Simplex Elements Stochastic Collocation for uncertainty propagation in robust design optimization

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

Volumn , Issue , 2010, Pages

  Witteveen, Jeroen A S ^a   Iaccarino, Gianluca ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MONTE CARLO METHODS; STOCHASTIC SYSTEMS;

ADAPTIVE REFINEMENT; DESIGN PARAMETERS; NON-UNIFORM DISTRIBUTION; POLYNOMIAL INTERPOLATION; ROBUST DESIGN OPTIMIZATION; STOCHASTIC COLLOCATION; UNCERTAIN PARAMETERS; UNCERTAINTY PROPAGATION;

UNCERTAINTY ANALYSIS;

EID: 78649853039     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2514/6.2010-1313     Document Type: Conference Paper

References (27)

1. I. Babuška, F. Nobile, R. Tempone, A stochastic collocation method for elliptic partial differential equations with random input data, SIAM J. Numer. Anal. 45 (2007) 1005-1034.
2. T. Chantrasmi, A. Doostan, G. Iaccarino, Padé-Legendre approximants for uncertainty analysis with discontinuous response surfaces, J. Comput. Phys. 228 (2009) 7159-7180.
3. M. Deb, I. Babuška, J. Oden, Solution of stochastic partial differential equations using Galerkin finite element techniques, Comput. Method. Appl. M. 190 (2001) 6359-6372.
4. A. Doostan, G. Iaccarino, A least-squares approximation of partial differential equations with high-dimensional random inputs, J. Comput. Phys. 228 (2009) 4332-4345.
5. J. Foo, X. Wan, G.E. Karniadakis, The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications, J. Comput. Phys. 227 (2008) 9572-9595.
6. B. Ganapathysubramanian, N. Zabaras, Sparse grid collocation schemes for stochastic natural convection problems, J. Comput. Phys. 225 (2007) 652-685.
7. R.G. Ghanem, P. Spanos, Stochastic finite elements: a spectral approach, Springer-Verlag, New York (1991).
8. J.M. Hammersley, D.C. Handscomb, Monte Carlo Methods, Fletcher & Son Ltd, Norwich (1964).
9. A. Harten, High resolution schemes for hyperbolic conservation laws, J. Comput. Phys 49 (1983) 357-393.
10. S. Hosder, R.W. Walters, R. Perez, A non-intrusive polynomial chaos method for uncertainty propagation in CFD simulations, 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada (2006) AIAA-2006-891.
11. A. Jameson, Positive schemes and shock modelling for compressible flows, Int. J. Num. Meth. Fluids 20 (1995) 743-776.
12. M. Loéve, Probability theory, 4th ed., Springer-Verlag, New York (1977).
13. X. Ma, N. Zabaras, An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations, J. Comput. Phys. 228 (2009) 3084-3113.
14. O.P. Le Maître, H.N. Najm, R.G. Ghanem, O.M. Knio, Multi-resolution analysis of Wiener-type uncertainty propagation schemes, J. Comput. Phys. 197 (2004) 502-531.
15. H.N. Najm, Uncertainty quantification and polynomial chaos techniques in computational fluid dynamics, Annu. Rev. Fluid Mech. 41 (2009) 35-52.
16. F. Nobile, R. Tempone, C.G. Webster, A sparse grid stochastic collocation method for partial differential equations with random input data, SIAM J. Numer. Anal. 46 (2008) 2309-2345.
17. S. Smolyak, Quadrature and interpolation formulas for tensor products of certain classes of functions, Soviet Math. Dokl. 4 (1963) 240-243.
18. M.A. Tatang, Direct incorporation of uncertainty in chemical and environmental engineering systems, PhD thesis, MIT, Cambridge (1995).
19. L.N. Trefethen, Is Gauss quadrature better than Clenshaw-Curtis? SIAM Rev. 50 (2008) 67-87.
20. X. Wan, G.E. Karniadakis, Multi-element generalized polynomial chaos for arbitrary probability measures, SIAM J. Sci. Comput. 28 (2006) 901-928.
21. N. Wiener, Nonlinear problems in random theory, MIT Technology Press and John Wiley & Sons, New York (1958).
22. J.A.S. Witteveen, H. Bijl, Effect of randomness on multi-frequency aeroelastic responses resolved by unsteady adaptive stochastic finite elements, J. Comput. Phys. 228 (2009) 7025-7045.
23. J.A.S. Witteveen, H. Bijl, A TVD uncertainty quantification method with bounded error applied to transonic airfoil flutter, Commun. Comput. Phys. 6 (2009) 406-432.
24. J.A.S. Witteveen, G.J.A. Loeven, H. Bijl, An adaptive stochastic finite elements approach based on Newton-Cotes quadrature in simplex elements, Comput. Fluids 38 (2009) 1270-1288.
25. D. Xiu, G.E. Karniadakis, The Wiener-Askey polynomial chaos for stochastic differential equations, SIAM J. Sci. Comput. 24 (2002) 619-644.
26. D. Xiu, J.S. Hesthaven, High-order collocation methods for differential equations with random inputs, SIAM J. Sci. Comput. 27 (2005) 1118-1139.
27. D. Xiu, Fast numerical methods for stochastic computations: A review, Commun. Comput. Phys. 5 (2009) 242-272.