Fast numerical methods for stochastic computations: A review
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[1] A. Stroud. Remarks on the disposition of points in numerical integration formulas. , 1957 .
[2] Steven A. Orszag,et al. Dynamical Properties of Truncated Wiener‐Hermite Expansions , 1967 .
[3] A. Chorin. Gaussian fields and random flow , 1974, Journal of Fluid Mechanics.
[4] D. Gottlieb,et al. Numerical analysis of spectral methods : theory and applications , 1977 .
[5] Humberto Contreras,et al. The stochastic finite-element method , 1980 .
[6] S. Swain. Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences , 1984 .
[7] 森山 昌彦,et al. 「確率有限要素法」(Stochastic Finite Element Method) , 1985 .
[8] B. Øksendal. Stochastic Differential Equations , 1985 .
[9] Wing Kam Liu,et al. Random field finite elements , 1986 .
[10] K. Vahala. Handbook of stochastic methods for physics, chemistry and the natural sciences , 1986, IEEE Journal of Quantum Electronics.
[11] Wing Kam Liu,et al. Probabilistic finite elements for nonlinear structural dynamics , 1986 .
[12] M. Stein. Large sample properties of simulations using latin hypercube sampling , 1987 .
[13] B. Øksendal. Stochastic differential equations : an introduction with applications , 1987 .
[14] Masanobu Shinozuka,et al. Neumann Expansion for Stochastic Finite Element Analysis , 1988 .
[15] M. Shinozuka,et al. Digital Generation of Non‐Gaussian Stochastic Fields , 1988 .
[16] Masanobu Shinozuka,et al. Response Variability of Stochastic Finite Element Systems , 1988 .
[17] R. Ghanem,et al. Stochastic Finite Element Expansion for Random Media , 1989 .
[18] R. Ghanem,et al. Stochastic Finite Elements: A Spectral Approach , 1990 .
[19] Masanobu Shinozuka,et al. Simulation of Stochastic Fields by Statistical Preconditioning , 1990 .
[20] N. Cutland,et al. On homogeneous chaos , 1991, Mathematical Proceedings of the Cambridge Philosophical Society.
[21] George Deodatis,et al. Weighted Integral Method. I: Stochastic Stiffness Matrix , 1991 .
[22] M. Shinozuka,et al. Simulation of Stochastic Processes by Spectral Representation , 1991 .
[23] Masanobu Shinozuka,et al. Weighted Integral Method. II: Response Variability and Reliability , 1991 .
[24] Harald Niederreiter,et al. Random number generation and Quasi-Monte Carlo methods , 1992, CBMS-NSF regional conference series in applied mathematics.
[25] Bruce R. Ellingwood,et al. Orthogonal Series Expansions of Random Fields in Reliability Analysis , 1994 .
[26] K. Ritter,et al. High dimensional integration of smooth functions over cubes , 1996 .
[27] Ronald L. Wasserstein,et al. Monte Carlo: Concepts, Algorithms, and Applications , 1997 .
[28] Menner A. Tatang,et al. An efficient method for parametric uncertainty analysis of numerical geophysical models , 1997 .
[29] R. Ghanem. Stochastic Finite Elements For Heterogeneous Media with Multiple Random Non-Gaussian Properties , 1997 .
[30] S. Shreve,et al. Stochastic differential equations , 1955, Mathematical Proceedings of the Cambridge Philosophical Society.
[31] Peter Zinterhof,et al. Monte Carlo and Quasi-Monte Carlo Methods 1996 , 1998 .
[32] M. Grigoriu. Simulation of stationary non-Gaussian translation processes , 1998 .
[33] R. Caflisch. Monte Carlo and quasi-Monte Carlo methods , 1998, Acta Numerica.
[34] Roger Ghanem,et al. Scales of fluctuation and the propagation of uncertainty in random porous media , 1998 .
[35] George Deodatis,et al. Simulation of homogeneous nonGaussian stochastic vector fields , 1998 .
[36] K. Ritter,et al. Simple Cubature Formulas with High Polynomial Exactness , 1999 .
[37] B. Fox. Strategies for Quasi-Monte Carlo , 1999, International Series in Operations Research & Management Science.
[38] J. Collins,et al. Construction of a genetic toggle switch in Escherichia coli , 2000, Nature.
[39] Erich Novak,et al. High dimensional polynomial interpolation on sparse grids , 2000, Adv. Comput. Math..
[40] R. Ghanem,et al. A stochastic projection method for fluid flow. I: basic formulation , 2001 .
[41] W. Chew,et al. Numerical simulation methods for rough surface scattering , 2001 .
[42] You‐Kuan Zhang. Stochastic Methods for Flow in Porous Media: Coping with Uncertainties , 2001 .
[43] Kok-Kwang Phoon,et al. Convergence study of the truncated Karhunen–Loeve expansion for simulation of stochastic processes , 2001 .
[44] D. Xiu,et al. Stochastic Modeling of Flow-Structure Interactions Using Generalized Polynomial Chaos , 2002 .
[45] D. Xiu,et al. Modeling Uncertainty in Steady State Diffusion Problems via Generalized Polynomial Chaos , 2002 .
[46] Christian Soize,et al. Non-Gaussian simulation using Hermite polynomial expansion: convergences and algorithms , 2002 .
[47] Dongbin Xiu,et al. The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations , 2002, SIAM J. Sci. Comput..
[48] H. Najm,et al. A stochastic projection method for fluid flow II.: random process , 2002 .
[49] Roger Ghanem,et al. Simulation of multi-dimensional non-gaussian non-stationary random fields , 2002 .
[50] Ronald Cools,et al. An encyclopaedia of cubature formulas , 2003, J. Complex..
[51] E. Paleologos,et al. Stochastic Methods for Flow in Porous Media, Coping With Uncertainties , 2003 .
[52] D. Xiu,et al. Modeling uncertainty in flow simulations via generalized polynomial chaos , 2003 .
[53] L. Mathelin,et al. A Stochastic Collocation Algorithm for Uncertainty Analysis , 2003 .
[54] D. Xiu,et al. A new stochastic approach to transient heat conduction modeling with uncertainty , 2003 .
[55] George Em Karniadakis,et al. Supersensitivity due to uncertain boundary conditions , 2004 .
[56] R. Ghanem,et al. Multi-resolution analysis of wiener-type uncertainty propagation schemes , 2004 .
[57] Adrian Sandu,et al. Modeling Multibody Dynamic Systems With Uncertainties . Part II : Numerical Applications , 2004 .
[58] R. Ghanem,et al. Uncertainty propagation using Wiener-Haar expansions , 2004 .
[59] Daniel M. Tartakovsky,et al. A Two-Scale Nonperturbative Approach to Uncertainty Analysis of Diffusion in Random Composites , 2004, Multiscale Model. Simul..
[60] Roger G. Ghanem,et al. Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure , 2005, SIAM J. Sci. Comput..
[61] Adrian Sandu,et al. Modeling Multibody Dynamic Systems With Uncertainties . Part I : Theoretical and Computational Aspects , 2004 .
[62] Dongbin Xiu,et al. High-Order Collocation Methods for Differential Equations with Random Inputs , 2005, SIAM J. Sci. Comput..
[63] Hermann G. Matthies,et al. Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations , 2005 .
[64] Dongbin Xiu,et al. Equation-Free, Multiscale Computation for Unsteady Random Diffusion , 2005, Multiscale Model. Simul..
[65] Jan S. Hesthaven,et al. Uncertainty analysis for the steady-state flows in a dual throat nozzle , 2005 .
[66] Roger G. Ghanem,et al. An equation-free, multiscale approach to uncertainty quantification , 2005, Computing in Science & Engineering.
[67] Sami F. Masri,et al. Identification and prediction of stochastic dynamical systems in a polynomial chaos basis , 2005 .
[68] G. Karniadakis,et al. An adaptive multi-element generalized polynomial chaos method for stochastic differential equations , 2005 .
[69] Nicholas Zabaras,et al. Using Bayesian statistics in the estimation of heat source in radiation , 2005 .
[70] Jan S. Hesthaven,et al. Computational modeling of uncertainty in time-domain electromagnetics , 2005, Workshop on Computational Electromagnetics in Time-Domain, 2005. CEM-TD 2005..
[71] P. Frauenfelder,et al. Finite elements for elliptic problems with stochastic coefficients , 2005 .
[72] Roger Ghanem,et al. A Stochastic Nonlocal Model for Materials with Multiscale Behavior , 2006 .
[73] Thomas Y. Hou,et al. Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics , 2006, J. Comput. Phys..
[74] Nicholas Zabaras,et al. A stochastic variational multiscale method for diffusion in heterogeneous random media , 2006, J. Comput. Phys..
[75] O. L. Maître,et al. Uncertainty propagation in CFD using polynomial chaos decomposition , 2006 .
[76] G. Karniadakis,et al. Long-Term Behavior of Polynomial Chaos in Stochastic Flow Simulations , 2006 .
[77] Daniel M. Tartakovsky,et al. Numerical Methods for Differential Equations in Random Domains , 2006, SIAM J. Sci. Comput..
[78] Christoph Schwab,et al. Karhunen-Loève approximation of random fields by generalized fast multipole methods , 2006, J. Comput. Phys..
[79] Daniel M. Tartakovsky,et al. Stochastic analysis of transport in tubes with rough walls , 2006, J. Comput. Phys..
[80] G. Karniadakis,et al. Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures , 2006, SIAM J. Sci. Comput..
[81] Roger G. Ghanem,et al. On the construction and analysis of stochastic models: Characterization and propagation of the errors associated with limited data , 2006, J. Comput. Phys..
[82] N. Zabaras,et al. Uncertainty propagation in finite deformations––A spectral stochastic Lagrangian approach , 2006 .
[83] Dongbin Xiu,et al. Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network , 2007, J. Comput. Phys..
[84] Raul Tempone,et al. An anisotropic sparse grid stochastic collocation method for elliptic partial differential equations with random input data , 2007 .
[85] D. Xiu. Efficient collocational approach for parametric uncertainty analysis , 2007 .
[86] Roger Ghanem,et al. Stochastic model reduction for chaos representations , 2007 .
[87] C. Chauviere,et al. Efficient Computation of RCS From Scatterers of Uncertain Shapes , 2007, IEEE Transactions on Antennas and Propagation.
[88] Habib N. Najm,et al. Stochastic spectral methods for efficient Bayesian solution of inverse problems , 2005, J. Comput. Phys..
[89] George Em Karniadakis,et al. Random roughness enhances lift in supersonic flow. , 2007, Physical review letters.
[90] Chao Jin,et al. Parallel Domain Decomposition Methods for Stochastic Elliptic Equations , 2007, SIAM J. Sci. Comput..
[91] Claudio Canuto,et al. A fictitious domain approach to the numerical solution of PDEs in stochastic domains , 2007, Numerische Mathematik.
[92] Fabio Nobile,et al. A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data , 2007, SIAM Rev..
[93] D. Xiu,et al. An efficient spectral method for acoustic scattering from rough surfaces , 2007 .
[94] Dongbin Xiu,et al. Stochastic Markovian modeling of electrophysiology of ion channels: reconstruction of standard deviations in macroscopic currents. , 2007, Journal of theoretical biology.
[95] Nitin Agarwal,et al. A stochastic Lagrangian approach for geometrical uncertainties in electrostatics , 2007, J. Comput. Phys..
[96] Guang Lin,et al. Stochastic Computational Fluid Mechanics , 2007, Computing in Science & Engineering.
[97] Christoph Schwab,et al. Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients , 2007 .
[98] Xiongzhi Chen. Brownian Motion and Stochastic Calculus , 2008 .
[99] D. Xiu. Numerical integration formulas of degree two , 2008 .
[100] Ronald L. Iman. Latin Hypercube Sampling , 2008 .
[101] Fabio Nobile,et al. An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data , 2008, SIAM J. Numer. Anal..
[102] Dongbin Xiu,et al. Galerkin method for wave equations with uncertain coefficients , 2008 .
[103] Jie Shen,et al. Efficient stochastic Galerkin methods for random diffusion equations , 2009, J. Comput. Phys..
[104] A. W. Wymore,et al. Numerical Evaluation of Multiple Integrals I , 2010 .