{"id":"https://openalex.org/W4416117076","doi":"https://doi.org/10.1016/j.camwa.2026.06.033","title":"Robust and scalable nonlinear solvers for finite element discretizations of biological transportation networks","display_name":"Robust and scalable nonlinear solvers for finite element discretizations of biological transportation networks","publication_year":2026,"publication_date":"2026-07-03","ids":{"openalex":"https://openalex.org/W4416117076","doi":"https://doi.org/10.1016/j.camwa.2026.06.033"},"language":"en","primary_location":{"id":"doi:10.1016/j.camwa.2026.06.033","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.camwa.2026.06.033","pdf_url":null,"source":{"id":"https://openalex.org/S4210205691","display_name":"Computers & Mathematics with Applications","issn_l":"0898-1221","issn":["0898-1221","1873-7668"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers & Mathematics with Applications","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2504.04447","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058484577","display_name":"Jan Ha\u0161kovec","orcid":"https://orcid.org/0000-0003-3464-304X"},"institutions":[{"id":"https://openalex.org/I71920554","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38","country_code":"SA","type":"education","lineage":["https://openalex.org/I71920554"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Jan Haskovec","raw_affiliation_strings":["Mathematical and Computer Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-3464-304X","affiliations":[{"raw_affiliation_string":"Mathematical and Computer Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia","institution_ids":["https://openalex.org/I71920554"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110260067","display_name":"Peter A. Markowich","orcid":"https://orcid.org/0000-0002-3704-1821"},"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/I71920554","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38","country_code":"SA","type":"education","lineage":["https://openalex.org/I71920554"]}],"countries":["AT","SA"],"is_corresponding":false,"raw_author_name":"Peter Markowich","raw_affiliation_strings":["Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, Vienna, 1090, Austria","Mathematical and Computer Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, Vienna, 1090, Austria","institution_ids":["https://openalex.org/I129774422"]},{"raw_affiliation_string":"Mathematical and Computer Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia","institution_ids":["https://openalex.org/I71920554"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030837260","display_name":"Simone Portaro","orcid":"https://orcid.org/0000-0001-9278-2705"},"institutions":[{"id":"https://openalex.org/I26415053","display_name":"University of L'Aquila","ror":"https://ror.org/01j9p1r26","country_code":"IT","type":"education","lineage":["https://openalex.org/I26415053"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Simone Portaro","raw_affiliation_strings":["Dipartimento di Ingegneria e Scienze dell\u2019Informazione e Matematica (DISIM), Universit\u00e0 degli Studi dell\u2019Aquila, L\u2019Aquila, Italy"],"raw_orcid":"https://orcid.org/0000-0001-9278-2705","affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria e Scienze dell\u2019Informazione e Matematica (DISIM), Universit\u00e0 degli Studi dell\u2019Aquila, L\u2019Aquila, Italy","institution_ids":["https://openalex.org/I26415053"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024375169","display_name":"Stefano Zampini","orcid":"https://orcid.org/0000-0002-0435-0433"},"institutions":[{"id":"https://openalex.org/I71920554","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38","country_code":"SA","type":"education","lineage":["https://openalex.org/I71920554"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Stefano Zampini","raw_affiliation_strings":["Mathematical and Computer Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-0435-0433","affiliations":[{"raw_affiliation_string":"Mathematical and Computer Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia","institution_ids":["https://openalex.org/I71920554"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5024375169"],"corresponding_institution_ids":["https://openalex.org/I71920554"],"apc_list":{"value":3480,"currency":"USD","value_usd":3480},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00534548,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"219","issue":null,"first_page":"21","last_page":"39"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13362","display_name":"Slime Mold and Myxomycetes Research","score":0.9642999768257141,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/T13362","display_name":"Slime Mold and Myxomycetes Research","score":0.9642999768257141,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.011599999852478504,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.007199999876320362,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6952000260353088},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6438999772071838},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5992000102996826},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.5629000067710876},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.5490999817848206},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5480999946594238},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5142999887466431},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.4555000066757202},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.40230000019073486}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6952000260353088},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6438999772071838},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6021000146865845},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5992000102996826},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.5629000067710876},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.5490999817848206},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5480999946594238},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5142999887466431},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.48730000853538513},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.4555000066757202},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4047999978065491},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.40230000019073486},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.40119999647140503},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.3797999918460846},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.3781000077724457},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3573000133037567},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.353300005197525},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.3208000063896179},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3176000118255615},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.3073999881744385},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.30379998683929443},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.27959999442100525},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.27090001106262207},{"id":"https://openalex.org/C14961307","wikidata":"https://www.wikidata.org/wiki/Q5377176","display_name":"Energy minimization","level":2,"score":0.26420000195503235},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.26260000467300415},{"id":"https://openalex.org/C2779585090","wikidata":"https://www.wikidata.org/wiki/Q3457762","display_name":"Resilience (materials science)","level":2,"score":0.2624000012874603},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.2615000009536743},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2558000087738037},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.2556000053882599}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1016/j.camwa.2026.06.033","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.camwa.2026.06.033","pdf_url":null,"source":{"id":"https://openalex.org/S4210205691","display_name":"Computers & Mathematics with Applications","issn_l":"0898-1221","issn":["0898-1221","1873-7668"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers & Mathematics with Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2504.04447","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2504.04447","pdf_url":"https://arxiv.org/pdf/2504.04447","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2504.04447","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2504.04447","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2504.04447","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2504.04447","pdf_url":"https://arxiv.org/pdf/2504.04447","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322320","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-08-13T07:04:57.449891","created_date":"2025-10-10T00:00:00"}