Convergence acceleration of polynomial chaos solutions via sequence transformation
We investigate convergence acceleration of the solution of stochastic differential equations characterized by their polynomial chaos expansions. Specifically, nonlinear sequence transformations are adapted to these expansions, viewed as a one-parameter family of functions with the parameter being th...
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| Published in | Computer methods in applied mechanics and engineering Vol. 271; pp. 167 - 184 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Elsevier B.V
01.04.2014
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0045-7825 1879-2138 |
| DOI | 10.1016/j.cma.2013.12.003 |
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| Abstract | We investigate convergence acceleration of the solution of stochastic differential equations characterized by their polynomial chaos expansions. Specifically, nonlinear sequence transformations are adapted to these expansions, viewed as a one-parameter family of functions with the parameter being the polynomial degree of the expansion. These transformations can be generally viewed as nonlinear generalizations of Richardson Extrapolation and permit the estimation of coefficients in higher order expansions having knowledge of the coefficients in lower order ones. Stochastic Galerkin closure that typically characterizes the solution of such equations yields polynomial chaos representations that have the requisite analytical properties to ensure suitable convergence of these nonlinear sequence transformations. We investigate specifically Shanks and Levin transformations, and explore their properties in the context of a stochastic initial value problem and a stochastic elliptic problem. |
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| AbstractList | We investigate convergence acceleration of the solution of stochastic differential equations characterized by their polynomial chaos expansions. Specifically, nonlinear sequence transformations are adapted to these expansions, viewed as a one-parameter family of functions with the parameter being the polynomial degree of the expansion. These transformations can be generally viewed as nonlinear generalizations of Richardson Extrapolation and permit the estimation of coefficients in higher order expansions having knowledge of the coefficients in lower order ones. Stochastic Galerkin closure that typically characterizes the solution of such equations yields polynomial chaos representations that have the requisite analytical properties to ensure suitable convergence of these nonlinear sequence transformations. We investigate specifically Shanks and Levin transformations, and explore their properties in the context of a stochastic initial value problem and a stochastic elliptic problem. |
| Author | Ghanem, R.G. Keshavarzzadeh, V. Masri, S.F. Aldraihem, O.J. |
| Author_xml | – sequence: 1 givenname: V. surname: Keshavarzzadeh fullname: Keshavarzzadeh, V. email: vkeshava@usc.edu organization: Viterbi School of Engineering, University of Southern California, Los Angeles, CA 90089-2531, USA – sequence: 2 givenname: R.G. surname: Ghanem fullname: Ghanem, R.G. email: ghanem@usc.edu organization: Viterbi School of Engineering, University of Southern California, Los Angeles, CA 90089-2531, USA – sequence: 3 givenname: S.F. surname: Masri fullname: Masri, S.F. email: masri@usc.edu organization: Viterbi School of Engineering, University of Southern California, Los Angeles, CA 90089-2531, USA – sequence: 4 givenname: O.J. surname: Aldraihem fullname: Aldraihem, O.J. email: odraihem@ksu.edu.sa organization: School of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia |
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| Cites_doi | 10.1016/j.cma.2011.07.005 10.1016/j.cma.2006.10.047 10.1137/0702030 10.1080/17442509808834153 10.1016/0168-9274(95)00110-7 10.1016/S0167-2789(99)00102-5 10.1137/050627630 10.1002/sapm19553411 10.1016/0315-0860(84)90002-8 10.1016/j.cma.2004.02.026 10.1137/S1064827501387826 10.1016/j.jcp.2003.12.020 10.1016/0167-7977(89)90011-7 10.1029/2008WR007148 10.1080/00207167308803075 10.1016/S0965-9978(00)00034-X 10.1137/S1064827503424505 10.1137/S0036142902418680 10.1061/(ASCE)0733-9399(2002)128:1(66) 10.1016/j.jcp.2006.12.014 10.1098/rsta.1911.0009 10.1007/BF02165234 10.1016/B978-008044046-0.50559-5 10.1017/S0370164600022070 10.1016/S0377-0427(00)00360-5 10.1002/nme.1576 10.1137/100787830 10.1016/j.jcp.2006.01.037 |
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| Keywords | Sequence transformations Stochastic Galerkin Polynomial chaos expansion Convergence acceleration |
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| References | Bulirsch, Stoer (b0125) 1966; 8 Le Maitre, Najm, Ghanem, Knio (b0075) 2004; 197 S. Das, R. Ghanem, J. Spall, Asymptotic sampling distribution for polynomial chaos representation of data: a maximum-entropy and fisher information approach, SIAM J. Sci. Comput., in press. Gragg (b0130) 1965; 2 Babuska, Tempone, Zouraris (b0165) 2005; 194 Richardson (b0090) 1911; 210 Wan, Karniadakis (b0085) 2006; 28 R. Ghanem, D. Ghiocel, A new implementation of the spectral stochastic finite element method for stochastic constitutive relations, in: ASCE 12th Engineering Mechanics Conference, La Jolla, CA, 1998. Ganapathysubramanian, Zabaras (b0030) 2007; 225 Soize, Descelliers (b0070) 2010; 32 Brezinski (b0100) 1996; 20 Aitken (b0135) 1926; 46 Doostan, Ghanem, Red-Horse (b0060) 2007; 196 R. Ghanem, J. Abras, A general purpose library for stochastic finite element computations, in: Second MIT Conference on Computational Mechanics, Cambridge, MA, 2003. Lax, Milgram (b0175) 1954; 33 Dutka (b0120) 1984; 11 Berveiller, Sudret, Lemaire (b0035) 2006; 15 Descelliers, Ghanem, Soize (b0140) 2006; 66 Ghanem, Red-Horse (b0050) 1999; 133 Ghanem, Doostan (b0150) 2006; 217 A. Nouy, C. Soize, Random fields representations for stochastic elliptic boundary value problems and statistical inverse problems, 2013. Xiu, Karniadakis (b0020) 2002; 24 Shanks (b0110) 1955; 34 Ghiocel, Ghanem (b0025) 2002; 128 Saad, Ghanem (b0155) 2009; 45 Soize (b0160) 2011; 200 . Le Maitre, Knio (b0010) 2010 Levin (b0115) 1973; 3 Weniger (b0105) 1989; 10 Soize, Ghanem (b0015) 2004; 26 Pellissetti, Ghanem (b0055) 2000; 31 Babuska, Tempone, Zouraris (b0065) 2004; 42 Benth, Gjerde (b0080) 1998; 63 Ghanem, Spanos (b0005) 2002 Brezinski (b0095) 2000; 122 Benth (10.1016/j.cma.2013.12.003_b0080) 1998; 63 Descelliers (10.1016/j.cma.2013.12.003_b0140) 2006; 66 10.1016/j.cma.2013.12.003_b0170 Ganapathysubramanian (10.1016/j.cma.2013.12.003_b0030) 2007; 225 Soize (10.1016/j.cma.2013.12.003_b0160) 2011; 200 Aitken (10.1016/j.cma.2013.12.003_b0135) 1926; 46 Gragg (10.1016/j.cma.2013.12.003_b0130) 1965; 2 Brezinski (10.1016/j.cma.2013.12.003_b0100) 1996; 20 Bulirsch (10.1016/j.cma.2013.12.003_b0125) 1966; 8 Le Maitre (10.1016/j.cma.2013.12.003_b0010) 2010 Shanks (10.1016/j.cma.2013.12.003_b0110) 1955; 34 Brezinski (10.1016/j.cma.2013.12.003_b0095) 2000; 122 Ghanem (10.1016/j.cma.2013.12.003_b0150) 2006; 217 Dutka (10.1016/j.cma.2013.12.003_b0120) 1984; 11 10.1016/j.cma.2013.12.003_b0045 10.1016/j.cma.2013.12.003_b0145 Ghiocel (10.1016/j.cma.2013.12.003_b0025) 2002; 128 Wan (10.1016/j.cma.2013.12.003_b0085) 2006; 28 Levin (10.1016/j.cma.2013.12.003_b0115) 1973; 3 Saad (10.1016/j.cma.2013.12.003_b0155) 2009; 45 10.1016/j.cma.2013.12.003_b0040 Weniger (10.1016/j.cma.2013.12.003_b0105) 1989; 10 Berveiller (10.1016/j.cma.2013.12.003_b0035) 2006; 15 Soize (10.1016/j.cma.2013.12.003_b0070) 2010; 32 Doostan (10.1016/j.cma.2013.12.003_b0060) 2007; 196 Richardson (10.1016/j.cma.2013.12.003_b0090) 1911; 210 Soize (10.1016/j.cma.2013.12.003_b0015) 2004; 26 Lax (10.1016/j.cma.2013.12.003_b0175) 1954; 33 Pellissetti (10.1016/j.cma.2013.12.003_b0055) 2000; 31 Le Maitre (10.1016/j.cma.2013.12.003_b0075) 2004; 197 Ghanem (10.1016/j.cma.2013.12.003_b0005) 2002 Xiu (10.1016/j.cma.2013.12.003_b0020) 2002; 24 Babuska (10.1016/j.cma.2013.12.003_b0065) 2004; 42 Babuska (10.1016/j.cma.2013.12.003_b0165) 2005; 194 Ghanem (10.1016/j.cma.2013.12.003_b0050) 1999; 133 |
| References_xml | – volume: 63 start-page: 313 year: 1998 end-page: 326 ident: b0080 article-title: Convergence rates for finite element approximations of stochastic partial differential equations publication-title: Stochastics Stochastics Rep. – volume: 10 start-page: 189 year: 1989 end-page: 371 ident: b0105 article-title: Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series publication-title: Comput. Phys. Rep. – year: 2002 ident: b0005 article-title: Stochastic Finite Elements: A Spectral Approach – volume: 197 start-page: 502 year: 2004 end-page: 531 ident: b0075 article-title: Multi-resolution analysis of wiener-type uncertainty propagation schemes publication-title: J. Comput. Phys. – volume: 20 start-page: 299 year: 1996 end-page: 318 ident: b0100 article-title: Extrapolation algorithms and pad approximations: a historical survey publication-title: Appl. Numer. Math. – volume: 33 start-page: 167 year: 1954 end-page: 190 ident: b0175 article-title: Parabolic equations publication-title: Ann. Math. Stud. – volume: 15 year: 2006 ident: b0035 article-title: Stochastic finite element: a non intrusive approach by regression publication-title: Eur. J. Comput. Mech. – volume: 225 start-page: 652 year: 2007 end-page: 685 ident: b0030 article-title: Sparse grid collocation schemes for stochastic natural convection problems publication-title: J. Comput. Phys. – volume: 34 start-page: 1 year: 1955 end-page: 42 ident: b0110 article-title: Non-linear transformations of divergent and slowly convergent sequences publication-title: J. Math. Phys. – reference: R. Ghanem, J. Abras, A general purpose library for stochastic finite element computations, in: Second MIT Conference on Computational Mechanics, Cambridge, MA, 2003. – volume: 32 start-page: 2820 year: 2010 end-page: 2831 ident: b0070 article-title: Computational aspects for constructing realizations of polynomial chaos in high dimension publication-title: SIAM J. Sci. Comput. – reference: A. Nouy, C. Soize, Random fields representations for stochastic elliptic boundary value problems and statistical inverse problems, 2013. – volume: 31 start-page: 607 year: 2000 end-page: 616 ident: b0055 article-title: Iterative solution of systems of linear equations arising in the context of the stochastic fem publication-title: J. Adv. Eng. Software – volume: 3 start-page: 371 year: 1973 end-page: 388 ident: b0115 article-title: Development of nonlinear transformations for improving convergence of sequences publication-title: Int. J. Comput. Math. – volume: 128 start-page: 66 year: 2002 end-page: 77 ident: b0025 article-title: Stochastic finite element analysis of seismic soil-structure interaction publication-title: ASCE, J. Eng. Mech. – volume: 8 start-page: 1 year: 1966 end-page: 13 ident: b0125 article-title: Numerical treatment of ordinary differential equations by extrapolation methods publication-title: Numer. Math. – volume: 26 start-page: 395 year: 2004 end-page: 410 ident: b0015 article-title: Physical systems with random uncertainties: chaos representations with arbitrary probability measure publication-title: SIAM J. Sci. Comput. – reference: S. Das, R. Ghanem, J. Spall, Asymptotic sampling distribution for polynomial chaos representation of data: a maximum-entropy and fisher information approach, SIAM J. Sci. Comput., in press. – volume: 196 start-page: 3951 year: 2007 end-page: 3966 ident: b0060 article-title: Stochastic model reduction for chaos representations publication-title: Comput. Methods Appl. Mech. Eng. – volume: 45 year: 2009 ident: b0155 article-title: Characterization of reservoir simulation models using a polynomial chaos-based ensemble Kalman filter publication-title: Water Resour. Res – volume: 217 start-page: 63 year: 2006 end-page: 81 ident: b0150 article-title: On the construction and analysis of stochastic models: characterization and propagation of the errors associated with limited data publication-title: J. Comput. Phys. – volume: 200 start-page: 3083 year: 2011 end-page: 3099 ident: b0160 article-title: A computational inverse method for identification of non-gaussian random fields using the bayesian approach in very high dimension publication-title: Comput. Methods Appl. Mech. Eng. – volume: 11 start-page: 3 year: 1984 end-page: 21 ident: b0120 article-title: Richardson extrapolation and romberg integration publication-title: Historia Math. – volume: 133 start-page: 137 year: 1999 end-page: 144 ident: b0050 article-title: Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element approach publication-title: Phys. D – volume: 210 start-page: 307 year: 1911 end-page: 357 ident: b0090 article-title: The approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry dam publication-title: Philos. Trans. R. Soc. London – volume: 42 start-page: 800 year: 2004 end-page: 825 ident: b0065 article-title: Galerkin finite element approximations of stochastic elliptic partial differential equations publication-title: SIAM J. Numer. Anal. – volume: 46 start-page: 289 year: 1926 end-page: 305 ident: b0135 article-title: On Bernoulli’s numerical solution of algebraic equations publication-title: Proc. R. Soc. Edinburgh – reference: . – volume: 122 start-page: 1 year: 2000 end-page: 21 ident: b0095 article-title: Convergence acceleration during the 20th century publication-title: J. Comput. Appl. Math. – volume: 24 start-page: 619 year: 2002 end-page: 644 ident: b0020 article-title: The Wiener–Askey polynomial chaos for stochastic differential equations publication-title: SIAM J. Sci. Comput. – volume: 194 start-page: 1251 year: 2005 end-page: 1294 ident: b0165 article-title: Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation publication-title: Comput. Methods Appl. Mech. Eng. – year: 2010 ident: b0010 article-title: Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics – volume: 2 start-page: 384 year: 1965 end-page: 403 ident: b0130 article-title: On extrapolation algorithms for ordinary initial value problems publication-title: J. Soc. Ind. Appl. Math. – reference: R. Ghanem, D. Ghiocel, A new implementation of the spectral stochastic finite element method for stochastic constitutive relations, in: ASCE 12th Engineering Mechanics Conference, La Jolla, CA, 1998. – volume: 66 start-page: 978 year: 2006 end-page: 1001 ident: b0140 article-title: Maximum likelihood estimation of stochastic chaos representation from experimental data publication-title: Int. J. Numer. Methods Eng. – volume: 28 start-page: 901 year: 2006 end-page: 928 ident: b0085 article-title: Multi-element generalized polynomial chaos for arbitrary probability measures publication-title: SIAM J. Sci. Comput. – volume: 200 start-page: 3083 issue: 4546 year: 2011 ident: 10.1016/j.cma.2013.12.003_b0160 article-title: A computational inverse method for identification of non-gaussian random fields using the bayesian approach in very high dimension publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2011.07.005 – volume: 196 start-page: 3951 issue: 37–40 year: 2007 ident: 10.1016/j.cma.2013.12.003_b0060 article-title: Stochastic model reduction for chaos representations publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2006.10.047 – volume: 2 start-page: 384 issue: 3 year: 1965 ident: 10.1016/j.cma.2013.12.003_b0130 article-title: On extrapolation algorithms for ordinary initial value problems publication-title: J. Soc. Ind. Appl. Math. doi: 10.1137/0702030 – volume: 63 start-page: 313 year: 1998 ident: 10.1016/j.cma.2013.12.003_b0080 article-title: Convergence rates for finite element approximations of stochastic partial differential equations publication-title: Stochastics Stochastics Rep. doi: 10.1080/17442509808834153 – volume: 20 start-page: 299 issue: 3 year: 1996 ident: 10.1016/j.cma.2013.12.003_b0100 article-title: Extrapolation algorithms and pad approximations: a historical survey publication-title: Appl. Numer. Math. doi: 10.1016/0168-9274(95)00110-7 – volume: 133 start-page: 137 year: 1999 ident: 10.1016/j.cma.2013.12.003_b0050 article-title: Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element approach publication-title: Phys. D doi: 10.1016/S0167-2789(99)00102-5 – volume: 28 start-page: 901 issue: 3 year: 2006 ident: 10.1016/j.cma.2013.12.003_b0085 article-title: Multi-element generalized polynomial chaos for arbitrary probability measures publication-title: SIAM J. Sci. Comput. doi: 10.1137/050627630 – volume: 34 start-page: 1 year: 1955 ident: 10.1016/j.cma.2013.12.003_b0110 article-title: Non-linear transformations of divergent and slowly convergent sequences publication-title: J. Math. Phys. doi: 10.1002/sapm19553411 – volume: 11 start-page: 3 issue: 1 year: 1984 ident: 10.1016/j.cma.2013.12.003_b0120 article-title: Richardson extrapolation and romberg integration publication-title: Historia Math. doi: 10.1016/0315-0860(84)90002-8 – volume: 15 issue: 1–3 year: 2006 ident: 10.1016/j.cma.2013.12.003_b0035 article-title: Stochastic finite element: a non intrusive approach by regression publication-title: Eur. J. Comput. Mech. – volume: 194 start-page: 1251 issue: 12–16 year: 2005 ident: 10.1016/j.cma.2013.12.003_b0165 article-title: Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2004.02.026 – volume: 24 start-page: 619 year: 2002 ident: 10.1016/j.cma.2013.12.003_b0020 article-title: The Wiener–Askey polynomial chaos for stochastic differential equations publication-title: SIAM J. Sci. Comput. doi: 10.1137/S1064827501387826 – ident: 10.1016/j.cma.2013.12.003_b0170 – year: 2010 ident: 10.1016/j.cma.2013.12.003_b0010 – ident: 10.1016/j.cma.2013.12.003_b0040 – volume: 197 start-page: 502 year: 2004 ident: 10.1016/j.cma.2013.12.003_b0075 article-title: Multi-resolution analysis of wiener-type uncertainty propagation schemes publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2003.12.020 – volume: 10 start-page: 189 year: 1989 ident: 10.1016/j.cma.2013.12.003_b0105 article-title: Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series publication-title: Comput. Phys. Rep. doi: 10.1016/0167-7977(89)90011-7 – volume: 45 year: 2009 ident: 10.1016/j.cma.2013.12.003_b0155 article-title: Characterization of reservoir simulation models using a polynomial chaos-based ensemble Kalman filter publication-title: Water Resour. Res doi: 10.1029/2008WR007148 – year: 2002 ident: 10.1016/j.cma.2013.12.003_b0005 – ident: 10.1016/j.cma.2013.12.003_b0145 – volume: 3 start-page: 371 year: 1973 ident: 10.1016/j.cma.2013.12.003_b0115 article-title: Development of nonlinear transformations for improving convergence of sequences publication-title: Int. J. Comput. Math. doi: 10.1080/00207167308803075 – volume: 31 start-page: 607 year: 2000 ident: 10.1016/j.cma.2013.12.003_b0055 article-title: Iterative solution of systems of linear equations arising in the context of the stochastic fem publication-title: J. Adv. Eng. Software doi: 10.1016/S0965-9978(00)00034-X – volume: 26 start-page: 395 issue: 2 year: 2004 ident: 10.1016/j.cma.2013.12.003_b0015 article-title: Physical systems with random uncertainties: chaos representations with arbitrary probability measure publication-title: SIAM J. Sci. Comput. doi: 10.1137/S1064827503424505 – volume: 42 start-page: 800 issue: 2 year: 2004 ident: 10.1016/j.cma.2013.12.003_b0065 article-title: Galerkin finite element approximations of stochastic elliptic partial differential equations publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142902418680 – volume: 128 start-page: 66 issue: 1 year: 2002 ident: 10.1016/j.cma.2013.12.003_b0025 article-title: Stochastic finite element analysis of seismic soil-structure interaction publication-title: ASCE, J. Eng. Mech. doi: 10.1061/(ASCE)0733-9399(2002)128:1(66) – volume: 225 start-page: 652 issue: 1 year: 2007 ident: 10.1016/j.cma.2013.12.003_b0030 article-title: Sparse grid collocation schemes for stochastic natural convection problems publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2006.12.014 – volume: 210 start-page: 307 year: 1911 ident: 10.1016/j.cma.2013.12.003_b0090 article-title: The approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry dam publication-title: Philos. Trans. R. Soc. London doi: 10.1098/rsta.1911.0009 – volume: 8 start-page: 1 issue: 1 year: 1966 ident: 10.1016/j.cma.2013.12.003_b0125 article-title: Numerical treatment of ordinary differential equations by extrapolation methods publication-title: Numer. Math. doi: 10.1007/BF02165234 – ident: 10.1016/j.cma.2013.12.003_b0045 doi: 10.1016/B978-008044046-0.50559-5 – volume: 46 start-page: 289 year: 1926 ident: 10.1016/j.cma.2013.12.003_b0135 article-title: On Bernoulli’s numerical solution of algebraic equations publication-title: Proc. R. Soc. Edinburgh doi: 10.1017/S0370164600022070 – volume: 122 start-page: 1 year: 2000 ident: 10.1016/j.cma.2013.12.003_b0095 article-title: Convergence acceleration during the 20th century publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(00)00360-5 – volume: 33 start-page: 167 year: 1954 ident: 10.1016/j.cma.2013.12.003_b0175 article-title: Parabolic equations publication-title: Ann. Math. Stud. – volume: 66 start-page: 978 issue: 6 year: 2006 ident: 10.1016/j.cma.2013.12.003_b0140 article-title: Maximum likelihood estimation of stochastic chaos representation from experimental data publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.1576 – volume: 32 start-page: 2820 issue: 5 year: 2010 ident: 10.1016/j.cma.2013.12.003_b0070 article-title: Computational aspects for constructing realizations of polynomial chaos in high dimension publication-title: SIAM J. Sci. Comput. doi: 10.1137/100787830 – volume: 217 start-page: 63 issue: 1 year: 2006 ident: 10.1016/j.cma.2013.12.003_b0150 article-title: On the construction and analysis of stochastic models: characterization and propagation of the errors associated with limited data publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2006.01.037 |
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| Snippet | We investigate convergence acceleration of the solution of stochastic differential equations characterized by their polynomial chaos expansions. Specifically,... |
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| SubjectTerms | Chaos theory Convergence Convergence acceleration Mathematical analysis Mathematical models Nonlinearity Polynomial chaos expansion Polynomials Sequence transformations Stochastic Galerkin Stochasticity Transformations |
| Title | Convergence acceleration of polynomial chaos solutions via sequence transformation |
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