{"id":"https://openalex.org/W1978525452","doi":"https://doi.org/10.1137/060664094","title":"Logically Rectangular Grids and Finite Volume Methods for PDEs in Circular and Spherical Domains","display_name":"Logically Rectangular Grids and Finite Volume Methods for PDEs in Circular and Spherical Domains","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1978525452","doi":"https://doi.org/10.1137/060664094","mag":"1978525452"},"language":"en","primary_location":{"id":"doi:10.1137/060664094","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060664094","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022248855","display_name":"Donna Calhoun","orcid":"https://orcid.org/0000-0002-6005-4575"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Donna A. Calhoun","raw_affiliation_strings":["calhoun@amath.washington.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"calhoun@amath.washington.edu#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071853554","display_name":"Christiane Helzel","orcid":"https://orcid.org/0000-0002-9901-7149"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christiane Helzel","raw_affiliation_strings":["christiane.helzel@rub.de#TAB#"],"affiliations":[{"raw_affiliation_string":"christiane.helzel@rub.de#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085592203","display_name":"Randall J. LeVeque","orcid":"https://orcid.org/0000-0003-1384-4504"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Randall J. LeVeque","raw_affiliation_strings":["rjl@amath.washington.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"rjl@amath.washington.edu#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5022248855"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.5504,"has_fulltext":false,"cited_by_count":101,"citation_normalized_percentile":{"value":0.98528924,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"50","issue":"4","first_page":"723","last_page":"752"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5915361642837524},{"id":"https://openalex.org/keywords/regular-grid","display_name":"Regular grid","score":0.5864943861961365},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.5530446767807007},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.5119982361793518},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.4980921745300293},{"id":"https://openalex.org/keywords/mesh-generation","display_name":"Mesh generation","score":0.4773036241531372},{"id":"https://openalex.org/keywords/cartesian-coordinate-system","display_name":"Cartesian coordinate system","score":0.47525832056999207},{"id":"https://openalex.org/keywords/quadrilateral","display_name":"Quadrilateral","score":0.45402106642723083},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.4474744498729706},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.43289878964424133},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43266725540161133},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.4317711293697357},{"id":"https://openalex.org/keywords/adaptive-mesh-refinement","display_name":"Adaptive mesh refinement","score":0.41774046421051025},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3659626245498657},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3537335991859436},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29961347579956055},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.2611943483352661},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12197962403297424}],"concepts":[{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5915361642837524},{"id":"https://openalex.org/C43173174","wikidata":"https://www.wikidata.org/wiki/Q2646942","display_name":"Regular grid","level":3,"score":0.5864943861961365},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.5530446767807007},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.5119982361793518},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.4980921745300293},{"id":"https://openalex.org/C181145010","wikidata":"https://www.wikidata.org/wiki/Q4418033","display_name":"Mesh generation","level":3,"score":0.4773036241531372},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.47525832056999207},{"id":"https://openalex.org/C151756577","wikidata":"https://www.wikidata.org/wiki/Q36810","display_name":"Quadrilateral","level":3,"score":0.45402106642723083},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4474744498729706},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.43289878964424133},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43266725540161133},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.4317711293697357},{"id":"https://openalex.org/C131053463","wikidata":"https://www.wikidata.org/wiki/Q4680751","display_name":"Adaptive mesh refinement","level":2,"score":0.41774046421051025},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3659626245498657},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3537335991859436},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29961347579956055},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2611943483352661},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12197962403297424},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/060664094","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060664094","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.111.7458","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.111.7458","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.amath.washington.edu/~rjl/pubs/circles/066409.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.140.7977","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.140.7977","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.amath.washington.edu/~rjl/pubs/circles/SIR000723.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W81825161","https://openalex.org/W277419578","https://openalex.org/W1555627060","https://openalex.org/W1560515057","https://openalex.org/W1595775464","https://openalex.org/W1965552352","https://openalex.org/W1966775587","https://openalex.org/W1975276805","https://openalex.org/W1976328693","https://openalex.org/W1993184792","https://openalex.org/W1995653039","https://openalex.org/W2005539970","https://openalex.org/W2011783432","https://openalex.org/W2014962640","https://openalex.org/W2022385500","https://openalex.org/W2025483160","https://openalex.org/W2025525725","https://openalex.org/W2025700795","https://openalex.org/W2028441661","https://openalex.org/W2039893955","https://openalex.org/W2042660758","https://openalex.org/W2045823378","https://openalex.org/W2053085806","https://openalex.org/W2055333229","https://openalex.org/W2067216123","https://openalex.org/W2071681524","https://openalex.org/W2076247888","https://openalex.org/W2077047259","https://openalex.org/W2087535883","https://openalex.org/W2091921470","https://openalex.org/W2111413571","https://openalex.org/W2115619606","https://openalex.org/W2118725377","https://openalex.org/W2119315866","https://openalex.org/W2134426542","https://openalex.org/W2142545569","https://openalex.org/W2145421992","https://openalex.org/W2146386022","https://openalex.org/W2169043969","https://openalex.org/W2172317270","https://openalex.org/W2177339763","https://openalex.org/W3002039101","https://openalex.org/W4250320447","https://openalex.org/W4292169137","https://openalex.org/W4382891143"],"related_works":["https://openalex.org/W62594467","https://openalex.org/W4297030193","https://openalex.org/W2348089490","https://openalex.org/W2388631251","https://openalex.org/W4226422313","https://openalex.org/W846467522","https://openalex.org/W4239311038","https://openalex.org/W4253024819","https://openalex.org/W2096834459","https://openalex.org/W2367222541"],"abstract_inverted_index":{"We":[0],"describe":[1],"a":[2,44,54,80,189,202,208],"class":[3],"of":[4,27,66,72,89,149,185,191],"logically":[5,37],"rectangular":[6,38],"quadrilateral":[7],"and":[8,16,30,39,69,141,199,226],"hexahedral":[9],"grids":[10,35,110,143,187],"for":[11,22,147,188,239],"solving":[12],"PDEs":[13],"in":[14,122,201,221],"circular":[15],"spherical":[17],"domains,":[18],"including":[19,193],"grid":[20,151],"mappings":[21,91],"the":[23,25,28,31,40,64,70,90,100,105,117,136,139,159,166,182,212,222,233,240],"circle,":[24],"surface":[26],"sphere,":[29],"three-dimensional":[32],"ball.":[33],"The":[34],"are":[36,111,219],"computational":[41],"domain":[42,78],"is":[43,144,214,230],"single":[45],"Cartesian":[46],"grid.":[47],"Compared":[48],"to":[49,104,128],"alternative":[50],"approaches":[51],"based":[52],"on":[53,132,211,232],"multiblock":[55],"data":[56],"structure":[57],"or":[58,102,168,175],"unstructured":[59],"triangulations,":[60],"this":[61,93],"approach":[62],"simplifies":[63],"implementation":[65],"numerical":[67],"methods":[68,156],"use":[71,184],"adaptive":[73],"refinement.":[74],"A":[75],"more":[76],"general":[77],"with":[79,95,173,236],"smooth":[81,97],"boundary":[82],"can":[83,124],"be":[84,125],"gridded":[85],"by":[86],"composing":[87],"one":[88],"from":[92,99,165,207],"paper":[94],"another":[96],"mapping":[98],"circle":[101],"sphere":[103,213],"desired":[106],"domain.":[107],"Although":[108],"these":[109,133,186],"highly":[112],"nonorthogonal,":[113],"we":[114],"show":[115],"that":[116,171],"high-resolution":[118],"wave-propagation":[119,160],"algorithm":[120,161],"implemented":[121,220],"clawpack":[123,223],"used":[126],"effectively":[127],"approximate":[129],"hyperbolic":[130],"problems":[131],"grids.":[134,177],"Since":[135],"ratio":[137],"between":[138],"largest":[140],"smallest":[142],"below":[145],"2":[146],"most":[148],"our":[150],"mappings,":[152],"explicit":[153],"finite":[154],"volume":[155],"such":[157],"as":[158],"do":[162],"not":[163],"suffer":[164],"center":[167],"pole":[169],"singularities":[170],"arise":[172],"polar":[174],"latitude-longitude":[176],"Numerical":[178],"test":[179],"calculations":[180],"illustrate":[181],"potential":[183],"variety":[190],"applications":[192],"Euler":[194],"equations,":[195,198],"shallow":[196],"water":[197],"acoustics":[200],"heterogeneous":[203],"medium.":[204],"Pattern":[205],"formation":[206],"reaction-diffusion":[209],"equation":[210],"also":[215],"considered.":[216],"All":[217],"examples":[218],"software":[224],"package":[225],"full":[227],"source":[228],"code":[229],"available":[231],"web,":[234],"along":[235],"MATLAB":[237],"routines":[238],"various":[241],"mappings.":[242]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}
