{"id":"https://openalex.org/W7128490767","doi":"https://doi.org/10.48550/arxiv.2602.07711","title":"High-Resolution Solvers for 3D Helmholtz Scattering Problems Using PFFT and Eigenvector-Based Preconditioning","display_name":"High-Resolution Solvers for 3D Helmholtz Scattering Problems Using PFFT and Eigenvector-Based Preconditioning","publication_year":2026,"publication_date":"2026-02-07","ids":{"openalex":"https://openalex.org/W7128490767","doi":"https://doi.org/10.48550/arxiv.2602.07711"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.07711","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5125568735","display_name":"Yury Gryazin","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gryazin, Yury","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007587557","display_name":"Ron L. Gonzales","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gonzales, Ron","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5006873445","display_name":"Xiaoye Sherry Li","orcid":"https://orcid.org/0000-0002-0747-698X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Xiaoye Sherry","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5125568735"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.2937000095844269,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.2937000095844269,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.29159998893737793,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.22020000219345093,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.7225000262260437},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.641700029373169},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.6279000043869019},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.5065000057220459},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.47269999980926514},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4343999922275543},{"id":"https://openalex.org/keywords/helmholtz-free-energy","display_name":"Helmholtz free energy","score":0.4223000109195709},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.41690000891685486},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.41589999198913574}],"concepts":[{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7225000262260437},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.641700029373169},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.6279000043869019},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5534999966621399},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5372999906539917},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.5065000057220459},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.47269999980926514},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4343999922275543},{"id":"https://openalex.org/C27592594","wikidata":"https://www.wikidata.org/wiki/Q865821","display_name":"Helmholtz free energy","level":2,"score":0.4223000109195709},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.41690000891685486},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.41589999198913574},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4081000089645386},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3928999900817871},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.38760000467300415},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.38260000944137573},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3634999990463257},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.35010001063346863},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.34380000829696655},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.323199987411499},{"id":"https://openalex.org/C177562468","wikidata":"https://www.wikidata.org/wiki/Q182893","display_name":"Dispersion (optics)","level":2,"score":0.322299987077713},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3133000135421753},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.30649998784065247},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30230000615119934},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2919999957084656},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.28839999437332153},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.2883000075817108},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.28459998965263367},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.2754000127315521},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.2522999942302704},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.2517000138759613}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.07711","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.07711","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.07711","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.07711","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":null,"raw_type":"Article"},"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9","score":0.44281119108200073}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"an":[3],"efficient":[4,79],"Krylov":[5],"subspace":[6],"iterative":[7],"solver":[8],"for":[9,127,157],"the":[10,48,70,73,109,114,138,154],"three-dimensional":[11],"(3D)":[12],"Helmholtz":[13],"equation":[14],"with":[15,26],"non-constant":[16],"coefficients":[17],"and":[18,33,40,91,120,161],"absorbing":[19,115],"boundary":[20,116],"conditions,":[21],"combining":[22],"high-resolution":[23,128],"compact":[24,42],"schemes":[25,129],"low-order":[27],"preconditioners.":[28],"To":[29],"mitigate":[30],"numerical":[31,151],"dispersion":[32],"reduce":[34],"pollution":[35],"error,":[36],"we":[37,75],"employ":[38],"fourth-":[39],"sixth-order":[41],"finite-difference":[43],"schemes,":[44],"thereby":[45],"significantly":[46],"softening":[47],"strict":[49],"points-per-wavelength":[50],"requirement.":[51],"The":[52,65,118,141],"resulting":[53],"large,":[54],"ill-conditioned":[55],"linear":[56],"systems":[57],"are":[58,130],"solved":[59],"using":[60],"a":[61,86,94,105,147],"preconditioned":[62],"GMRES":[63],"method.":[64],"key":[66],"innovation":[67],"lies":[68],"in":[69],"construction":[71],"of":[72,108,122,150],"preconditioner:":[74],"introduce":[76],"two":[77],"highly":[78],"direct":[80],"solvers":[81],"-":[82,101],"one":[83],"based":[84],"on":[85,93],"low-dimensional":[87],"eigenvector":[88],"transformation":[89],"(EigT)":[90],"another":[92],"partial":[95],"Fast":[96],"Fourier":[97],"Transform":[98],"(PFFT)":[99],"algorithm":[100],"both":[102],"derived":[103],"from":[104],"lower-order":[106,124],"approximation":[107],"original":[110],"problem":[111,159],"that":[112],"incorporates":[113],"conditions.":[117],"motivation":[119],"efficacy":[121],"this":[123],"preconditioning":[125],"strategy":[126],"analyzed":[131],"through":[132],"model":[133],"problems,":[134],"providing":[135],"insight":[136],"into":[137],"convergence":[139],"rate.":[140],"theoretical":[142],"analysis":[143],"is":[144],"validated":[145],"by":[146],"comprehensive":[148],"set":[149],"experiments,":[152],"demonstrating":[153],"method's":[155],"performance":[156],"realistic":[158],"sizes":[160],"parameters.":[162]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2026-02-11T00:00:00"}