{"id":"https://openalex.org/W1978806864","doi":"https://doi.org/10.1137/050635961","title":"Rapid Prolate Pseudospectral Differentiation and Interpolation with the Fast Multipole Method","display_name":"Rapid Prolate Pseudospectral Differentiation and Interpolation with the Fast Multipole Method","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1978806864","doi":"https://doi.org/10.1137/050635961","mag":"1978806864"},"language":"en","primary_location":{"id":"doi:10.1137/050635961","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050635961","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":["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/A5088158268","display_name":"Narayan Kovvali","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Narayan Kovvali","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028875553","display_name":"Wenbin Lin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wenbin Lin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111296047","display_name":"Zhiqin Zhao","orcid":"https://orcid.org/0000-0002-9681-1910"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhiqin Zhao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060693978","display_name":"Luise S. Couchman","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luise Couchman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5016448581","display_name":"Lawrence Carin","orcid":"https://orcid.org/0000-0001-6277-7948"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lawrence Carin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7626,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.69978582,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"28","issue":"2","first_page":"485","last_page":"497"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9959999918937683,"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/pseudospectral-optimal-control","display_name":"Pseudospectral optimal control","score":0.8319722414016724},{"id":"https://openalex.org/keywords/pseudo-spectral-method","display_name":"Pseudo-spectral method","score":0.8061175346374512},{"id":"https://openalex.org/keywords/gauss-pseudospectral-method","display_name":"Gauss pseudospectral method","score":0.7303762435913086},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6861667633056641},{"id":"https://openalex.org/keywords/chebyshev-pseudospectral-method","display_name":"Chebyshev pseudospectral method","score":0.6394225358963013},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6080136895179749},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5902001261711121},{"id":"https://openalex.org/keywords/fast-multipole-method","display_name":"Fast multipole method","score":0.5076395273208618},{"id":"https://openalex.org/keywords/multipole-expansion","display_name":"Multipole expansion","score":0.45273134112358093},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.4164888262748718},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39156657457351685},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38982143998146057},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34286263585090637},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.22670990228652954},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2197989821434021},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.19017836451530457},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.11602780222892761},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10849812626838684}],"concepts":[{"id":"https://openalex.org/C154304650","wikidata":"https://www.wikidata.org/wiki/Q7255577","display_name":"Pseudospectral optimal control","level":5,"score":0.8319722414016724},{"id":"https://openalex.org/C177937620","wikidata":"https://www.wikidata.org/wiki/Q7254447","display_name":"Pseudo-spectral method","level":4,"score":0.8061175346374512},{"id":"https://openalex.org/C71026131","wikidata":"https://www.wikidata.org/wiki/Q5527825","display_name":"Gauss pseudospectral method","level":5,"score":0.7303762435913086},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6861667633056641},{"id":"https://openalex.org/C122107654","wikidata":"https://www.wikidata.org/wiki/Q5089017","display_name":"Chebyshev pseudospectral method","level":5,"score":0.6394225358963013},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6080136895179749},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5902001261711121},{"id":"https://openalex.org/C135115559","wikidata":"https://www.wikidata.org/wiki/Q5437040","display_name":"Fast multipole method","level":3,"score":0.5076395273208618},{"id":"https://openalex.org/C52765159","wikidata":"https://www.wikidata.org/wiki/Q1027847","display_name":"Multipole expansion","level":2,"score":0.45273134112358093},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.4164888262748718},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39156657457351685},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38982143998146057},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34286263585090637},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.22670990228652954},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2197989821434021},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.19017836451530457},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.11602780222892761},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10849812626838684},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"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/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.0},{"id":"https://openalex.org/C142484921","wikidata":"https://www.wikidata.org/wiki/Q3890369","display_name":"Chebyshev equation","level":4,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050635961","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050635961","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1490180844","https://openalex.org/W1549220217","https://openalex.org/W1558122728","https://openalex.org/W1647247758","https://openalex.org/W1805381866","https://openalex.org/W1912930600","https://openalex.org/W1970610912","https://openalex.org/W1972649231","https://openalex.org/W1974943103","https://openalex.org/W1984051533","https://openalex.org/W1995816184","https://openalex.org/W2004682961","https://openalex.org/W2005998530","https://openalex.org/W2021953266","https://openalex.org/W2023583513","https://openalex.org/W2035383464","https://openalex.org/W2054557822","https://openalex.org/W2067111814","https://openalex.org/W2083206954","https://openalex.org/W2086213908","https://openalex.org/W2097898402","https://openalex.org/W2098533238","https://openalex.org/W2103604791","https://openalex.org/W2147163796","https://openalex.org/W2158575547","https://openalex.org/W2313443574","https://openalex.org/W4240906956"],"related_works":["https://openalex.org/W2550657075","https://openalex.org/W2281601070","https://openalex.org/W2761671048","https://openalex.org/W2143234151","https://openalex.org/W2354694671","https://openalex.org/W2503830135","https://openalex.org/W2360369146","https://openalex.org/W2027623489","https://openalex.org/W2192624384","https://openalex.org/W1512809069"],"abstract_inverted_index":{"Pseudospectral":[0],"methods":[1,20],"utilizing":[2],"prolate":[3,36,89,106],"spheroidal":[4],"wave":[5],"functions":[6,9],"as":[7],"basis":[8],"have":[10],"been":[11],"shown":[12],"to":[13,79,92],"possess":[14],"advantages":[15],"over":[16],"the":[17,28,35,56,71,81,88,98,103],"conventional":[18],"pseudospectral":[19,37,90,107],"based":[21],"on":[22],"trigonometric":[23],"and":[24,31,50,63,84,100],"orthogonal":[25],"polynomials.":[26],"However,":[27],"spectral":[29],"differentiation":[30],"interpolation":[32],"steps":[33],"of":[34,58,87,102],"method":[38,74,91],"involve":[39],"matrix-vector":[40],"products,":[41],"which,":[42],"if":[43],"evaluated":[44],"directly,":[45],"entail":[46],"O(N2)":[47],"memory":[48,82],"requirement":[49,83],"computational":[51,85],"complexity":[52,86],"(where":[53],"N":[54],"is":[55],"number":[57],"unknowns":[59],"utilized":[60],"for":[61],"discretization":[62],"interpolation).":[64],"In":[65],"this":[66],"work":[67],"we":[68],"show":[69],"that":[70],"fast":[72,105],"multipole":[73],"(FMM)":[75],"can":[76],"be":[77],"used":[78],"reduce":[80],"O(N).":[93],"Example":[94],"simulation":[95],"results":[96],"demonstrate":[97],"speed":[99],"accuracy":[101],"resulting":[104],"solver.":[108]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}