Cover Image

Circulant embedding with QMC: analysis for elliptic PDE with lognormal coefficients

In a previous paper (Graham et al. in J Comput Phys 230:3668-3694, 2011), the authors proposed a new practical method for computing expected values of functionals of solutions for certain classes of elliptic partial differential equations with random coefficients. This method was based on combining...

Full description

Saved in:
Bibliographic Details
Main Authors: Graham, Ivan (Author) , Scheichl, Robert (Author)
Format: Article (Journal)
Language:English
Published: October 2018
In: Numerische Mathematik
Year: 2018, Volume: 140, Issue: 2, Pages: 479-511
ISSN:0945-3245
DOI:10.1007/s00211-018-0968-0
Online Access:Resolving-System, kostenfrei, Volltext: http://dx.doi.org/10.1007/s00211-018-0968-0
Verlag, kostenfrei, Volltext: https://link.springer.com/article/10.1007/s00211-018-0968-0
Get full text
Author Notes:Ivan G. Graham, Frances Y. Kuo, Dirk Nuyens, Rob Scheichl, Ian H. Sloan

MARC

LEADER 00000caa a2200000 c 4500
001 1585751197
003 DE-627
005 20220815083834.0
007 cr uuu---uuuuu
008 181219s2018 xx |||||o 00| ||eng c
024 7 |a 10.1007/s00211-018-0968-0  |2 doi 
035 |a (DE-627)1585751197 
035 |a (DE-576)515751197 
035 |a (DE-599)BSZ515751197 
035 |a (OCoLC)1341031258 
040 |a DE-627  |b ger  |c DE-627  |e rda 
041 |a eng 
084 |a 27  |2 sdnb 
100 1 |a Graham, Ivan  |e VerfasserIn  |0 (DE-588)1173843736  |0 (DE-627)1043657959  |0 (DE-576)51575062X  |4 aut 
245 1 0 |a Circulant embedding with QMC  |b analysis for elliptic PDE with lognormal coefficients  |c Ivan G. Graham, Frances Y. Kuo, Dirk Nuyens, Rob Scheichl, Ian H. Sloan 
264 1 |c October 2018 
300 |a 33 
336 |a Text  |b txt  |2 rdacontent 
337 |a Computermedien  |b c  |2 rdamedia 
338 |a Online-Ressource  |b cr  |2 rdacarrier 
500 |a Gesehen am 19.12.2018 
520 |a In a previous paper (Graham et al. in J Comput Phys 230:3668-3694, 2011), the authors proposed a new practical method for computing expected values of functionals of solutions for certain classes of elliptic partial differential equations with random coefficients. This method was based on combining quasi-Monte Carlo (QMC) methods for computing the expected values with circulant embedding methods for sampling the random field on a regular grid. It was found capable of handling fluid flow problems in random heterogeneous media with high stochastic dimension, but no convergence theory was provided. This paper provides a convergence analysis for the method in the case when the QMC method is a specially designed randomly shifted lattice rule. The convergence result depends on the eigenvalues of the underlying nested block circulant matrix and can be independent of the number of stochastic variables under certain assumptions. In fact the QMC analysis applies to general factorisations of the covariance matrix to sample the random field. The error analysis for the underlying fully discrete finite element method allows for locally refined meshes (via interpolation from a regular sampling grid of the random field). Numerical results on a non-regular domain with corner singularities in two spatial dimensions and on a regular domain in three spatial dimensions are included. 
650 4 |a 35Q86 
650 4 |a 60G10 
650 4 |a 60G60 
650 4 |a 65C05 
650 4 |a 65C60 
650 4 |a 65D32 
700 1 |a Scheichl, Robert  |d 1972-  |e VerfasserIn  |0 (DE-588)1173753842  |0 (DE-627)1043602305  |0 (DE-576)515668532  |4 aut 
773 0 8 |i Enthalten in  |t Numerische Mathematik  |d Berlin : Springer, 1959  |g 140(2018), 2, Seite 479-511  |h Online-Ressource  |w (DE-627)225690438  |w (DE-600)1364300-9  |w (DE-576)074528831  |x 0945-3245  |7 nnas  |a Circulant embedding with QMC analysis for elliptic PDE with lognormal coefficients 
773 1 8 |g volume:140  |g year:2018  |g number:2  |g pages:479-511  |g extent:33  |a Circulant embedding with QMC analysis for elliptic PDE with lognormal coefficients 
856 4 0 |u http://dx.doi.org/10.1007/s00211-018-0968-0  |x Resolving-System  |x Verlag  |z kostenfrei  |3 Volltext 
856 4 0 |u https://link.springer.com/article/10.1007/s00211-018-0968-0  |x Verlag  |z kostenfrei  |3 Volltext 
951 |a AR 
992 |a 20181219 
993 |a Article 
994 |a 2018 
998 |g 1173753842  |a Scheichl, Robert  |m 1173753842:Scheichl, Robert  |p 4 
999 |a KXP-PPN1585751197  |e 3038782343 
BIB |a Y 
SER |a journal 
JSO |a {"physDesc":[{"extent":"33 S."}],"title":[{"title":"Circulant embedding with QMC","title_sort":"Circulant embedding with QMC","subtitle":"analysis for elliptic PDE with lognormal coefficients"}],"person":[{"family":"Graham","given":"Ivan","display":"Graham, Ivan","role":"aut"},{"role":"aut","display":"Scheichl, Robert","family":"Scheichl","given":"Robert"}],"relHost":[{"part":{"pages":"479-511","text":"140(2018), 2, Seite 479-511","issue":"2","volume":"140","year":"2018","extent":"33"},"title":[{"title":"Numerische Mathematik","title_sort":"Numerische Mathematik"}],"language":["eng"],"disp":"Circulant embedding with QMC analysis for elliptic PDE with lognormal coefficientsNumerische Mathematik","type":{"bibl":"periodical","media":"Online-Ressource"},"physDesc":[{"extent":"Online-Ressource"}],"origin":[{"dateIssuedKey":"1959","publisherPlace":"Berlin ; Heidelberg ; Berlin ; Heidelberg [u.a.]","publisher":"Springer ; Springer","dateIssuedDisp":"1959-"}],"note":["Gesehen am 06.05.2022"],"pubHistory":["1.1959 -"],"id":{"eki":["225690438"],"issn":["0945-3245"],"zdb":["1364300-9"]},"recId":"225690438"}],"origin":[{"dateIssuedKey":"2018","dateIssuedDisp":"October 2018"}],"note":["Gesehen am 19.12.2018"],"id":{"doi":["10.1007/s00211-018-0968-0"],"eki":["1585751197"]},"language":["eng"],"name":{"displayForm":["Ivan G. Graham, Frances Y. Kuo, Dirk Nuyens, Rob Scheichl, Ian H. Sloan"]},"type":{"bibl":"article-journal","media":"Online-Ressource"},"recId":"1585751197"} 
SRT |a GRAHAMIVANCIRCULANTE2018 

Similar Items