Uncertainty quantification for random domains using periodic random variables
We consider uncertainty quantification for the Poisson problem subject to domain uncertainty. For the stochastic parameterization of the random domain, we use the model recently introduced by Kaarnioja et al. (SIAM J. Numer. Anal., 2020) in which a countably infinite number of independent random var...
Saved in:
| Published in | Numerische Mathematik Vol. 156; no. 1; pp. 273 - 317 |
|---|---|
| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.02.2024
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | We consider uncertainty quantification for the Poisson problem subject to domain uncertainty. For the stochastic parameterization of the random domain, we use the model recently introduced by Kaarnioja et al. (SIAM J. Numer. Anal., 2020) in which a countably infinite number of independent random variables enter the random field as periodic functions. We develop lattice quasi-Monte Carlo (QMC) cubature rules for computing the expected value of the solution to the Poisson problem subject to domain uncertainty. These QMC rules can be shown to exhibit higher order cubature convergence rates permitted by the periodic setting independently of the stochastic dimension of the problem. In addition, we present a complete error analysis for the problem by taking into account the approximation errors incurred by truncating the input random field to a finite number of terms and discretizing the spatial domain using finite elements. The paper concludes with numerical experiments demonstrating the theoretical error estimates. |
|---|---|
| AbstractList | We consider uncertainty quantification for the Poisson problem subject to domain uncertainty. For the stochastic parameterization of the random domain, we use the model recently introduced by Kaarnioja et al. (SIAM J. Numer. Anal., 2020) in which a countably infinite number of independent random variables enter the random field as periodic functions. We develop lattice quasi-Monte Carlo (QMC) cubature rules for computing the expected value of the solution to the Poisson problem subject to domain uncertainty. These QMC rules can be shown to exhibit higher order cubature convergence rates permitted by the periodic setting independently of the stochastic dimension of the problem. In addition, we present a complete error analysis for the problem by taking into account the approximation errors incurred by truncating the input random field to a finite number of terms and discretizing the spatial domain using finite elements. The paper concludes with numerical experiments demonstrating the theoretical error estimates. We consider uncertainty quantification for the Poisson problem subject to domain uncertainty. For the stochastic parameterization of the random domain, we use the model recently introduced by Kaarnioja et al. (SIAM J. Numer. Anal., 2020) in which a countably infinite number of independent random variables enter the random field as periodic functions. We develop lattice quasi-Monte Carlo (QMC) cubature rules for computing the expected value of the solution to the Poisson problem subject to domain uncertainty. These QMC rules can be shown to exhibit higher order cubature convergence rates permitted by the periodic setting independently of the stochastic dimension of the problem. In addition, we present a complete error analysis for the problem by taking into account the approximation errors incurred by truncating the input random field to a finite number of terms and discretizing the spatial domain using finite elements. The paper concludes with numerical experiments demonstrating the theoretical error estimates. |
| Author | Kaarnioja, Vesa Kuo, Frances Y. Harbrecht, Helmut Hakula, Harri Sloan, Ian H. |
| Author_xml | – sequence: 1 givenname: Harri surname: Hakula fullname: Hakula, Harri organization: Department of Mathematics and Systems Analysis, Aalto University School of Science – sequence: 2 givenname: Helmut surname: Harbrecht fullname: Harbrecht, Helmut organization: Departement Mathematik und Informatik, Universität Basel – sequence: 3 givenname: Vesa surname: Kaarnioja fullname: Kaarnioja, Vesa email: vesa.kaarnioja@fu-berlin.de organization: Fachbereich Mathematik und Informatik, Freie Universität Berlin – sequence: 4 givenname: Frances Y. surname: Kuo fullname: Kuo, Frances Y. organization: School of Mathematics and Statistics, UNSW Sydney – sequence: 5 givenname: Ian H. surname: Sloan fullname: Sloan, Ian H. organization: School of Mathematics and Statistics, UNSW Sydney |
| BookMark | eNp9kE1LAzEQhoNUsK3-AU8LnqOZJPuRoxS_oOLFgreQzSYlpU3aZFfovzd1FW_CDDMwz_sOvDM08cEbhK6B3AIh9V0ihAJgQhkmwATF1RmaEsFLzCgvJ3knVOBSiI8LNEtpQwjUFYcpel15bWKvnO-PxWFQvnfWadW74AsbYhGV78KuyJ2RVAzJ-XWxN9GFzunf66eKTrVbky7RuVXbZK5-5hytHh_eF894-fb0srhfYs2A9xgE440RVrOu0pwxDoKU0Gpb0tZyrgRtO9W0QjdlrpJ1tOagedtWFdMUOjZHN6PvPobDYFIvN2GIPr-UVFCoWRZVmaIjpWNIKRor99HtVDxKIPIUmxxjkzk2-R2bPInYKEoZ9msT_6z_UX0BQkZySg |
| Cites_doi | 10.1137/0724010 10.1137/19M1262796 10.1007/s00211-008-0147-9 10.1007/s00211-019-01046-6 10.1002/nme.3004 10.1137/16M1099406 10.1137/110845537 10.1007/978-3-319-91436-7_13 10.1007/978-3-642-61798-0 10.1142/S0218202517500439 10.1007/s00211-016-0791-4 10.1016/S0045-7825(02)00354-7 10.1016/j.camwa.2016.01.005 10.26190/669X-A286 10.1007/s40072-021-00214-w 10.1137/100799010 10.1137/040613160 10.1137/130943984 10.1007/s10444-018-9594-8 10.1007/s00211-005-0674-6 10.1016/j.jmva.2006.03.001 |
| ContentType | Journal Article |
| Copyright | The Author(s) 2024 The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| Copyright_xml | – notice: The Author(s) 2024 – notice: The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| DBID | C6C AAYXX CITATION |
| DOI | 10.1007/s00211-023-01392-6 |
| DatabaseName | Springer Nature OA Free Journals CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | CrossRef |
| Database_xml | – sequence: 1 dbid: C6C name: SpringerOpen Free (Free internet resource, activated by CARLI) url: http://www.springeropen.com/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics Computer Science |
| EISSN | 0945-3245 |
| EndPage | 317 |
| ExternalDocumentID | 10_1007_s00211_023_01392_6 |
| GrantInformation_xml | – fundername: Freie Universität Berlin (1008) |
| GroupedDBID | --Z -52 -5D -5G -BR -EM -Y2 -~C -~X .86 .DC .VR 06D 0R~ 0VY 123 199 1N0 1SB 203 29N 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2WC 2~H 30V 4.4 406 408 409 40D 40E 41~ 5QI 5VS 67Z 692 6NX 6TJ 78A 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABLJU ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACGFO ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACREN ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADYOE ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFDYV AFEXP AFFNX AFGCZ AFLOW AFQWF AFWTZ AFYQB AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMTXH AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BAPOH BBWZM BDATZ BGNMA BSONS C6C CAG COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ H~9 I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV KOW KQ8 LAS LLZTM LO0 M4Y MA- N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OK1 P19 P2P P9R PF0 PKN PT4 PT5 QOK QOS R4E R89 R9I REI RHV RIG RNI RNS ROL RPX RSV RYB RZK RZZ S16 S1Z S26 S27 S28 S3B SAP SCLPG SDD SDH SDM SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TN5 TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WH7 WK8 XJT YLTOR YNT YQT Z45 Z5O Z7R Z7X Z83 Z86 Z88 Z8M Z8R Z8W Z92 ZMTXR ZWQNP ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ACMFV ACSTC ADHKG AEZWR AFDZB AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR AYFIA CITATION ABRTQ |
| ID | FETCH-LOGICAL-c314t-19348e9fc3d6c433419051bcf52bf44a92bda8b9c85c8553d2741c4bb663c21d3 |
| IEDL.DBID | C6C |
| ISSN | 0029-599X |
| IngestDate | Sun Jul 13 05:39:00 EDT 2025 Tue Jul 01 00:36:51 EDT 2025 Fri Feb 21 02:40:28 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | 65D30 35R60 65D32 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c314t-19348e9fc3d6c433419051bcf52bf44a92bda8b9c85c8553d2741c4bb663c21d3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| OpenAccessLink | https://doi.org/10.1007/s00211-023-01392-6 |
| PQID | 2921735536 |
| PQPubID | 2043616 |
| PageCount | 45 |
| ParticipantIDs | proquest_journals_2921735536 crossref_primary_10_1007_s00211_023_01392_6 springer_journals_10_1007_s00211_023_01392_6 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2024-02-01 |
| PublicationDateYYYYMMDD | 2024-02-01 |
| PublicationDate_xml | – month: 02 year: 2024 text: 2024-02-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | Berlin/Heidelberg |
| PublicationPlace_xml | – name: Berlin/Heidelberg – name: Heidelberg |
| PublicationTitle | Numerische Mathematik |
| PublicationTitleAbbrev | Numer. Math |
| PublicationYear | 2024 |
| Publisher | Springer Berlin Heidelberg Springer Nature B.V |
| Publisher_xml | – name: Springer Berlin Heidelberg – name: Springer Nature B.V |
| References | Castrillón-CandásJENobileFTemponeRFAnalytic regularity and collocation approximation for elliptic PDEs with random domain deformationsComput. Math. Appl.201671611731197347191710.1016/j.camwa.2016.01.005 GrisvardPElliptic Problems in Nonsmooth Domains1985New YorkPitman Publishing Inc KressnerDToblerCLow-rank tensor Krylov subspace methods for parametrized linear systemsSIAM J. Matrix Anal. Appl.201132412881316285461410.1137/100799010 MohanPSNairPBKeaneAJStochastic projection schemes for deterministic linear elliptic partial differential equations on random domainsInt. J. Numer. Methods Eng.2011857874895279122810.1002/nme.3004 AhlforsLVConformal Invariants: Topics in Geometric Function Theory. Higher Mathematics Series1973New YorkMcGraw-Hill DickJKuoFYLe GiaQTNuyensDSchwabCHigher order QMC Petrov-Galerkin discretization for affine parametric operator equations with random field inputsSIAM J. Numer. Anal.201452626762702327642810.1137/130943984 HarbrechtHOn output functionals of boundary value problems on stochastic domainsMath. Methods Appl. Sci.2010331911022591227 Olver, F.W.J., Olde Daalhuis, A.B., Lozier, D.W., Schneider, B.I., Boisvert, R.F., Clark, C.W., Miller, B.R., Saunders, B.V., Cohl, H.S., McClain, M.A., eds.: NIST Digital Library of Mathematical Functions. Release 1.1.6 of 2022-06-30., http://dlmf.nist.gov Harbrecht, H., Karnaev, V., Schmidlin, M.: Quantifying domain uncertainty in linear elasticity. Tech. Rep. 2023-06, Fachbereich Mathematik, Universität Basel, Switzerland (2023) Guth, P.A., Kaarnioja, V.: Generalized dimension truncation error analysis for high-dimensional numerical integration: lognormal setting and beyond (2022). Preprint at arXiv:2209.06176 HarbrechtHPetersMSiebenmorgenMAnalysis of the domain mapping method for elliptic diffusion problems on random domainsNumer. Math.20161344823856356328210.1007/s00211-016-0791-4 Jerez-HanckesCSchwabCZechJElectromagnetic wave scattering by random surfaces: Shape holomorphyMath. Models Methods Appl. Sci.2017271222292259370355710.1142/S0218202517500439 KaarniojaVKuoFYSloanIHUncertainty quantification using periodic random variablesSIAM J. Numer. Anal.202058210681091408038910.1137/19M1262796 XiuDTartakovskyDMNumerical methods for differential equations in random domainsSIAM J. Sci. Comput.200628311671185224080910.1137/040613160 BabuškaIChatzipantelidisPOn solving elliptic stochastic partial differential equationsComput. Methods Appl. Mech. Eng.2002191409341222002CMAME.191.4093B191979010.1016/S0045-7825(02)00354-7 Hörmander, L.: An Introduction to Complex Analysis in Several Variables, 3rd edn. North-Holland (1990) HiptmairRScarabosioLSchillingsCSchwabCLarge deformation shape uncertainty quantification in acoustic scatteringAdv. Comput. Math.201844514751518387402710.1007/s10444-018-9594-8 Kaarnioja, V., Kuo, F.Y., Sloan, I.H.: Lattice-based kernel approximation and serendipitous weights for parametric PDEs in very high dimensions. To appear in: A. Hinrichs, P. Kritzer, F. Pillichshammer (eds.). Monte Carlo and Quasi-Monte Carlo Methods (2022). Springer Verlag Katana: Published online (2010). https://doi.org/10.26190/669X-A286 KuoFYSchwabCSloanIHQuasi-Monte Carlo finite element methods for a class of elliptic partial differential equations with random coefficientsSIAM J. Numer. Anal.201250633513374302415910.1137/110845537 GantnerRNOwenABGlynnPWDimension truncation in QMC for affine-parametric operator equationsMonte Carlo and Quasi-Monte Carlo Methods 20162018Stanford, CASpringer24926410.1007/978-3-319-91436-7_13 SloanIHKachoyanPJLattice methods for multiple integration: Theory, error analysis and examplesSIAM J. Numer. Anal.19872411161281987SJNA...24..116S87473910.1137/0724010 SavitsTHSome statistical applications of Faa di BrunoJ. Multivariate Anal.2006971021312140230162910.1016/j.jmva.2006.03.001 Guth, P.A., Kaarnioja, V., Kuo, F.Y., Schillings, C., Sloan, I.H.: Parabolic PDE-constrained optimal control under uncertainty with entropic risk measure using quasi-Monte Carlo integration (2022). Preprint at arXiv:2208.02767 CohenASchwabCZechJShape holomorphy of the stationary Navier-Stokes equationsSIAM J. Math. Anal.201850217201752378074210.1137/16M1099406 HarbrechtHSchneiderRSchwabCSparse second moment analysis for elliptic problems in stochastic domainsNumer. Math.20081093385414239915010.1007/s00211-008-0147-9 GilbertADGrahamIGKuoFYScheichlRSloanIHAnalysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficientsNumer. Math.20191424863915397585210.1007/s00211-019-01046-6 Harbrecht, H., Schmidlin, M.: Multilevel quadrature for elliptic problems on random domains by the coupling of FEM and BEM. Stoch. Partial Differ. Equ. Anal. Comput. 10(4), 1619–1650 (2022) HardyGHLittlewoodJEPólyaGInequalities1934CambridgeCambridge University Press GilbargDTrudingerNSElliptic Partial Differential Equations of Second Order20012BerlinSpringer10.1007/978-3-642-61798-0 DickJSloanIHWangXWoźniakowskiHGood lattice rules in weighted Korobov spaces with general weightsNumer. Math.200610316397220761510.1007/s00211-005-0674-6 LV Ahlfors (1392_CR1) 1973 V Kaarnioja (1392_CR23) 2020; 58 H Harbrecht (1392_CR17) 2008; 109 GH Hardy (1392_CR18) 1934 JE Castrillón-Candás (1392_CR3) 2016; 71 D Kressner (1392_CR25) 2011; 32 1392_CR24 1392_CR20 1392_CR22 RN Gantner (1392_CR7) 2018 TH Savits (1392_CR29) 2006; 97 1392_CR28 AD Gilbert (1392_CR9) 2019; 142 I Babuška (1392_CR2) 2002; 191 PS Mohan (1392_CR27) 2011; 85 H Harbrecht (1392_CR13) 2010; 33 J Dick (1392_CR6) 2006; 103 1392_CR12 D Xiu (1392_CR31) 2006; 28 1392_CR14 A Cohen (1392_CR4) 2018; 50 1392_CR11 P Grisvard (1392_CR10) 1985 R Hiptmair (1392_CR19) 2018; 44 IH Sloan (1392_CR30) 1987; 24 C Jerez-Hanckes (1392_CR21) 2017; 27 D Gilbarg (1392_CR8) 2001 H Harbrecht (1392_CR15) 2016; 134 J Dick (1392_CR5) 2014; 52 1392_CR16 FY Kuo (1392_CR26) 2012; 50 |
| References_xml | – reference: HarbrechtHOn output functionals of boundary value problems on stochastic domainsMath. Methods Appl. Sci.2010331911022591227 – reference: HarbrechtHSchneiderRSchwabCSparse second moment analysis for elliptic problems in stochastic domainsNumer. Math.20081093385414239915010.1007/s00211-008-0147-9 – reference: MohanPSNairPBKeaneAJStochastic projection schemes for deterministic linear elliptic partial differential equations on random domainsInt. J. Numer. Methods Eng.2011857874895279122810.1002/nme.3004 – reference: SloanIHKachoyanPJLattice methods for multiple integration: Theory, error analysis and examplesSIAM J. Numer. Anal.19872411161281987SJNA...24..116S87473910.1137/0724010 – reference: Olver, F.W.J., Olde Daalhuis, A.B., Lozier, D.W., Schneider, B.I., Boisvert, R.F., Clark, C.W., Miller, B.R., Saunders, B.V., Cohl, H.S., McClain, M.A., eds.: NIST Digital Library of Mathematical Functions. Release 1.1.6 of 2022-06-30., http://dlmf.nist.gov/ – reference: GilbertADGrahamIGKuoFYScheichlRSloanIHAnalysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficientsNumer. Math.20191424863915397585210.1007/s00211-019-01046-6 – reference: CohenASchwabCZechJShape holomorphy of the stationary Navier-Stokes equationsSIAM J. Math. Anal.201850217201752378074210.1137/16M1099406 – reference: Guth, P.A., Kaarnioja, V.: Generalized dimension truncation error analysis for high-dimensional numerical integration: lognormal setting and beyond (2022). Preprint at arXiv:2209.06176 – reference: GantnerRNOwenABGlynnPWDimension truncation in QMC for affine-parametric operator equationsMonte Carlo and Quasi-Monte Carlo Methods 20162018Stanford, CASpringer24926410.1007/978-3-319-91436-7_13 – reference: Katana: Published online (2010). https://doi.org/10.26190/669X-A286 – reference: KressnerDToblerCLow-rank tensor Krylov subspace methods for parametrized linear systemsSIAM J. Matrix Anal. Appl.201132412881316285461410.1137/100799010 – reference: XiuDTartakovskyDMNumerical methods for differential equations in random domainsSIAM J. Sci. Comput.200628311671185224080910.1137/040613160 – reference: Castrillón-CandásJENobileFTemponeRFAnalytic regularity and collocation approximation for elliptic PDEs with random domain deformationsComput. Math. Appl.201671611731197347191710.1016/j.camwa.2016.01.005 – reference: HardyGHLittlewoodJEPólyaGInequalities1934CambridgeCambridge University Press – reference: HiptmairRScarabosioLSchillingsCSchwabCLarge deformation shape uncertainty quantification in acoustic scatteringAdv. Comput. Math.201844514751518387402710.1007/s10444-018-9594-8 – reference: Guth, P.A., Kaarnioja, V., Kuo, F.Y., Schillings, C., Sloan, I.H.: Parabolic PDE-constrained optimal control under uncertainty with entropic risk measure using quasi-Monte Carlo integration (2022). Preprint at arXiv:2208.02767 – reference: GilbargDTrudingerNSElliptic Partial Differential Equations of Second Order20012BerlinSpringer10.1007/978-3-642-61798-0 – reference: Harbrecht, H., Schmidlin, M.: Multilevel quadrature for elliptic problems on random domains by the coupling of FEM and BEM. Stoch. Partial Differ. Equ. Anal. Comput. 10(4), 1619–1650 (2022) – reference: DickJKuoFYLe GiaQTNuyensDSchwabCHigher order QMC Petrov-Galerkin discretization for affine parametric operator equations with random field inputsSIAM J. Numer. Anal.201452626762702327642810.1137/130943984 – reference: Hörmander, L.: An Introduction to Complex Analysis in Several Variables, 3rd edn. North-Holland (1990) – reference: GrisvardPElliptic Problems in Nonsmooth Domains1985New YorkPitman Publishing Inc – reference: KuoFYSchwabCSloanIHQuasi-Monte Carlo finite element methods for a class of elliptic partial differential equations with random coefficientsSIAM J. Numer. Anal.201250633513374302415910.1137/110845537 – reference: KaarniojaVKuoFYSloanIHUncertainty quantification using periodic random variablesSIAM J. Numer. Anal.202058210681091408038910.1137/19M1262796 – reference: SavitsTHSome statistical applications of Faa di BrunoJ. Multivariate Anal.2006971021312140230162910.1016/j.jmva.2006.03.001 – reference: AhlforsLVConformal Invariants: Topics in Geometric Function Theory. Higher Mathematics Series1973New YorkMcGraw-Hill – reference: Harbrecht, H., Karnaev, V., Schmidlin, M.: Quantifying domain uncertainty in linear elasticity. Tech. Rep. 2023-06, Fachbereich Mathematik, Universität Basel, Switzerland (2023) – reference: DickJSloanIHWangXWoźniakowskiHGood lattice rules in weighted Korobov spaces with general weightsNumer. Math.200610316397220761510.1007/s00211-005-0674-6 – reference: HarbrechtHPetersMSiebenmorgenMAnalysis of the domain mapping method for elliptic diffusion problems on random domainsNumer. Math.20161344823856356328210.1007/s00211-016-0791-4 – reference: Jerez-HanckesCSchwabCZechJElectromagnetic wave scattering by random surfaces: Shape holomorphyMath. Models Methods Appl. Sci.2017271222292259370355710.1142/S0218202517500439 – reference: BabuškaIChatzipantelidisPOn solving elliptic stochastic partial differential equationsComput. Methods Appl. Mech. Eng.2002191409341222002CMAME.191.4093B191979010.1016/S0045-7825(02)00354-7 – reference: Kaarnioja, V., Kuo, F.Y., Sloan, I.H.: Lattice-based kernel approximation and serendipitous weights for parametric PDEs in very high dimensions. To appear in: A. Hinrichs, P. Kritzer, F. Pillichshammer (eds.). Monte Carlo and Quasi-Monte Carlo Methods (2022). Springer Verlag – volume-title: Elliptic Problems in Nonsmooth Domains year: 1985 ident: 1392_CR10 – ident: 1392_CR22 – volume: 24 start-page: 116 issue: 1 year: 1987 ident: 1392_CR30 publication-title: SIAM J. Numer. Anal. doi: 10.1137/0724010 – volume: 58 start-page: 1068 issue: 2 year: 2020 ident: 1392_CR23 publication-title: SIAM J. Numer. Anal. doi: 10.1137/19M1262796 – volume: 109 start-page: 385 issue: 3 year: 2008 ident: 1392_CR17 publication-title: Numer. Math. doi: 10.1007/s00211-008-0147-9 – ident: 1392_CR20 – volume-title: Conformal Invariants: Topics in Geometric Function Theory. Higher Mathematics Series year: 1973 ident: 1392_CR1 – ident: 1392_CR14 – volume: 142 start-page: 863 issue: 4 year: 2019 ident: 1392_CR9 publication-title: Numer. Math. doi: 10.1007/s00211-019-01046-6 – volume: 85 start-page: 874 issue: 7 year: 2011 ident: 1392_CR27 publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.3004 – volume: 50 start-page: 1720 issue: 2 year: 2018 ident: 1392_CR4 publication-title: SIAM J. Math. Anal. doi: 10.1137/16M1099406 – volume: 50 start-page: 3351 issue: 6 year: 2012 ident: 1392_CR26 publication-title: SIAM J. Numer. Anal. doi: 10.1137/110845537 – start-page: 249 volume-title: Monte Carlo and Quasi-Monte Carlo Methods 2016 year: 2018 ident: 1392_CR7 doi: 10.1007/978-3-319-91436-7_13 – volume-title: Elliptic Partial Differential Equations of Second Order year: 2001 ident: 1392_CR8 doi: 10.1007/978-3-642-61798-0 – volume: 27 start-page: 2229 issue: 12 year: 2017 ident: 1392_CR21 publication-title: Math. Models Methods Appl. Sci. doi: 10.1142/S0218202517500439 – volume: 134 start-page: 823 issue: 4 year: 2016 ident: 1392_CR15 publication-title: Numer. Math. doi: 10.1007/s00211-016-0791-4 – ident: 1392_CR11 – volume: 191 start-page: 4093 year: 2002 ident: 1392_CR2 publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/S0045-7825(02)00354-7 – volume: 71 start-page: 1173 issue: 6 year: 2016 ident: 1392_CR3 publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2016.01.005 – volume: 33 start-page: 91 issue: 1 year: 2010 ident: 1392_CR13 publication-title: Math. Methods Appl. Sci. – ident: 1392_CR24 doi: 10.26190/669X-A286 – volume-title: Inequalities year: 1934 ident: 1392_CR18 – ident: 1392_CR16 doi: 10.1007/s40072-021-00214-w – volume: 32 start-page: 1288 issue: 4 year: 2011 ident: 1392_CR25 publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/100799010 – ident: 1392_CR12 – volume: 28 start-page: 1167 issue: 3 year: 2006 ident: 1392_CR31 publication-title: SIAM J. Sci. Comput. doi: 10.1137/040613160 – ident: 1392_CR28 – volume: 52 start-page: 2676 issue: 6 year: 2014 ident: 1392_CR5 publication-title: SIAM J. Numer. Anal. doi: 10.1137/130943984 – volume: 44 start-page: 1475 issue: 5 year: 2018 ident: 1392_CR19 publication-title: Adv. Comput. Math. doi: 10.1007/s10444-018-9594-8 – volume: 103 start-page: 63 issue: 1 year: 2006 ident: 1392_CR6 publication-title: Numer. Math. doi: 10.1007/s00211-005-0674-6 – volume: 97 start-page: 2131 issue: 10 year: 2006 ident: 1392_CR29 publication-title: J. Multivariate Anal. doi: 10.1016/j.jmva.2006.03.001 |
| SSID | ssj0017641 |
| Score | 2.3996773 |
| Snippet | We consider uncertainty quantification for the Poisson problem subject to domain uncertainty. For the stochastic parameterization of the random domain, we use... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Index Database Publisher |
| StartPage | 273 |
| SubjectTerms | Domains Error analysis Fields (mathematics) Independent variables Mathematical and Computational Engineering Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Numerical Analysis Numerical and Computational Physics Parameterization Periodic functions Random variables Simulation Stochastic processes Theoretical Uncertainty |
| Title | Uncertainty quantification for random domains using periodic random variables |
| URI | https://link.springer.com/article/10.1007/s00211-023-01392-6 https://www.proquest.com/docview/2921735536 |
| Volume | 156 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV07T8MwELagXWDgUUAUSuWBDSwaP5J4rKqWClQmKpUp8iNGDLRAUiT-Pec8WlHBgJRkiC0Pn3O5z7q77xC67LlISLAb4rSxhCuqiQ6YIhb-koqpFCiHL06ePITjKb-biVklk-NrYTbi9zdF1yQ48FKf9QO-nITbqCkCFvk2DYNwsIoYRCEP6nQOIeWsKpD5fY2fTmjNLDeCoYWPGR2gvYoc4n65m4doK5230H7deAFXdthCu5OV2Gp2hCZTeFkE9vMv_L5UZfpPgTgGSorBG9nFK4YbpmTYZ7o_Yy9wvLAvph79hDOzr6LKjtF0NHwcjEnVJYEYFvCcAAPjcSqdYTY0nHl9NjA0bZyg2nGuJNVWxVqaWMAlmPWCNYZrDVzD0MCyE9SYL-bpKcJCCRlw17NSGh4pp3z-a2S9m6Ohi2UbXdWwJW-lGEaykj0uQE4A5KQAOQnbqFMjm1SGkSVUwhkIOA6D4esa7fXw36ud_W_6OdqhQD_K_OoOauQfy_QC6EOuu6jZv326H3aL7weeU9r_BkrovY4 |
| linkProvider | Springer Nature |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV07T8MwED5BGYCBRwFRKOABJojUOM7DA0MFVC1tOrVSt-BHghhogbSg_h9-KOc0aQWCgaFSssSWFX0--76TvzsDnNcS3-W4bqxEKm0xQaUlbUdYGndJ4YgYKYdJTg67XrPP7gfuYAU-i1yYTO1eHElmO_U82c24Iwx9qdH_oFe3vFxK2Y6nHxiopdetW5zVC0obd72bppXfJWApx2ZjC3kKC2KeKEd7ijmmihmao1SJS2XCmOBUahFIrgIXH9fRpqyLYlKiR1bU1g6OuwprSD4Cs3b6tD4_q_A9ZhdCEpfzQZ6a8_s_f3d_C0774xg2826NHdjKaSmpz-xoF1biYRm2iysfSL4DlGEznJd5Tfcg7OPHTFIwnpLXiZgJj7K5JkiGCfpBPXom-GKXlBiN_SMxpZVH-kkVre8YrZv8rXQf-kvB9ABKw9EwPgTiCpfbLKlpzhXzRSKM8tbXxsFSLwl4BS4L2KKXWRmOaF5wOQM5QpCjDOTIq0C1QDbKl2QaUY7RF7IrB5uvCrQXzX-PdvS_7mew3uyFnajT6raPYYMiCZqpvKtQGr9N4hMkMWN5mtkQgYdlG-0X7837lg |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV07T8MwED6VIiEYeBQQbzzABFEbx0nqgQEVKqAUMVCpW_AjRgy0QFIQ_4qfyDmPViAYGColS2xZ0eez7zv5uzPAQcOEPsd14xiptMMElY50PeFo3CWFJ2KkHDY5uXsTXPTYVd_vV-CzzIXJ1O7lkWSe02CrNA3S-rM29XHim3VNGAZTqwVCD-8EhayyE3-8Y9CWnFye4QwfUto-v2tdOMW9Ao7yXJY6yFlYM-ZGeTpQzLMVzdA0pTI-lYYxwanUoim5avr4-J62JV4UkxK9s6Ku9nDcGZjFyMi14V4raI3PLcKAuaWoxOe8X6Tp_P7P313hhN_-OJLNPF17GRYLikpOc5tagUo8qMFSef0DKXaDGix0xyVfk1Xo9vBjJi9IP8jLSOQipGzeCRJjgj5RD58IvtglIVZv_0BsmeWhflRl6xtG7jaXK1mD3lQwXYfqYDiIN4D4wucuMw3NuWKhMMKqcENtnS0NTJNvwlEJW_Scl-SIxsWXM5AjBDnKQI6CTdgpkY2K5ZlElGMkhkzLw-bjEu1J89-jbf2v-z7M3Z61o-vLm842zFPkQ7ngeweq6eso3kU-k8q9zIQI3E_bZr8A7CP_vA |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Uncertainty+quantification+for+random+domains+using+periodic+random+variables&rft.jtitle=Numerische+Mathematik&rft.au=Hakula%2C+Harri&rft.au=Harbrecht%2C+Helmut&rft.au=Kaarnioja%2C+Vesa&rft.au=Kuo%2C+Frances+Y.&rft.date=2024-02-01&rft.pub=Springer+Berlin+Heidelberg&rft.issn=0029-599X&rft.eissn=0945-3245&rft.volume=156&rft.issue=1&rft.spage=273&rft.epage=317&rft_id=info:doi/10.1007%2Fs00211-023-01392-6&rft.externalDocID=10_1007_s00211_023_01392_6 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0029-599X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0029-599X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0029-599X&client=summon |