{"id":"https://openalex.org/W2139680668","doi":"https://doi.org/10.1137/s1064827599356171","title":"Numerical Methods for the Einstein Equations in Null Quasi-Spherical Coordinates","display_name":"Numerical Methods for the Einstein Equations in Null Quasi-Spherical Coordinates","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2139680668","doi":"https://doi.org/10.1137/s1064827599356171","mag":"2139680668"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827599356171","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827599356171","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/gr-qc/9904045","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078885185","display_name":"Robert Bartnik","orcid":null},"institutions":[{"id":"https://openalex.org/I188329596","display_name":"University of Canberra","ror":"https://ror.org/04s1nv328","country_code":"AU","type":"education","lineage":["https://openalex.org/I188329596"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Robert Bartnik","raw_affiliation_strings":["University of Canberra;"],"affiliations":[{"raw_affiliation_string":"University of Canberra;","institution_ids":["https://openalex.org/I188329596"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110036263","display_name":"Andrew H. Norton","orcid":null},"institutions":[{"id":"https://openalex.org/I188329596","display_name":"University of Canberra","ror":"https://ror.org/04s1nv328","country_code":"AU","type":"education","lineage":["https://openalex.org/I188329596"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Andrew H. Norton","raw_affiliation_strings":["University of Canberra;"],"affiliations":[{"raw_affiliation_string":"University of Canberra;","institution_ids":["https://openalex.org/I188329596"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5078885185"],"corresponding_institution_ids":["https://openalex.org/I188329596"],"apc_list":null,"apc_paid":null,"fwci":2.9955,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.91671298,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"22","issue":"3","first_page":"917","last_page":"950"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10025","display_name":"Black Holes and Theoretical Physics","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10025","display_name":"Black Holes and Theoretical Physics","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"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/T10095","display_name":"Cosmology and Gravitation Theories","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/T11405","display_name":"Geophysics and Gravity Measurements","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7707117795944214},{"id":"https://openalex.org/keywords/spherical-harmonics","display_name":"Spherical harmonics","score":0.5824757218360901},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49589475989341736},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.43013498187065125},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.42906653881073},{"id":"https://openalex.org/keywords/null","display_name":"Null (SQL)","score":0.4273304343223572},{"id":"https://openalex.org/keywords/spherical-coordinate-system","display_name":"Spherical coordinate system","score":0.42187464237213135},{"id":"https://openalex.org/keywords/coordinate-system","display_name":"Coordinate system","score":0.4137769341468811},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3327710032463074},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.27012360095977783},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.16991651058197021},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15494093298912048},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.10875147581100464}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7707117795944214},{"id":"https://openalex.org/C3768446","wikidata":"https://www.wikidata.org/wiki/Q877100","display_name":"Spherical harmonics","level":2,"score":0.5824757218360901},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49589475989341736},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.43013498187065125},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.42906653881073},{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.4273304343223572},{"id":"https://openalex.org/C126990412","wikidata":"https://www.wikidata.org/wiki/Q203218","display_name":"Spherical coordinate system","level":2,"score":0.42187464237213135},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.4137769341468811},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3327710032463074},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.27012360095977783},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.16991651058197021},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15494093298912048},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.10875147581100464},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s1064827599356171","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827599356171","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:gr-qc/9904045","is_oa":true,"landing_page_url":"http://arxiv.org/abs/gr-qc/9904045","pdf_url":"https://arxiv.org/pdf/gr-qc/9904045","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":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:gr-qc/9904045","is_oa":true,"landing_page_url":"http://arxiv.org/abs/gr-qc/9904045","pdf_url":"https://arxiv.org/pdf/gr-qc/9904045","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":71,"referenced_works":["https://openalex.org/W29185981","https://openalex.org/W641232363","https://openalex.org/W1484390400","https://openalex.org/W1499891147","https://openalex.org/W1526444941","https://openalex.org/W1638269932","https://openalex.org/W1789645782","https://openalex.org/W1805381866","https://openalex.org/W1965352509","https://openalex.org/W1967656590","https://openalex.org/W1968444060","https://openalex.org/W1973663906","https://openalex.org/W1979020487","https://openalex.org/W1979962982","https://openalex.org/W1984330431","https://openalex.org/W1987380803","https://openalex.org/W1987582921","https://openalex.org/W1988281968","https://openalex.org/W1995112015","https://openalex.org/W1995356931","https://openalex.org/W2002267783","https://openalex.org/W2006245583","https://openalex.org/W2006390736","https://openalex.org/W2006924732","https://openalex.org/W2012627235","https://openalex.org/W2012703912","https://openalex.org/W2017036002","https://openalex.org/W2017693571","https://openalex.org/W2018350372","https://openalex.org/W2021547757","https://openalex.org/W2028342982","https://openalex.org/W2036539190","https://openalex.org/W2048211332","https://openalex.org/W2054708802","https://openalex.org/W2056318444","https://openalex.org/W2057038741","https://openalex.org/W2060170348","https://openalex.org/W2061376823","https://openalex.org/W2066067035","https://openalex.org/W2077135959","https://openalex.org/W2088646430","https://openalex.org/W2090670432","https://openalex.org/W2092429904","https://openalex.org/W2092565853","https://openalex.org/W2110477814","https://openalex.org/W2127243291","https://openalex.org/W2131778920","https://openalex.org/W2138077665","https://openalex.org/W2144101903","https://openalex.org/W2153344483","https://openalex.org/W2187606436","https://openalex.org/W2231773349","https://openalex.org/W2293599327","https://openalex.org/W2472444483","https://openalex.org/W2484028276","https://openalex.org/W2593034150","https://openalex.org/W2792386146","https://openalex.org/W2794162265","https://openalex.org/W2991044660","https://openalex.org/W2998871297","https://openalex.org/W3092596371","https://openalex.org/W3098131225","https://openalex.org/W3101948707","https://openalex.org/W3105747650","https://openalex.org/W4237292901","https://openalex.org/W4245238886","https://openalex.org/W4293185733","https://openalex.org/W4298060601","https://openalex.org/W4298512876","https://openalex.org/W4300868822","https://openalex.org/W4388323349"],"related_works":["https://openalex.org/W4239999982","https://openalex.org/W2372486955","https://openalex.org/W2587023163","https://openalex.org/W2611466209","https://openalex.org/W4315557013","https://openalex.org/W3172489585","https://openalex.org/W4306147894","https://openalex.org/W2381527840","https://openalex.org/W2753519068","https://openalex.org/W4288443354"],"abstract_inverted_index":{"We":[0],"describe":[1],"algorithms":[2],"used":[3],"in":[4,10,115,125],"our":[5],"construction":[6],"of":[7,22,47,56,82,107,111],"a":[8,36,44,54,75,80,99],"fourth-order":[9],"time":[11,129],"evolution":[12,93],"for":[13,61,78,91],"the":[14,20,48,92,112,118,132],"full":[15],"Einstein":[16],"equations":[17],"and":[18,32,66,74],"assess":[19],"accuracy":[21],"some":[23],"representative":[24],"solutions.":[25],"The":[26],"scheme":[27],"employs":[28],"several":[29],"novel":[30],"geometric":[31],"numerical":[33],"techniques,":[34],"including":[35],"geometrically":[37],"invariant":[38],"coordinate":[39,133],"gauge,":[40],"which":[41],"leads":[42],"to":[43,98,122],"characteristic-transport":[45],"formulation":[46],"underlying":[49],"hyperbolic":[50],"system,":[51],"combined":[52],"with":[53],"\"method":[55],"lines\"":[57],"evolution;":[58],"convolution":[59],"splines":[60],"radial":[62],"interpolation,":[63],"regridding,":[64],"differentiation,":[65],"noise":[67],"suppression;":[68],"representations":[69],"using":[70],"spin-weighted":[71],"spherical":[72],"harmonics;":[73],"spectral":[76],"preconditioner":[77],"solving":[79],"class":[81],"first-order":[83],"elliptic":[84],"systems":[85],"on":[86],"S2":[87],".":[88],"Initial":[89],"data":[90,106],"is":[94,120],"unconstrained,":[95],"subject":[96],"only":[97],"mild":[100],"size":[101],"condition.":[102],"For":[103],"sample":[104],"initial":[105],"\"intermediate\"":[108],"strength":[109],"(19%":[110],"total":[113],"mass":[114],"gravitational":[116],"energy),":[117],"code":[119],"accurate":[121],"1":[123],"part":[124],"105,":[126],"until":[127],"null":[128],"z=55M":[130],"when":[131],"condition":[134],"breaks":[135],"down.":[136]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}