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Volumn 239, Issue , 2013, Pages 1-21

Simplex stochastic collocation with ENO-type stencil selection for robust uncertainty quantification

Author keywords

Discontinuities; Essentially non oscillatory; Stencil selection; Stochastic collocation; Uncertainty quantification

Indexed keywords

PIECEWISE LINEAR TECHNIQUES; POLYNOMIAL APPROXIMATION; SHOCK TUBES; STOCHASTIC MODELS; UNCERTAINTY ANALYSIS;

EID: 84873297222     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2012.12.030     Document Type: Article
Times cited : (41)

References (37)
  • 1
    • 85190281856 scopus 로고    scopus 로고
    • A simple, flexible and generic deterministic approach to uncertainty quantifications in nonlinear problems: application to fluid flow problems, 5th European Conference on Computational Fluid Dynamics, ECCOMAS CFD, Lisbon, Portugal
    • R. Abgrall, A simple, flexible and generic deterministic approach to uncertainty quantifications in nonlinear problems: application to fluid flow problems, 5th European Conference on Computational Fluid Dynamics, ECCOMAS CFD, Lisbon, Portugal, 2010.
    • (2010)
    • Abgrall, R.1
  • 2
    • 69049117091 scopus 로고    scopus 로고
    • A domain adaptive stochastic collocation approach for analysis of MEMS under uncertainty
    • Agarwal N., Aluru N.R. A domain adaptive stochastic collocation approach for analysis of MEMS under uncertainty. J. Comput. Phys. 2009, 228:7662-7688.
    • (2009) J. Comput. Phys. , vol.228 , pp. 7662-7688
    • Agarwal, N.1    Aluru, N.R.2
  • 3
    • 13844319204 scopus 로고    scopus 로고
    • Galerkin finite elements approximation of stochastic finite elements
    • BabuŠka I., Tempone R., Zouraris G.E. Galerkin finite elements approximation of stochastic finite elements. SIAM J. Numer. Anal. 2004, 42:800-825.
    • (2004) SIAM J. Numer. Anal. , vol.42 , pp. 800-825
    • BabuŠka, I.1    Tempone, R.2    Zouraris, G.E.3
  • 4
    • 34548216854 scopus 로고    scopus 로고
    • A stochastic collocation method for elliptic partial differential equations with random input data
    • BabuŠka I., Nobile F., Tempone R. A stochastic collocation method for elliptic partial differential equations with random input data. SIAM J. Numer. Anal. 2007, 45:1005-1034.
    • (2007) SIAM J. Numer. Anal. , vol.45 , pp. 1005-1034
    • BabuŠka, I.1    Nobile, F.2    Tempone, R.3
  • 5
    • 23544474504 scopus 로고
    • A model for fast computer simulation of waves in excitable media
    • Barkley D. A model for fast computer simulation of waves in excitable media. Physica D 1991, 49:61-70.
    • (1991) Physica D , vol.49 , pp. 61-70
    • Barkley, D.1
  • 6
    • 84869088124 scopus 로고    scopus 로고
    • On the propagation of statistical model parameter uncertainty in CFD calculations
    • DOI: 10.1007/s00162-011-0221-2.
    • T. Barth, On the propagation of statistical model parameter uncertainty in CFD calculations, Theor. Comput. Fluid Dyn. (2011) DOI: 10.1007/s00162-011-0221-2.
    • (2011) Theor. Comput. Fluid Dyn.
    • Barth, T.1
  • 8
    • 52749087886 scopus 로고    scopus 로고
    • The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
    • Foo J., Wan X., Karniadakis G.E. The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications. J. Comput. Phys. 2008, 227:9572-9595.
    • (2008) J. Comput. Phys. , vol.227 , pp. 9572-9595
    • Foo, J.1    Wan, X.2    Karniadakis, G.E.3
  • 11
    • 40549120328 scopus 로고    scopus 로고
    • Galerkin method for wave equations with uncertain coefficients
    • Gottlieb D., Xiu D. Galerkin method for wave equations with uncertain coefficients. Commun. Comput. Phys. 2008, 3:505-518.
    • (2008) Commun. Comput. Phys. , vol.3 , pp. 505-518
    • Gottlieb, D.1    Xiu, D.2
  • 12
    • 40749159424 scopus 로고
    • High resolution schemes for hyperbolic conservation laws
    • Harten A. High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 1983, 49:357-393.
    • (1983) J. Comput. Phys. , vol.49 , pp. 357-393
    • Harten, A.1
  • 13
    • 0023329384 scopus 로고
    • Uniformly high-order accurate nonoscillatory schemes I
    • Harten A., Osher S. Uniformly high-order accurate nonoscillatory schemes I. SIAM J. Numer. Anal. 1987, 24:279-309.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 279-309
    • Harten, A.1    Osher, S.2
  • 15
    • 84954695021 scopus 로고
    • Analysis and design of numerical schemes for gas dynamics. I: Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence
    • Jameson A. Analysis and design of numerical schemes for gas dynamics. I: Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence. Int. J. Comput. Fluid D 1995, 4:171-218.
    • (1995) Int. J. Comput. Fluid D , vol.4 , pp. 171-218
    • Jameson, A.1
  • 16
    • 0000592595 scopus 로고
    • Weighted essentially non-oscillatory schemes
    • Liu X.-D., Osher S., Chan T. Weighted essentially non-oscillatory schemes. J. Comput. Phys. 1994, 115:200-212.
    • (1994) J. Comput. Phys. , vol.115 , pp. 200-212
    • Liu, X.-D.1    Osher, S.2    Chan, T.3
  • 17
    • 61349191533 scopus 로고    scopus 로고
    • An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations
    • Ma X., Zabaras N. An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations. J. Comput. Phys. 2009, 228:3084-3113.
    • (2009) J. Comput. Phys. , vol.228 , pp. 3084-3113
    • Ma, X.1    Zabaras, N.2
  • 19
    • 3242712896 scopus 로고    scopus 로고
    • Multi-resolution analysis of Wiener-type uncertainty propagation schemes
    • Le Maître O.P., Najm H.N., Ghanem R.G., Knio O.M. Multi-resolution analysis of Wiener-type uncertainty propagation schemes. J. Comput. Phys. 2004, 197:502-531.
    • (2004) J. Comput. Phys. , vol.197 , pp. 502-531
    • Le Maître, O.P.1    Najm, H.N.2    Ghanem, R.G.3    Knio, O.M.4
  • 20
  • 21
    • 77954340408 scopus 로고    scopus 로고
    • Asynchronous time integration for polynomial chaos expansion of uncertain periodic dynamics
    • Le Maître O.P., Mathelin L., Knio O.M., Hussaini M.Y. Asynchronous time integration for polynomial chaos expansion of uncertain periodic dynamics. Discret. Contin. Dyn. S. 2010, 28:199-226.
    • (2010) Discret. Contin. Dyn. S. , vol.28 , pp. 199-226
    • Le Maître, O.P.1    Mathelin, L.2    Knio, O.M.3    Hussaini, M.Y.4
  • 22
    • 60149088861 scopus 로고    scopus 로고
    • Uncertainty quantification for systems of conservation laws
    • Poëtte G., Després B., Lucor D. Uncertainty quantification for systems of conservation laws. J. Comput. Phys. 2009, 228:2443-2467.
    • (2009) J. Comput. Phys. , vol.228 , pp. 2443-2467
    • Poëtte, G.1    Després, B.2    Lucor, D.3
  • 24
    • 45449125925 scopus 로고
    • Efficient implementation of essentially non-oscillatory shock-capturing schemes
    • Shu C.-W., Osher S. Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 1988, 77:439-471.
    • (1988) J. Comput. Phys. , vol.77 , pp. 439-471
    • Shu, C.-W.1    Osher, S.2
  • 25
    • 0001568854 scopus 로고
    • Efficient implementation of essentially non-oscillatory shock-capturing schemes II
    • Shu C.-W., Osher S. Efficient implementation of essentially non-oscillatory shock-capturing schemes II. J. Comput. Phys. 1989, 83:32-78.
    • (1989) J. Comput. Phys. , vol.83 , pp. 32-78
    • Shu, C.-W.1    Osher, S.2
  • 26
    • 2942705023 scopus 로고
    • A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
    • Sod G.A. A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. J. Comput. Phys. 1978, 27:1-31.
    • (1978) J. Comput. Phys. , vol.27 , pp. 1-31
    • Sod, G.A.1
  • 27
    • 77954144803 scopus 로고    scopus 로고
    • Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems
    • Tryoen J., Le Maître O., Ndjinga M., Ern A. Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems. J. Comput. Phys. 2010, 229:6485-6511.
    • (2010) J. Comput. Phys. , vol.229 , pp. 6485-6511
    • Tryoen, J.1    Le Maître, O.2    Ndjinga, M.3    Ern, A.4
  • 28
    • 21444449245 scopus 로고    scopus 로고
    • An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
    • Wan X., Karniadakis G.E. An adaptive multi-element generalized polynomial chaos method for stochastic differential equations. J. Comput. Phys. 2005, 209:617-642.
    • (2005) J. Comput. Phys. , vol.209 , pp. 617-642
    • Wan, X.1    Karniadakis, G.E.2
  • 29
    • 34248583576 scopus 로고    scopus 로고
    • An improved front tracking method for the Euler equations
    • Witteveen J.A.S., Koren B., Bakker P.G. An improved front tracking method for the Euler equations. J. Comput. Phys. 2007, 224:712-728.
    • (2007) J. Comput. Phys. , vol.224 , pp. 712-728
    • Witteveen, J.A.S.1    Koren, B.2    Bakker, P.G.3
  • 30
    • 67849124148 scopus 로고    scopus 로고
    • Effect of randomness on multi-frequency aeroelastic responses resolved by unsteady adaptive stochastic finite elements
    • Witteveen J.A.S., Bijl H. Effect of randomness on multi-frequency aeroelastic responses resolved by unsteady adaptive stochastic finite elements. J. Comput. Phys. 2009, 228:7025-7045.
    • (2009) J. Comput. Phys. , vol.228 , pp. 7025-7045
    • Witteveen, J.A.S.1    Bijl, H.2
  • 31
    • 67650938584 scopus 로고    scopus 로고
    • A TVD uncertainty quantification method with bounded error applied to transonic airfoil flutter
    • Witteveen J.A.S., Bijl H. A TVD uncertainty quantification method with bounded error applied to transonic airfoil flutter. Commun. Comput. Phys. 2009, 6:406-432.
    • (2009) Commun. Comput. Phys. , vol.6 , pp. 406-432
    • Witteveen, J.A.S.1    Bijl, H.2
  • 32
    • 74449088134 scopus 로고    scopus 로고
    • Second order front tracking for the Euler equations
    • Witteveen J.A.S. Second order front tracking for the Euler equations. J. Comput. Phys. 2010, 229:2719-2739.
    • (2010) J. Comput. Phys. , vol.229 , pp. 2719-2739
    • Witteveen, J.A.S.1
  • 33
    • 84869088048 scopus 로고    scopus 로고
    • Transonic velocity fluctuations simulated using extremum diminishing uncertainty quantification based on inverse distance weighting
    • Witteveen J.A.S., Bijl H. Transonic velocity fluctuations simulated using extremum diminishing uncertainty quantification based on inverse distance weighting. Theoret. Comput. Fluid Dyn. 2012, 26:459-479.
    • (2012) Theoret. Comput. Fluid Dyn. , vol.26 , pp. 459-479
    • Witteveen, J.A.S.1    Bijl, H.2
  • 34
    • 84861394267 scopus 로고    scopus 로고
    • Simplex stochastic collocation with random sampling and extrapolation for nonhypercube parametric spaces
    • Witteveen J.A.S., Iaccarino G. Simplex stochastic collocation with random sampling and extrapolation for nonhypercube parametric spaces. SIAM J. Sci. Comput. 2012, 34:A814-A838.
    • (2012) SIAM J. Sci. Comput. , vol.34
    • Witteveen, J.A.S.1    Iaccarino, G.2
  • 35
    • 84873303737 scopus 로고    scopus 로고
    • Refinement criteria for simplex stochastic collocation with local extremum diminishing robustness
    • Witteveen J.A.S., Iaccarino G. Refinement criteria for simplex stochastic collocation with local extremum diminishing robustness. SIAM J. Sci. Comput. 2012, 34:A1522-A1543.
    • (2012) SIAM J. Sci. Comput. , vol.34
    • Witteveen, J.A.S.1    Iaccarino, G.2
  • 36
    • 0037249229 scopus 로고    scopus 로고
    • The Wiener-Askey polynomial chaos for stochastic differential equations
    • Xiu D., Karniadakis G.E. The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 2002, 24:619-644.
    • (2002) SIAM J. Sci. Comput. , vol.24 , pp. 619-644
    • Xiu, D.1    Karniadakis, G.E.2
  • 37
    • 33646577797 scopus 로고    scopus 로고
    • High-order collocation methods for differential equations with random inputs
    • Xiu D., Hesthaven J.S. High-order collocation methods for differential equations with random inputs. SIAM J. Sci. Comput. 2005, 27:1118-1139.
    • (2005) SIAM J. Sci. Comput. , vol.27 , pp. 1118-1139
    • Xiu, D.1    Hesthaven, J.S.2


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