{"id":"https://openalex.org/W2046448057","doi":"https://doi.org/10.1016/j.cageo.2008.02.020","title":"On preconditioning for a parallel solution of the Richards equation","display_name":"On preconditioning for a parallel solution of the Richards equation","publication_year":2008,"publication_date":"2008-05-04","ids":{"openalex":"https://openalex.org/W2046448057","doi":"https://doi.org/10.1016/j.cageo.2008.02.020","mag":"2046448057"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.cageo.2008.02.020","pdf_url":null,"source":{"id":"https://openalex.org/S61699894","display_name":"Computers & Geosciences","issn_l":"0098-3004","issn":["0098-3004","1873-7803"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5070376588","display_name":"M. Herbst","orcid":"https://orcid.org/0000-0003-1371-4208"},"institutions":[{"id":"https://openalex.org/I171892758","display_name":"Forschungszentrum J\u00fclich","ror":"https://ror.org/02nv7yv05","country_code":"DE","type":"funder","lineage":["https://openalex.org/I1305996414","https://openalex.org/I171892758"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Michael Herbst","raw_affiliation_strings":["Agrosphere, ICG-4, Forschungszentrum J\u00fclich GmbH, D-52428 J\u00fclich, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Agrosphere, ICG-4, Forschungszentrum J\u00fclich GmbH, D-52428 J\u00fclich, Germany#TAB#","institution_ids":["https://openalex.org/I171892758"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070616057","display_name":"S. Gottschalk","orcid":null},"institutions":[{"id":"https://openalex.org/I171892758","display_name":"Forschungszentrum J\u00fclich","ror":"https://ror.org/02nv7yv05","country_code":"DE","type":"funder","lineage":["https://openalex.org/I1305996414","https://openalex.org/I171892758"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Swen Gottschalk","raw_affiliation_strings":["Agrosphere, ICG-4, Forschungszentrum J\u00fclich GmbH, D-52428 J\u00fclich, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Agrosphere, ICG-4, Forschungszentrum J\u00fclich GmbH, D-52428 J\u00fclich, Germany#TAB#","institution_ids":["https://openalex.org/I171892758"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110031122","display_name":"M. Rei\u00dfel","orcid":null},"institutions":[{"id":"https://openalex.org/I99977706","display_name":"FH Aachen","ror":"https://ror.org/04tqgg260","country_code":"DE","type":"education","lineage":["https://openalex.org/I99977706"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Rei\u00dfel","raw_affiliation_strings":["Fachhochschule Aachen, Standort J\u00fclich, Fachbereich Technomathematik, Ginsterweg 1, D-52428 J\u00fclich, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Fachhochschule Aachen, Standort J\u00fclich, Fachbereich Technomathematik, Ginsterweg 1, D-52428 J\u00fclich, Germany#TAB#","institution_ids":["https://openalex.org/I99977706"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079866708","display_name":"H. Hardelauf","orcid":null},"institutions":[{"id":"https://openalex.org/I171892758","display_name":"Forschungszentrum J\u00fclich","ror":"https://ror.org/02nv7yv05","country_code":"DE","type":"funder","lineage":["https://openalex.org/I1305996414","https://openalex.org/I171892758"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Horst Hardelauf","raw_affiliation_strings":["Agrosphere, ICG-4, Forschungszentrum J\u00fclich GmbH, D-52428 J\u00fclich, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Agrosphere, ICG-4, Forschungszentrum J\u00fclich GmbH, D-52428 J\u00fclich, Germany#TAB#","institution_ids":["https://openalex.org/I171892758"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031191525","display_name":"R. Kasteel","orcid":"https://orcid.org/0000-0003-3132-2056"},"institutions":[{"id":"https://openalex.org/I171892758","display_name":"Forschungszentrum J\u00fclich","ror":"https://ror.org/02nv7yv05","country_code":"DE","type":"funder","lineage":["https://openalex.org/I1305996414","https://openalex.org/I171892758"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Roy Kasteel","raw_affiliation_strings":["Agrosphere, ICG-4, Forschungszentrum J\u00fclich GmbH, D-52428 J\u00fclich, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Agrosphere, ICG-4, Forschungszentrum J\u00fclich GmbH, D-52428 J\u00fclich, Germany#TAB#","institution_ids":["https://openalex.org/I171892758"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029471525","display_name":"Mathieu Javaux","orcid":"https://orcid.org/0000-0002-6168-5467"},"institutions":[{"id":"https://openalex.org/I171892758","display_name":"Forschungszentrum J\u00fclich","ror":"https://ror.org/02nv7yv05","country_code":"DE","type":"funder","lineage":["https://openalex.org/I1305996414","https://openalex.org/I171892758"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Matthieu Javaux","raw_affiliation_strings":["Agrosphere, ICG-4, Forschungszentrum J\u00fclich GmbH, D-52428 J\u00fclich, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Agrosphere, ICG-4, Forschungszentrum J\u00fclich GmbH, D-52428 J\u00fclich, Germany#TAB#","institution_ids":["https://openalex.org/I171892758"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088502900","display_name":"Jan Vanderborght","orcid":"https://orcid.org/0000-0001-7381-3211"},"institutions":[{"id":"https://openalex.org/I171892758","display_name":"Forschungszentrum J\u00fclich","ror":"https://ror.org/02nv7yv05","country_code":"DE","type":"funder","lineage":["https://openalex.org/I1305996414","https://openalex.org/I171892758"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jan Vanderborght","raw_affiliation_strings":["Agrosphere, ICG-4, Forschungszentrum J\u00fclich GmbH, D-52428 J\u00fclich, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Agrosphere, ICG-4, Forschungszentrum J\u00fclich GmbH, D-52428 J\u00fclich, Germany#TAB#","institution_ids":["https://openalex.org/I171892758"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028331853","display_name":"Harry Vereecken","orcid":"https://orcid.org/0000-0002-8051-8517"},"institutions":[{"id":"https://openalex.org/I171892758","display_name":"Forschungszentrum J\u00fclich","ror":"https://ror.org/02nv7yv05","country_code":"DE","type":"funder","lineage":["https://openalex.org/I1305996414","https://openalex.org/I171892758"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Harry Vereecken","raw_affiliation_strings":["Agrosphere, ICG-4, Forschungszentrum J\u00fclich GmbH, D-52428 J\u00fclich, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Agrosphere, ICG-4, Forschungszentrum J\u00fclich GmbH, D-52428 J\u00fclich, Germany#TAB#","institution_ids":["https://openalex.org/I171892758"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3630,"currency":"USD","value_usd":3630},"apc_paid":null,"fwci":0.899,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":13,"citation_normalized_percentile":{"value":0.903385,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":85,"max":86},"biblio":{"volume":"34","issue":"12","first_page":"1958","last_page":"1963"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10716","display_name":"Soil and Unsaturated Flow","score":0.997,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T10716","display_name":"Soil and Unsaturated Flow","score":0.997,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9944,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9922,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.8261633},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.67474383},{"id":"https://openalex.org/keywords/richards-equation","display_name":"Richards equation","score":0.621763},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness","score":0.52267236},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.46726766},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.41990045}],"concepts":[{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.8261633},{"id":"https://openalex.org/C34727166","wikidata":"https://www.wikidata.org/wiki/Q515375","display_name":"Cholesky decomposition","level":3,"score":0.74226993},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.67474383},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.6418969},{"id":"https://openalex.org/C103272765","wikidata":"https://www.wikidata.org/wiki/Q2151066","display_name":"Richards equation","level":3,"score":0.621763},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.60068095},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.55427116},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.52267236},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5007107},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.46726766},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.4585213},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.42288283},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.41990045},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.41879928},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36108178},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3376833},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31517377},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31503505},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.25245476},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13444084},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10375792},{"id":"https://openalex.org/C159750122","wikidata":"https://www.wikidata.org/wiki/Q96621023","display_name":"Soil water","level":2,"score":0.09308624},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C39432304","wikidata":"https://www.wikidata.org/wiki/Q188847","display_name":"Environmental science","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C159390177","wikidata":"https://www.wikidata.org/wiki/Q9161265","display_name":"Soil science","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.cageo.2008.02.020","pdf_url":null,"source":{"id":"https://openalex.org/S61699894","display_name":"Computers & Geosciences","issn_l":"0098-3004","issn":["0098-3004","1873-7803"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","score":0.64,"display_name":"Life on land"}],"grants":[],"datasets":[],"versions":[],"referenced_works_count":15,"referenced_works":["https://openalex.org/W1542622005","https://openalex.org/W1603402595","https://openalex.org/W1702699184","https://openalex.org/W1885725396","https://openalex.org/W1965568221","https://openalex.org/W2006631142","https://openalex.org/W2035353632","https://openalex.org/W2039789965","https://openalex.org/W2075108083","https://openalex.org/W2096874741","https://openalex.org/W2110568140","https://openalex.org/W2117209730","https://openalex.org/W2131605326","https://openalex.org/W2137698624","https://openalex.org/W2162604832"],"related_works":["https://openalex.org/W4253880741","https://openalex.org/W4235544854","https://openalex.org/W2887042214","https://openalex.org/W2380565408","https://openalex.org/W2365612721","https://openalex.org/W2361205607","https://openalex.org/W2155025153","https://openalex.org/W2114781389","https://openalex.org/W2063502215","https://openalex.org/W1983864973"],"abstract_inverted_index":null,"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2046448057","counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-04-21T07:03:28.412916","created_date":"2016-06-24"}