{"id":"https://openalex.org/W4281298440","doi":"https://doi.org/10.1007/s11075-022-01315-w","title":"Effective numerical methods for simulating diffusion on a spherical surface in three dimensions","display_name":"Effective numerical methods for simulating diffusion on a spherical surface in three dimensions","publication_year":2022,"publication_date":"2022-05-14","ids":{"openalex":"https://openalex.org/W4281298440","doi":"https://doi.org/10.1007/s11075-022-01315-w"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-022-01315-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-022-01315-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-022-01315-w.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11075-022-01315-w.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003330950","display_name":"Kevin Burrage","orcid":"https://orcid.org/0000-0002-8111-1137"},"institutions":[{"id":"https://openalex.org/I160993911","display_name":"Queensland University of Technology","ror":"https://ror.org/03pnv4752","country_code":"AU","type":"education","lineage":["https://openalex.org/I160993911"]},{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]},{"id":"https://openalex.org/I4210123005","display_name":"ARC Centre of Excellence for Mathematical and Statistical Frontiers","ror":"https://ror.org/02vcqg248","country_code":"AU","type":"facility","lineage":["https://openalex.org/I1337719021","https://openalex.org/I165779595","https://openalex.org/I2801453606","https://openalex.org/I4210123005","https://openalex.org/I4210132349"]}],"countries":["AU","GB"],"is_corresponding":true,"raw_author_name":"Kevin Burrage","raw_affiliation_strings":["ARC Centre of Excellence for Mathematical and Statistical Frontiers, and School of Mathematical Sciences, Queensland University of Technology (QUT), Brisbane, Australia","Department of Computer Science, University of Oxford, Oxford, UK"],"raw_orcid":"https://orcid.org/0000-0002-8111-1137","affiliations":[{"raw_affiliation_string":"ARC Centre of Excellence for Mathematical and Statistical Frontiers, and School of Mathematical Sciences, Queensland University of Technology (QUT), Brisbane, Australia","institution_ids":["https://openalex.org/I4210123005","https://openalex.org/I160993911"]},{"raw_affiliation_string":"Department of Computer Science, University of Oxford, Oxford, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016673913","display_name":"Pamela Burrage","orcid":"https://orcid.org/0000-0002-6612-3084"},"institutions":[{"id":"https://openalex.org/I160993911","display_name":"Queensland University of Technology","ror":"https://ror.org/03pnv4752","country_code":"AU","type":"education","lineage":["https://openalex.org/I160993911"]},{"id":"https://openalex.org/I4210123005","display_name":"ARC Centre of Excellence for Mathematical and Statistical Frontiers","ror":"https://ror.org/02vcqg248","country_code":"AU","type":"facility","lineage":["https://openalex.org/I1337719021","https://openalex.org/I165779595","https://openalex.org/I2801453606","https://openalex.org/I4210123005","https://openalex.org/I4210132349"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Pamela M. Burrage","raw_affiliation_strings":["ARC Centre of Excellence for Mathematical and Statistical Frontiers, and School of Mathematical Sciences, Queensland University of Technology (QUT), Brisbane, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ARC Centre of Excellence for Mathematical and Statistical Frontiers, and School of Mathematical Sciences, Queensland University of Technology (QUT), Brisbane, Australia","institution_ids":["https://openalex.org/I4210123005","https://openalex.org/I160993911"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022689831","display_name":"Grant Lythe","orcid":"https://orcid.org/0000-0001-7966-5571"},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Grant Lythe","raw_affiliation_strings":["School of Mathematics, University of Leeds, Leeds, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Leeds, Leeds, UK","institution_ids":["https://openalex.org/I130828816"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5003330950"],"corresponding_institution_ids":["https://openalex.org/I160993911","https://openalex.org/I40120149","https://openalex.org/I4210123005"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.4305,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.63084185,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"91","issue":"4","first_page":"1577","last_page":"1596"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9714000225067139,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9714000225067139,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10770","display_name":"Soil Geostatistics and Mapping","score":0.9484999775886536,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9362999796867371,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/antisymmetric-relation","display_name":"Antisymmetric relation","score":0.8041713237762451},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7994047403335571},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4737825393676758},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4560123085975647},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.45078790187835693},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4383425712585449},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.4311394989490509},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.430345356464386},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4245760142803192},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.42207932472229004},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.24219968914985657},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11777350306510925},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.11625608801841736}],"concepts":[{"id":"https://openalex.org/C152401794","wikidata":"https://www.wikidata.org/wiki/Q583760","display_name":"Antisymmetric relation","level":2,"score":0.8041713237762451},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7994047403335571},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4737825393676758},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4560123085975647},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.45078790187835693},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4383425712585449},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.4311394989490509},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.430345356464386},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4245760142803192},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.42207932472229004},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.24219968914985657},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11777350306510925},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.11625608801841736},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s11075-022-01315-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-022-01315-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-022-01315-w.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:eprints.whiterose.ac.uk:197515","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400854","display_name":"White Rose Research Online (University of Leeds, The University of Sheffield, University of York)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2800616092","host_organization_name":"White Rose University Consortium","host_organization_lineage":["https://openalex.org/I2800616092"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:eprints.qut.edu.au:234265","is_oa":true,"landing_page_url":"http://purl.org/au-research/grants/arc/CE140100049","pdf_url":null,"source":{"id":"https://openalex.org/S4306402607","display_name":"QUT ePrints (Queensland University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I160993911","host_organization_name":"Queensland University of Technology","host_organization_lineage":["https://openalex.org/I160993911"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Numerical Algorithms","raw_type":"Contribution to Journal"}],"best_oa_location":{"id":"doi:10.1007/s11075-022-01315-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-022-01315-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-022-01315-w.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.5099999904632568,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4281298440.pdf","grobid_xml":"https://content.openalex.org/works/W4281298440.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1994384777","https://openalex.org/W2006533898","https://openalex.org/W2113413753","https://openalex.org/W2592871158","https://openalex.org/W2964057629","https://openalex.org/W3007741472","https://openalex.org/W4231021340","https://openalex.org/W4254294289"],"related_works":["https://openalex.org/W1968494762","https://openalex.org/W2527696949","https://openalex.org/W2366107444","https://openalex.org/W2075821346","https://openalex.org/W2385749544","https://openalex.org/W2046907195","https://openalex.org/W2095817824","https://openalex.org/W4388145910","https://openalex.org/W1976205134","https://openalex.org/W2381570729"],"abstract_inverted_index":{"In":[0],"order":[1],"to":[2],"construct":[3,41],"an":[4,62],"algorithm":[5],"for":[6,54],"homogeneous":[7],"diffusive":[8],"motion":[9],"that":[10,48,71],"lives":[11],"on":[12,37],"a":[13,21],"sphere,":[14],"we":[15,40],"consider":[16],"the":[17,51,75],"equivalent":[18],"process":[19],"of":[20,26,33,43],"randomly":[22],"rotating":[23],"spin":[24,52],"vector":[25],"constant":[27],"length.":[28],"By":[29],"introducing":[30],"appropriate":[31],"sets":[32],"random":[34,69],"variables":[35,70],"based":[36],"cross":[38],"products,":[39],"families":[42],"methods":[44],"with":[45],"increasing":[46],"efficacy":[47],"exactly":[49],"preserve":[50],"modulus":[53],"every":[55],"realisation.":[56],"This":[57],"is":[58],"done":[59],"by":[60],"exponentiating":[61],"antisymmetric":[63],"matrix":[64],"whose":[65],"entries":[66],"are":[67,72],"these":[68],"Gaussian":[73],"in":[74],"simplest":[76],"case.":[77]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}
