443","https://openalex.org/W2166447449","https://openalex.org/W2170987671","https://openalex.org/W2376817935","https://openalex.org/W2496081756","https://openalex.org/W2602232473","https://openalex.org/W2785730518","https://openalex.org/W2961425540","https://openalex.org/W2963180515","https://openalex.org/W2963314385","https://openalex.org/W3010309843","https://openalex.org/W3021722416","https://openalex.org/W3095347060","https://openalex.org/W3099692878","https://openalex.org/W3110134061","https://openalex.org/W3148434010","https://openalex.org/W3176715688","https://openalex.org/W4210885577","https://openalex.org/W4255871072","https://openalex.org/W4293238311","https://openalex.org/W6751552446"],"related_works":["https://openalex.org/W2963180515","https://openalex.org/W1603983975","https://openalex.org/W2103725449","https://openalex.org/W2078875148","https://openalex.org/W2014672328","https://openalex.org/W2111173707","https://openalex.org/W2111134212","https://openalex.org/W2079867604","https://openalex.org/W3179760003","https://openalex.org/W2950026178","https://openalex.org/W3012411109","https://openalex.org/W2580794896","https://openalex.org/W1873489324","https://openalex.org/W2132934916","https://openalex.org/W77927023","https://openalex.org/W644048992","https://openalex.org/W2767697744","https://openalex.org/W1588869500","https://openalex.org/W2013768849","https://openalex.org/W2028810944"],"abstract_inverted_index":{"Abstract":[0],"The":[1,16,54,78],"semidiscretization":[2],"of":[3,57,75,103],"a":[4,82,115],"sound":[5],"soft":[6],"scattering":[7],"problem":[8],"modelled":[9],"by":[10,21,100],"the":[11,38,45,58,69,76,86,94,123],"wave":[12,40],"equation":[13,23],"is":[14,19,48,60],"analyzed.":[15],"spatial":[17],"treatment":[18],"done":[20],"integral":[22],"methods.":[24],"Two":[25],"temporal":[26,52],"discretizations":[27],"based":[28,49],"on":[29,37,50,81,85],"Runge\u2013Kutta":[30],"convolution":[31],"quadrature":[32],"are":[33],"compared:":[34],"one":[35,47,101],"relies":[36],"incoming":[39],"as":[41],"input":[42],"data":[43],"and":[44],"other":[46],"its":[51],"derivative.":[53],"convergence":[55],"rate":[56],"latter":[59],"shown":[61],"to":[62,114,122],"be":[63,98],"higher":[64],"than":[65],"previously":[66],"established":[67],"in":[68],"literature.":[70],"Numerical":[71],"results":[72],"indicate":[73],"sharpness":[74],"analysis.":[77],"proof":[79],"hinges":[80],"novel":[83],"estimate":[84],"Dirichlet-to-Impedance":[87],"map":[88],"for":[89,118],"certain":[90],"Helmholtz":[91],"problems.":[92],"Namely,":[93],"frequency":[95],"dependence":[96],"can":[97],"lowered":[99],"power":[102],"$$\\left|":[104],"s\\right|":[105],"$$":[106],"<mml:math":[107],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[108],"<mml:mfenced>":[109],"<mml:mi>s</mml:mi>":[110],"</mml:mfenced>":[111],"</mml:math>":[112],"(up":[113],"logarithmic":[116],"term":[117],"polygonal":[119],"domains)":[120],"compared":[121],"Dirichlet-to-Neumann":[124],"map.":[125]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}
