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Relevant bibliographies by topics / Stochastic collocation methods

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Academic literature on the topic 'Stochastic collocation methods'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 February 2022

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Journal articles on the topic "Stochastic collocation methods"

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Pulch, Roland. "Stochastic collocation and stochastic Galerkin methods for linear differential algebraic equations." Journal of Computational and Applied Mathematics 262 (May 2014): 281–91. http://dx.doi.org/10.1016/j.cam.2013.10.046.

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VAN DER STOEP, ANTHONIE W., LECH A. GRZELAK, and CORNELIS W. OOSTERLEE. "COLLOCATING VOLATILITY: A COMPETITIVE ALTERNATIVE TO STOCHASTIC LOCAL VOLATILITY MODELS." International Journal of Theoretical and Applied Finance 23, no. 06 (2020): 2050038. http://dx.doi.org/10.1142/s0219024920500387.

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We discuss a competitive alternative to stochastic local volatility models, namely the Collocating Volatility (CV) framework, introduced in [L. A. Grzelak (2019) The CLV framework — A fresh look at efficient pricing with smile, International Journal of Computer Mathematics 96 (11), 2209–2228]. The CV framework consists of two elements, a “kernel process” that can be efficiently evaluated and a local volatility function. The latter, based on stochastic collocation — e.g. [I. Babuška, F. Nobile & R. Tempone (2007) A stochastic collocation method for elliptic partial differential equations wi

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Xiao, Y., J. N. Shi, and Z. W. Yang. "Split-step collocation methods for stochastic Volterra integral equations." Journal of Integral Equations and Applications 30, no. 1 (2018): 197–218. http://dx.doi.org/10.1216/jie-2018-30-1-197.

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Guo, Ling, Akil Narayan, Tao Zhou, and Yuhang Chen. "Stochastic Collocation Methods via $\ell_1$ Minimization Using Randomized Quadratures." SIAM Journal on Scientific Computing 39, no. 1 (2017): A333—A359. http://dx.doi.org/10.1137/16m1059680.

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dos Santos Azevedo, Juarez, and Saulo Pomponet Oliveira. "A Numerical Comparison Between Quasi-Monte Carlo and Sparse Grid Stochastic Collocation Methods." Communications in Computational Physics 12, no. 4 (2012): 1051–69. http://dx.doi.org/10.4208/cicp.260111.230911a.

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AbstractQuasi-Monte Carlo methods and stochastic collocation methods based on sparse grids have become popular with solving stochastic partial differential equations. These methods use deterministic points for multi-dimensional integration or interpolation without suffering from the curse of dimensionality. It is not evident which method is best, specially on random models of physical phenomena. We numerically study the error of quasi-Monte Carlo and sparse grid methods in the context of ground-water flow in heterogeneous media. In particular, we consider the dependence of the variance error o

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Narayan, Akil, and Tao Zhou. "Stochastic Collocation on Unstructured Multivariate Meshes." Communications in Computational Physics 18, no. 1 (2015): 1–36. http://dx.doi.org/10.4208/cicp.020215.070515a.

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AbstractCollocation has become a standard tool for approximation of parameterized systems in the uncertainty quantification (UQ) community. Techniques for least-squares regularization, compressive sampling recovery, and interpolatory reconstruction are becoming standard tools used in a variety of applications. Selection of a collocation mesh is frequently a challenge, but methods that construct geometricallyunstructuredcollocation meshes have shown great potential due to attractive theoretical properties and direct, simple generation and implementation. We investigate properties of these meshe

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Barajas-Solano, David A., and Daniel M. Tartakovsky. "Stochastic Collocation Methods for Nonlinear Parabolic Equations with Random Coefficients." SIAM/ASA Journal on Uncertainty Quantification 4, no. 1 (2016): 475–94. http://dx.doi.org/10.1137/130930108.

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Miranda, Mario J., and Joseph W. Glauber. "Solving Stochastic Models of Competitive Storage and Trade by Chebychev Collocation Methods." Agricultural and Resource Economics Review 24, no. 1 (1995): 70–77. http://dx.doi.org/10.1017/s1068280500003622.

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We show how to solve the stochastic spatial-temporal price equilibrium model numerically using the Chebychev collocation method. We then use the model to analyze the joint and interactive stabilizing effects of competitive storage and trade.

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Zhao, Qinghai, Xiaokai Chen, Zheng-Dong Ma, and Yi Lin. "Robust Topology Optimization Based on Stochastic Collocation Methods under Loading Uncertainties." Mathematical Problems in Engineering 2015 (2015): 1–14. http://dx.doi.org/10.1155/2015/580980.

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A robust topology optimization (RTO) approach with consideration of loading uncertainties is developed in this paper. The stochastic collocation method combined with full tensor product grid and Smolyak sparse grid transforms the robust formulation into a weighted multiple loading deterministic problem at the collocation points. The proposed approach is amenable to implementation in existing commercial topology optimization software package and thus feasible to practical engineering problems. Numerical examples of two- and three-dimensional topology optimization problems are provided to demons

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Hakula, Harri, Vesa Kaarnioja, and Mikael Laaksonen. "Cylindrical Shell with Junctions: Uncertainty Quantification of Free Vibration and Frequency Response Analysis." Shock and Vibration 2018 (December 2, 2018): 1–16. http://dx.doi.org/10.1155/2018/5817940.

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Numerical simulation of thin solids remains one of the challenges in computational mechanics. The 3D elasticity problems of shells of revolution are dimensionally reduced in different ways depending on the symmetries of the configurations resulting in corresponding 2D models. In this paper, we solve the multiparametric free vibration of complex shell configurations under uncertainty using stochastic collocation with the p-version of finite element method and apply the collocation approach to frequency response analysis. In numerical examples, the sources of uncertainty are related to material

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Dissertations / Theses on the topic "Stochastic collocation methods"

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Schieche, Bettina [Verfasser]. "Unsteady Adaptive Stochastic Collocation Methods on Sparse Grids / Bettina Schieche." München : Verlag Dr. Hut, 2012. http://d-nb.info/1029399905/34.

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van, Wyk Hans-Werner. "A Variational Approach to Estimating Uncertain Parameters in Elliptic Systems." Diss., Virginia Tech, 2012. http://hdl.handle.net/10919/27635.

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As simulation plays an increasingly central role in modern science and engineering research, by supplementing experiments, aiding in the prototyping of engineering systems or informing decisions on safety and reliability, the need to quantify uncertainty in model outputs due to uncertainties in the model parameters becomes critical. However, the statistical characterization of the model parameters is rarely known. In this thesis, we propose a variational approach to solve the stochastic inverse problem of obtaining a statistical description of the diffusion coefficient in an elliptic partial d

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Zhang, Jingwei. "Numerical Methods for the Chemical Master Equation." Diss., Virginia Tech, 2009. http://hdl.handle.net/10919/30018.

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The chemical master equation, formulated on the Markov assumption of underlying chemical kinetics, offers an accurate stochastic description of general chemical reaction systems on the mesoscopic scale. The chemical master equation is especially useful when formulating mathematical models of gene regulatory networks and protein-protein interaction networks, where the numbers of molecules of most species are around tens or hundreds. However, solving the master equation directly suffers from the so called "curse of dimensionality" issue. This thesis first tries to study the numerical properties

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Chandra, Sekhar D. "Stochastic engineering simulations using sparse grid collocation method and Kriging based approaches." Thesis, University of Southampton, 2017. https://eprints.soton.ac.uk/418266/.

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The estimation of probabilistic moments is central to robust design process. Typically one would like to estimate the mean and variance of some performance critical metric such as stress, life, etc., of a component in any engineering system, aiming a robustly optimized design that is less sensitive to the input variations/uncertainties. For complex aerospace engineering systems such as aero-engine, a single numerical simulation of any component can often take a substantial amount of time and few samples can be aﬀorded at which the deterministic simulations can be carried out. Considering the v

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Mesogitis, Tassos. "Stochastic simulation of the cure of advanced composites." Thesis, Cranfield University, 2015. http://dspace.lib.cranfield.ac.uk/handle/1826/9216.

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This study focuses on the development of a stochastic simulation methodology to study the effects of cure kinetics uncertainty, in plane fibre misalignment and boundary conditions uncertainty on the cure process of composite materials. Differential Scanning Calorimetry was used to characterise cure kinetics variability of a commercial epoxy resin used in aerospace applications. It was found that cure kinetics uncertainty is associated with variations in the initial degree of cure, activation energy and reaction order. Image analysis was employed to characterise in plane fibre misalignment in a

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Allen, James Brandon. "Estimating Uncertainties in the Joint Reaction Forces of Construction Machinery." Thesis, Virginia Tech, 2009. http://hdl.handle.net/10919/33046.

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In this study we investigate the propagation of uncertainties in the input forces through a mechanical system. The system of interest was a wheel loader, but the methodology developed can be applied to any multibody systems. The modeling technique implemented focused on efficiently modeling stochastic systems for which the equations of motion are not available. The analysis targeted the reaction forces in joints of interest. <p> The modeling approach developed in this thesis builds a foundation for determining the uncertainties in a Caterpillar 980G II wheel loader. The study begins with const

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Charrier, Julia. "Analyse numérique d’équations aux dérivées aléatoires, applications à l’hydrogéologie." Thesis, Cachan, Ecole normale supérieure, 2011. http://www.theses.fr/2011DENS0030/document.

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Ce travail présente quelques résultats concernant des méthodes numériques déterministes et probabilistes pour des équations aux dérivées partielles à coefficients aléatoires, avec des applications à l'hydrogéologie. On s'intéresse tout d'abord à l'équation d'écoulement dans un milieu poreux en régime stationnaire avec un coefficient de perméabilité lognormal homogène, incluant le cas d'une fonction de covariance peu régulière. On établit des estimations aux sens fort et faible de l'erreur commise sur la solution en tronquant le développement de Karhunen-Loève du coefficient. Puis on établit de

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Oumouni, Mestapha. "Analyse numérique de méthodes performantes pour les EDP stochastiques modélisant l'écoulement et le transport en milieux poreux." Phd thesis, Université Rennes 1, 2013. http://tel.archives-ouvertes.fr/tel-00904512.

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Ce travail présente un développement et une analyse des approches numériques déterministes et probabilistes efficaces pour les équations aux dérivées partielles avec des coefficients et données aléatoires. On s'intéresse au problème d'écoulement stationnaire avec des données aléatoires. Une méthode de projection dans le cas unidimensionnel est présentée, permettant de calculer efficacement la moyenne de la solution. Nous utilisons la méthode de collocation anisotrope des grilles clairsemées. D'abord, un indicateur de l'erreur satisfaisant une borne supérieure de l'erreur est introduit, il perm

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Deng, Jian. "Stochastic collocation methods for aeroelastic system with uncertainty." Master's thesis, 2009. http://hdl.handle.net/10048/557.

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Thesis (M. Sc.)--University of Alberta, 2009.<br>Title from pdf file main screen (viewed on Sept. 3, 2009). "A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Master of Science in Applied Mathematics, Department of Mathematical and Statistical Sciences, University of Alberta." Includes bibliographical references.

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Vidličková, Eva. "Fourierova-Galerkinova metoda pro řešení úloh stochastické homogenizace eliptických parciálních diferenciálních rovnic." Master's thesis, 2017. http://www.nusl.cz/ntk/nusl-357265.

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This thesis covers the basics in the stochastic homogenization of elliptic partial differential equations, from underlying theory up to numerical ap- proaches. In particular, we introduce and analyze a combination of the Fourier-Galerkin method in the spatial domain with a collocation method in the stochastic domain. The material coefficients are assumed to depend on a finite number of random variables. We present a comparison of the Monte Carlo method with the full tensor grid and sparse grid collocation method for two applications. The first one is the checkerboard problem with continuous ra

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Books on the topic "Stochastic collocation methods"

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Malin, Benjamin. Computing stochastic dynamic economic models with a large number of state variables: A description and application of a Smolyak-collocation method. National Bureau of Economic Research, 2007.

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Malin, Benjamin. Computing stochastic dynamic economic models with a large number of state variables: A description and application of a smolyak-collocation method. National Bureau of Economic Research, 2007.

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Book chapters on the topic "Stochastic collocation methods"

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Xiu, Dongbin. "Stochastic Collocation Methods: A Survey." In Handbook of Uncertainty Quantification. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-12385-1_26.

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Xiu, Dongbin. "Stochastic Collocation Methods: A Survey." In Handbook of Uncertainty Quantification. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-11259-6_26-1.

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Schieche, Bettina, and Jens Lang. "Adjoint Error Estimation for Stochastic Collocation Methods." In Lecture Notes in Computational Science and Engineering. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-04537-5_12.

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Zhang, Zhongqiang, and George Em Karniadakis. "Comparison between Wiener chaos methods and stochastic collocation methods." In Numerical Methods for Stochastic Partial Differential Equations with White Noise. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-57511-7_8.

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Gunzburger, Max, Clayton G. Webster, and Guannan Zhang. "Sparse Collocation Methods for Stochastic Interpolation and Quadrature." In Handbook of Uncertainty Quantification. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-12385-1_29.

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Gunzburger, Max, Clayton G. Webster, and Guannan Zhang. "Sparse Collocation Methods for Stochastic Interpolation and Quadrature." In Handbook of Uncertainty Quantification. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-11259-6_29-1.

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Zhang, Zhongqiang, and George Em Karniadakis. "Application of collocation method to stochastic conservation laws." In Numerical Methods for Stochastic Partial Differential Equations with White Noise. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-57511-7_9.

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Zhang, Zhongqiang, and George Em Karniadakis. "Stochastic collocation methods for differential equations with white noise." In Numerical Methods for Stochastic Partial Differential Equations with White Noise. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-57511-7_7.

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Fasshauer, Gregory E., and Qi Ye. "Kernel-Based Collocation Methods Versus Galerkin Finite Element Methods for Approximating Elliptic Stochastic Partial Differential Equations." In Meshfree Methods for Partial Differential Equations VI. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-32979-1_10.

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Bäck, Joakim, Fabio Nobile, Lorenzo Tamellini, and Raul Tempone. "Stochastic Spectral Galerkin and Collocation Methods for PDEs with Random Coefficients: A Numerical Comparison." In Lecture Notes in Computational Science and Engineering. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-15337-2_3.

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Conference papers on the topic "Stochastic collocation methods"

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Lallechere, Sebastien, Pierre Bonnet, Ibrahim El Baba, and Francoise Paladian. "Unscented transform and stochastic collocation methods for stochastic electromagnetic compatibility." In 2011 Computational Electromagnetics International Workshop (CEM). IEEE, 2011. http://dx.doi.org/10.1109/cem.2011.6047322.

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Eldred, Michael, and Laura Swiler. "Towards Goal-Oriented Stochastic Design Employing Adaptive Collocation Methods." In 13th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference. American Institute of Aeronautics and Astronautics, 2010. http://dx.doi.org/10.2514/6.2010-9125.

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Zhouxiang Fei, Yi Huang, Jiafeng Zhou, and Chaoyun Song. "Comparison of stochastic reduced order model and stochastic collocation methods for the sensitivity analysis of crosstalk." In Tenth International Conference on Computational Electromagnetics (CEM 2019). Institution of Engineering and Technology, 2019. http://dx.doi.org/10.1049/cp.2019.0118.

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Eldred, Michael, and John Burkardt. "Comparison of Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Quantification." In 47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition. American Institute of Aeronautics and Astronautics, 2009. http://dx.doi.org/10.2514/6.2009-976.

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Li, Heng, Haibin Chang, and Dongxiao Zhang. "Stochastic Collocation Methods for Efficient and Accurate Quantification of Uncertainty in Multiphase Reservoir Simulations." In SPE Reservoir Simulation Symposium. Society of Petroleum Engineers, 2009. http://dx.doi.org/10.2118/118964-ms.

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Bajars, Janis, and David Chappell. "Boundary integral models of stochastic ray propagation: Discretisation via the collocation and Nyström methods." In APPLIED MATHEMATICS AND COMPUTER SCIENCE: Proceedings of the 1st International Conference on Applied Mathematics and Computer Science. Author(s), 2017. http://dx.doi.org/10.1063/1.4981994.

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Archibald, Rick. "Error estimation in high dimensional space for stochastic collocation methods on arbitrary sparse samples." In 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4825645.

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Delgado, Paul, and Vinod Kumar. "A Stochastic Galerkin Approach to Uncertainty Quantification in Poroelastic Media." In ASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting collocated with the ASME 2014 12th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/fedsm2014-21577.

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Recent concerns over the safety of oil and natural gas extraction, fracking, and carbon sequestration have driven the need to develop methods for uncertainty quantification for coupled subsurface flow & deformation processes. Traditional monte-carlo methods are versatile, but exhibit prohibitively slow convergence. In this work, we develop an intrusive polynomial chaos expansion method for Biot’s Poroelasticity Equations based on galerkin projection with uniform and log-normally distributed material parameters. We analyze accuracy and efficiency of our method and compare it to monte-carlo

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Montomoli, F., A. D’Ammaro, and S. Uchida. "Uncertainty Quantification and Conjugate Heat Transfer: A Stochastic Analysis." In ASME Turbo Expo 2012: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/gt2012-68203.

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Conjugate Heat Transfer studies are a common method to predict the thermal loading in high pressure nozzles. Despite the accuracy of nowadays tools, it is not clear how to include the uncertainties associated to the turbulence level, the temperature distribution or the thermal barrier coating thickness in the numerical simulations. All these parameters are stochastic even if their value is commonly assumed to be deterministic. For the first time, in this work a stochastic analysis is used to predict the metal temperature in a real high pressure nozzle. The domain is the complete high pressure

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Eldred, Michael. "Recent Advances in Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Analysis and Design." In 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. American Institute of Aeronautics and Astronautics, 2009. http://dx.doi.org/10.2514/6.2009-2274.

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Reports on the topic "Stochastic collocation methods"

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Webster, Clayton G., Guannan Zhang, and Max D. Gunzburger. An adaptive wavelet stochastic collocation method for irregular solutions of stochastic partial differential equations. Office of Scientific and Technical Information (OSTI), 2012. http://dx.doi.org/10.2172/1081925.

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Tran, Hoang, Catalin Trenchea, and Clayton Webster. A convergence analysis of stochastic collocation method for Navier-Stokes equations with random input data. Office of Scientific and Technical Information (OSTI), 2014. http://dx.doi.org/10.2172/1649669.

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Zhang, Guannan, Clayton G. Webster, and Max D. Gunzburger. An adaptive sparse-grid high-order stochastic collocation method for Bayesian inference in groundwater reactive transport modeling. Office of Scientific and Technical Information (OSTI), 2012. http://dx.doi.org/10.2172/1055118.

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Webster, Clayton, Raul Tempone, and Fabio Nobile. The analysis of a sparse grid stochastic collocation method for partial differential equations with high-dimensional random input data. Office of Scientific and Technical Information (OSTI), 2007. http://dx.doi.org/10.2172/934852.

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Malin, Benjamin, Dirk Krueger, and Felix Kubler. Computing Stochastic Dynamic Economic Models with a Large Number of State Variables: A Description and Application of a Smolyak-Collocation Method. National Bureau of Economic Research, 2007. http://dx.doi.org/10.3386/t0345.

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Malin, Benjamin, Dirk Krueger, and Felix Kubler. Computing Stochastic Dynamic Economic Models with a Large Number of State Variables: A Description and Application of a Smolyak-Collocation Method. National Bureau of Economic Research, 2007. http://dx.doi.org/10.3386/w13517.

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