Relevant bibliographies by topics / Stochastic collocation methods / Journal articles
To see the other types of publications on this topic, follow the link: Stochastic collocation methods.

Journal articles on the topic 'Stochastic collocation methods'

Author: Grafiati
Published: 4 June 2021
Last updated: 14 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Stochastic collocation methods.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

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.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

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.

Full text
Abstract:
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
APA, Harvard, Vancouver, ISO, and other styles
3

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.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

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.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

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.

Full text
Abstract:
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
APA, Harvard, Vancouver, ISO, and other styles
6

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.

Full text
Abstract:
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
APA, Harvard, Vancouver, ISO, and other styles
7

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.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

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.

Full text
Abstract:
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.
APA, Harvard, Vancouver, ISO, and other styles
9

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.

Full text
Abstract:
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
APA, Harvard, Vancouver, ISO, and other styles
10

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.

Full text
Abstract:
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
APA, Harvard, Vancouver, ISO, and other styles
11

Buzzard, Gregery T., and Dongbin Xiu. "Variance-Based Global Sensitivity Analysis via Sparse-Grid Interpolation and Cubature." Communications in Computational Physics 9, no. 3 (2011): 542–67. http://dx.doi.org/10.4208/cicp.230909.160310s.

Full text
Abstract:
AbstractThe stochastic collocation method using sparse grids has become a popular choice for performing stochastic computations in high dimensional (random) parameter space. In addition to providing highly accurate stochastic solutions, the sparse grid collocation results naturally contain sensitivity information with respect to the input random parameters. In this paper, we use the sparse grid interpolation and cubature methods of Smolyak together with combinatorial analysis to give a computationally efficient method for computing the global sensitivity values of Sobol’. This method allows fo
APA, Harvard, Vancouver, ISO, and other styles
12

Narayan, Akil, and Dongbin Xiu. "Stochastic Collocation Methods on Unstructured Grids in High Dimensions via Interpolation." SIAM Journal on Scientific Computing 34, no. 3 (2012): A1729—A1752. http://dx.doi.org/10.1137/110854059.

Full text
APA, Harvard, Vancouver, ISO, and other styles
13

Lazarov, Boyan S., Mattias Schevenels, and Ole Sigmund. "Topology optimization considering material and geometric uncertainties using stochastic collocation methods." Structural and Multidisciplinary Optimization 46, no. 4 (2012): 597–612. http://dx.doi.org/10.1007/s00158-012-0791-7.

Full text
APA, Harvard, Vancouver, ISO, and other styles
14

Chen, Peng, Alfio Quarteroni, and Gianluigi Rozza. "Comparison Between Reduced Basis and Stochastic Collocation Methods for Elliptic Problems." Journal of Scientific Computing 59, no. 1 (2013): 187–216. http://dx.doi.org/10.1007/s10915-013-9764-2.

Full text
APA, Harvard, Vancouver, ISO, and other styles
15

Liu, Yongle, and Ling Guo. "Stochastic Collocation vial1-Minimisation on Low Discrepancy Point Sets with Application to Uncertainty Quantification." East Asian Journal on Applied Mathematics 6, no. 2 (2016): 171–91. http://dx.doi.org/10.4208/eajam.090615.060216a.

Full text
Abstract:
AbstractVarious numerical methods have been developed in order to solve complex systems with uncertainties, and the stochastic collocation method usingl1-minimisation on low discrepancy point sets is investigated here. Halton and Sobol' sequences are considered, and low discrepancy point sets and random points are compared. The tests discussed involve a given target function in polynomial form, high-dimensional functions and a random ODE model. Our numerical results show that the low discrepancy point sets perform as well or better than random sampling for stochastic collocation vial1-minimisa
APA, Harvard, Vancouver, ISO, and other styles
16

BECK, JOAKIM, RAUL TEMPONE, FABIO NOBILE, and LORENZO TAMELLINI. "ON THE OPTIMAL POLYNOMIAL APPROXIMATION OF STOCHASTIC PDES BY GALERKIN AND COLLOCATION METHODS." Mathematical Models and Methods in Applied Sciences 22, no. 09 (2012): 1250023. http://dx.doi.org/10.1142/s0218202512500236.

Full text
Abstract:
In this work we focus on the numerical approximation of the solution u of a linear elliptic PDE with stochastic coefficients. The problem is rewritten as a parametric PDE and the functional dependence of the solution on the parameters is approximated by multivariate polynomials. We first consider the stochastic Galerkin method, and rely on sharp estimates for the decay of the Fourier coefficients of the spectral expansion of u on an orthogonal polynomial basis to build a sequence of polynomial subspaces that features better convergence properties, in terms of error versus number of degrees of
APA, Harvard, Vancouver, ISO, and other styles
17

Liu, Hong Fu, Yu Zhang, Shao Fei Chen, and Jing Chen. "Autonomous Vehicle Trajectory Planning under Uncertainty Using Stochastic Collocation." Advanced Materials Research 580 (October 2012): 175–79. http://dx.doi.org/10.4028/www.scientific.net/amr.580.175.

Full text
Abstract:
We propose a framework based on stochastic collocation to solve autonomous vehicle optimal trajectory planning problems with probabilistic uncertainty. We model uncertainty from the location and size of obstacles. We develop stochastic pseudospectral methods to solve the minimum expectation cost of differential equation, which meets path, control, and boundary constraints. Results are shown on two examples of autonomous vehicle trajectory planning under uncertainty, which illustrated the feasibility and applicability of our method.
APA, Harvard, Vancouver, ISO, and other styles
18

Cheng, Lizheng. "Convergence Analysis of Stochastic Collocation Methods for Maxwell Equations with Random Inputs." Numerical Mathematics: Theory, Methods and Applications 12, no. 3 (2019): 824–44. http://dx.doi.org/10.4208/nmtma.oa-2018-0023.

Full text
APA, Harvard, Vancouver, ISO, and other styles
19

Chantasiriwan, Somchart. "Collocation methods based on radial basis functions for solving stochastic Poisson problems." Communications in Numerical Methods in Engineering 23, no. 3 (2006): 169–78. http://dx.doi.org/10.1002/cnm.888.

Full text
APA, Harvard, Vancouver, ISO, and other styles
20

Galindo, D., P. Jantsch, C. G. Webster, and G. Zhang. "Accelerating Stochastic Collocation Methods for Partial Differential Equations with Random Input Data." SIAM/ASA Journal on Uncertainty Quantification 4, no. 1 (2016): 1111–37. http://dx.doi.org/10.1137/15m1019568.

Full text
APA, Harvard, Vancouver, ISO, and other styles
21

Makroglou, Athena. "Collocation methods for stochastic Volterra integro-differential equations with random forcing functions." Mathematics and Computers in Simulation 34, no. 5 (1992): 459–66. http://dx.doi.org/10.1016/0378-4754(92)90077-t.

Full text
APA, Harvard, Vancouver, ISO, and other styles
22

Guo, Ling. "Stochastic Collocation Methods via Minimisation of the Transformed L1-Penalty." East Asian Journal on Applied Mathematics 8, no. 3 (2018): 566–85. http://dx.doi.org/10.4208/eajam.060518.130618.

Full text
APA, Harvard, Vancouver, ISO, and other styles
23

Jakeman, John Davis, and Stephen Gwyn Roberts. "Stochastic galerkin and collocation methods for quantifying uncertainty in differential equations: a review." ANZIAM Journal 50 (February 24, 2009): 815. http://dx.doi.org/10.21914/anziamj.v50i0.1410.

Full text
APA, Harvard, Vancouver, ISO, and other styles
24

Fang, Jichun Li and Zhiwei. "Analysis and Application of Stochastic Collocation Methods for Maxwell’s Equations with Random Inputs." Advances in Applied Mathematics and Mechanics 10, no. 6 (2018): 1305–26. http://dx.doi.org/10.4208/aamm.oa-2018-0101.

Full text
APA, Harvard, Vancouver, ISO, and other styles
25

D'Elia, M., H. C. Edwards, J. Hu, E. Phipps, and S. Rajamanickam. "Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems." SIAM/ASA Journal on Uncertainty Quantification 6, no. 1 (2018): 87–117. http://dx.doi.org/10.1137/16m1066324.

Full text
APA, Harvard, Vancouver, ISO, and other styles
26

Lee, Hyung-Chun, and Yun Nam. "Distributed Control of the Stochastic Burgers Equation with Random Input Data." East Asian Journal on Applied Mathematics 6, no. 1 (2016): 89–108. http://dx.doi.org/10.4208/eajam.180615.080116a.

Full text
Abstract:
AbstractWe discuss a control problem involving a stochastic Burgers equation with a random diffusion coefficient. Numerical schemes are developed, involving the finite element method for the spatial discretisation and the sparse grid stochastic collocation method in the random parameter space. We also use these schemes to compute closed-loop suboptimal state feedback control. Several numerical experiments are performed, to demonstrate the efficiency and plausibility of our approximation methods for the stochastic Burgers equation and the related control problem.
APA, Harvard, Vancouver, ISO, and other styles
27

Xia, Yan Hua. "A Stochastic Finite Element Heterogeneous Multiscale Method for Seepage Field in Heterogeneous Ground." Advanced Materials Research 594-597 (November 2012): 2545–51. http://dx.doi.org/10.4028/www.scientific.net/amr.594-597.2545.

Full text
Abstract:
The finite element heterogeneous multiscale method (FEHM) combined with stochastic collocation method (SCM) called SHMFE is applied to studying the seepage field of naturally heterogeneous multiscale subsurface formations. Kinds of stochastic finite element (SFEM) are mainly computational techniques for the class of problems. But those methods do not report the multiscale nature of the properties of subsurface formations. When the random permeability field is heterogeneous in fine scale comparing to study domain, the simulation by the classic SFEM is not a trivial task. The SHMFE can efficient
APA, Harvard, Vancouver, ISO, and other styles
28

Gunzburger, Max D., Clayton G. Webster, and Guannan Zhang. "Stochastic finite element methods for partial differential equations with random input data." Acta Numerica 23 (May 2014): 521–650. http://dx.doi.org/10.1017/s0962492914000075.

Full text
Abstract:
The quantification of probabilistic uncertainties in the outputs of physical, biological, and social systems governed by partial differential equations with random inputs require, in practice, the discretization of those equations. Stochastic finite element methods refer to an extensive class of algorithms for the approximate solution of partial differential equations having random input data, for which spatial discretization is effected by a finite element method. Fully discrete approximations require further discretization with respect to solution dependences on the random variables. For thi
APA, Harvard, Vancouver, ISO, and other styles
29

Huang, Zhizhang Wu &. Zhongyi. "Convergence Analysis on Stochastic Collocation Methods for the Linear Schrodinger Equation with Random Inputs." Advances in Applied Mathematics and Mechanics 12, no. 1 (2020): 30–56. http://dx.doi.org/10.4208/aamm.oa-2019-0008.

Full text
APA, Harvard, Vancouver, ISO, and other styles
30

Lalléchère, S., B. Jannet, P. Bonnet, and F. Paladian. "Sensitivity analysis to compute advanced stochastic problems in uncertain and complex electromagnetic environments." Advanced Electromagnetics 1, no. 3 (2012): 13. http://dx.doi.org/10.7716/aem.v1i3.43.

Full text
Abstract:
This paper deals with the advanced integration of uncertainties in electromagnetic interferences (EMI) and electromagnetic compatibility (EMC) problems. In this context, the Monte Carlo formalism may provide a reliable reference to proceed to statistical assessments. After all, other less expensive and efficient techniques have been implemented more recently (the unscented transform and stochastic collocation methods for instance) and will be illustrated through uncertain EMC problems. Finally, we will present how the use of sensitivity analysis techniques may offer an efficient complement to ro
APA, Harvard, Vancouver, ISO, and other styles
31

Aldosary, Muhannad, Jinsheng Wang, and Chenfeng Li. "Structural reliability and stochastic finite element methods." Engineering Computations 35, no. 6 (2018): 2165–214. http://dx.doi.org/10.1108/ec-04-2018-0157.

Full text
Abstract:
Purpose This paper aims to provide a comprehensive review of uncertainty quantification methods supported by evidence-based comparison studies. Uncertainties are widely encountered in engineering practice, arising from such diverse sources as heterogeneity of materials, variability in measurement, lack of data and ambiguity in knowledge. Academia and industries have long been researching for uncertainty quantification (UQ) methods to quantitatively account for the effects of various input uncertainties on the system response. Despite the rich literature of relevant research, UQ is not an easy
APA, Harvard, Vancouver, ISO, and other styles
32

Zhou, Tao Tang and Tao. "Convergence Analysis for Stochastic Collocation Methods to Scalar Hyperbolic Equations with a Random Wave Speed." Communications in Computational Physics 8, no. 1 (2010): 226–48. http://dx.doi.org/10.4208/cicp.060109.130110a.

Full text
APA, Harvard, Vancouver, ISO, and other styles
33

Rosseel, Eveline. "Nonlinear Stochastic Galerkin and Collocation Methods: Application to a Ferromagnetic Cylinder Rotating at High Speed." Communications in Computational Physics 8, no. 5 (2010): 947–75. http://dx.doi.org/10.4208/cicp.220509.200110a.

Full text
APA, Harvard, Vancouver, ISO, and other styles
34

Li, Dian-Qing, Shui-Hua Jiang, Yong-Gang Cheng, and Chuang-Bing Zhou. "A comparative study of three collocation point methods for odd order stochastic response surface method." Structural Engineering and Mechanics 45, no. 5 (2013): 595–611. http://dx.doi.org/10.12989/sem.2013.45.5.595.

Full text
APA, Harvard, Vancouver, ISO, and other styles
35

Khoromskij, B. N., and I. Oseledets. "Quantics-TT Collocation Approximation of Parameter-Dependent and Stochastic Elliptic PDEs." Computational Methods in Applied Mathematics 10, no. 4 (2010): 376–94. http://dx.doi.org/10.2478/cmam-2010-0023.

Full text
Abstract:
Abstract We investigate the convergence rate of the quantics-TT (QTT) stochas- tic collocation tensor approximations to solutions of multiparametric elliptic PDEs and construct efficient iterative methods for solving arising high-dimensional parameter- dependent algebraic systems of equations. Such PDEs arise, for example, in the para- metric, deterministic reformulation of elliptic PDEs with random field inputs, based, for example, on the M-term truncated Karhunen-Loève expansion. We consider both the case of additive and log-additive dependence on the multivariate parameter. The local-global
APA, Harvard, Vancouver, ISO, and other styles
36

Zhang, Zhongqiang, Michael V. Tretyakov, Boris Rozovskii, and George E. Karniadakis. "Wiener Chaos Versus Stochastic Collocation Methods for Linear Advection-Diffusion-Reaction Equations with Multiplicative White Noise." SIAM Journal on Numerical Analysis 53, no. 1 (2015): 153–83. http://dx.doi.org/10.1137/130932156.

Full text
APA, Harvard, Vancouver, ISO, and other styles
37

Swenson, Darrell J., Sarah E. Geneser, Jeroen G. Stinstra, Robert M. Kirby, and Rob S. MacLeod. "Cardiac Position Sensitivity Study in the Electrocardiographic Forward Problem Using Stochastic Collocation and Boundary Element Methods." Annals of Biomedical Engineering 39, no. 12 (2011): 2900–2910. http://dx.doi.org/10.1007/s10439-011-0391-5.

Full text
APA, Harvard, Vancouver, ISO, and other styles
38

Zhang, Dawei, Peijuan Xu, and Daniele Bigoni. "Application and Comparison of Uncertainty Quantification Methods for Railway Vehicle Dynamics with Random Mechanical Parameters." Mechanics 25, no. 6 (2019): 455–62. http://dx.doi.org/10.5755/j01.mech.25.6.23278.

Full text
Abstract:
This paper aims to investigate uncertainties in railway vehicle suspension components and the implement of uncertainty quantification methods in railway vehicle dynamics. The sampling-based method represented by Latin Hypercube Sampling (LHS) and generalized polynomial chaos approaches including the stochastic Galerkin and Collocation methods (SGM and SCM) are employed to analyze the propagation of uncertainties from the parameters input in a vehicle-track mathematical model to the results of running dynamics. In order to illustrate the performance qualities of SGM, SCM and LHS, a stochastic w
APA, Harvard, Vancouver, ISO, and other styles
39

Silly-Carette, J., D. Lautru, M. F. Wong, A. Gati, J. Wiart, and V. Fouad Hanna. "Variability on the Propagation of a Plane Wave Using Stochastic Collocation Methods in a Bio Electromagnetic Application." IEEE Microwave and Wireless Components Letters 19, no. 4 (2009): 185–87. http://dx.doi.org/10.1109/lmwc.2009.2015481.

Full text
APA, Harvard, Vancouver, ISO, and other styles
40

Beck, Joakim, Ben Mansour Dia, Luis Espath, and Raúl Tempone. "Multilevel double loop Monte Carlo and stochastic collocation methods with importance sampling for Bayesian optimal experimental design." International Journal for Numerical Methods in Engineering 121, no. 15 (2020): 3482–503. http://dx.doi.org/10.1002/nme.6367.

Full text
APA, Harvard, Vancouver, ISO, and other styles
41

Mathelin, L., and K. A. Gallivan. "A Compressed Sensing Approach for Partial Differential Equations with Random Input Data." Communications in Computational Physics 12, no. 4 (2012): 919–54. http://dx.doi.org/10.4208/cicp.151110.090911a.

Full text
Abstract:
AbstractIn this paper, a novel approach for quantifying the parametric uncertainty associated with a stochastic problem output is presented. As with Monte-Carlo and stochastic collocation methods, only point-wise evaluations of the stochastic output response surface are required allowing the use of legacy deterministic codes and precluding the need for any dedicated stochastic code to solve the uncertain problem of interest. The new approach differs from these standard methods in that it is based on ideas directly linked to the recently developed compressed sensing theory. The technique allows
APA, Harvard, Vancouver, ISO, and other styles
42

SEPAHVAND, K., S. MARBURG, and H. J. HARDTKE. "UNCERTAINTY QUANTIFICATION IN STOCHASTIC SYSTEMS USING POLYNOMIAL CHAOS EXPANSION." International Journal of Applied Mechanics 02, no. 02 (2010): 305–53. http://dx.doi.org/10.1142/s1758825110000524.

Full text
Abstract:
In recent years, extensive research has been reported about a method which is called the generalized polynomial chaos expansion. In contrast to the sampling methods, e.g., Monte Carlo simulations, polynomial chaos expansion is a nonsampling method which represents the uncertain quantities as an expansion including the decomposition of deterministic coefficients and random orthogonal bases. The generalized polynomial chaos expansion uses more orthogonal polynomials as the expansion bases in various random spaces which are not necessarily Gaussian. A general review of uncertainty quantification
APA, Harvard, Vancouver, ISO, and other styles
43

Braun, Mathias, Olivier Piller, Jochen Deuerlein, Iraj Mortazavi, and Angelo Iollo. "Uncertainty quantification of water age in water supply systems by use of spectral propagation." Journal of Hydroinformatics 22, no. 1 (2019): 111–20. http://dx.doi.org/10.2166/hydro.2019.017.

Full text
Abstract:
Abstract Water distribution networks are critical infrastructures that should ensure the reliable supply of high quality potable water to its users. Numerical models of these networks are generally governed by many parameters for which the exact value is not known. This may be due to a lack of precise knowledge like for consumer demand or due to a lack of accessibility as for the pipe roughness. For network managers, the effect of these uncertainties on the network state is important information that supports them in the decision-making process. This effect is generally evaluated by propagatin
APA, Harvard, Vancouver, ISO, and other styles
44

Hakula, Harri, and Mikael Laaksonen. "Frequency Response Analysis of Perforated Shells with Uncertain Materials and Damage." Applied Sciences 9, no. 24 (2019): 5299. http://dx.doi.org/10.3390/app9245299.

Full text
Abstract:
In this paper, we give an overview of the issues one must consider when designing methods for vibration based health monitoring systems for perforated thin shells especially in relation to frequency response analysis. In particular, we allow either the material parameters or the structure or both to be random. The numerical experiments are computed using the standard high order finite element method with stochastic collocation for the cases with random material and Monte Carlo for those with damaged or random structures. The results display a wide range of responses over the experimental confi
APA, Harvard, Vancouver, ISO, and other styles
45

Dũng, Dinh. "Sparse-grid polynomial interpolation approximation and integration for parametric and stochastic elliptic PDEs with lognormal inputs." ESAIM: Mathematical Modelling and Numerical Analysis 55, no. 3 (2021): 1163–98. http://dx.doi.org/10.1051/m2an/2021017.

Full text
Abstract:
By combining a certain approximation property in the spatial domain, and weighted 𝓁2-summability of the Hermite polynomial expansion coefficients in the parametric domain obtained in Bachmayr et al. [ESAIM: M2AN 51 (2017) 341–363] and Bachmayr et al. [SIAM J. Numer. Anal. 55 (2017) 2151–2186], we investigate linear non-adaptive methods of fully discrete polynomial interpolation approximation as well as fully discrete weighted quadrature methods of integration for parametric and stochastic elliptic PDEs with lognormal inputs. We construct such methods and prove convergence rates of the approxim
APA, Harvard, Vancouver, ISO, and other styles
46

Morales, Ociel, Francisco Periago, and José A. Vallejo. "Robust Optimal Design of Quantum Electronic Devices." Mathematical Problems in Engineering 2018 (2018): 1–10. http://dx.doi.org/10.1155/2018/3095257.

Full text
Abstract:
We consider the optimal design of a sequence of quantum barriers, in order to manufacture an electronic device at the nanoscale such that the dependence of its transmission coefficient on the bias voltage is linear. The technique presented here is easily adaptable to other response characteristics. There are two distinguishing features of our approach. First, the transmission coefficient is determined using a semiclassical approximation, so we can explicitly compute the gradient of the objective function. Second, in contrast with earlier treatments, manufacturing uncertainties are incorporated
APA, Harvard, Vancouver, ISO, and other styles
47

Alkhatib, A. M., and P. R. King. "The Use of the Least-Squares Probabilistic-Collocation Method in Decision Making in the Presence of Uncertainty for Chemical-Enhanced-Oil-Recovery Processes." SPE Journal 20, no. 04 (2015): 747–66. http://dx.doi.org/10.2118/170587-pa.

Full text
Abstract:
Summary The least-squares Monte Carlo method (LSM) is a decision-evaluation method that can capture the value of flexibility of a process. This method was shown to provide us with some insight into the effect of uncertainty on decision making and to help us capture the upside potential or mitigate the downside effects for a chemical enhanced-oil-recovery (EOR) process. The method is a stochastic approximate dynamic programming approach to decision making. It is modeled after a forward simulation coupled with a recursive algorithm, which produces the near-optimal policy. It relies on Monte Carl
APA, Harvard, Vancouver, ISO, and other styles
48

Rathi, Amit Kumar, P. V. Sudhi Sharma, and Arunasis Chakraborty. "Sequential Stochastic Response Surface Method Using Moving Least Squares-Based Sparse Grid Scheme for Efficient Reliability Analysis." International Journal of Computational Methods 16, no. 05 (2019): 1840017. http://dx.doi.org/10.1142/s0219876218400170.

Full text
Abstract:
The present work demonstrates an efficient method for reliability analysis using sequential development of the stochastic response surface. Here, orthogonal Hermite polynomials are used whose unknown coefficients are evaluated using moving least square technique. To do so, collocation points in the conventional stochastic response surface method (SRSM) are replaced by the sparse grid scheme so as to reduce the number of function evaluations. Moreover, the domain is populated sequentially by the sparse grid based on the outcome of the optimization to find out the most probable failure point. He
APA, Harvard, Vancouver, ISO, and other styles
49

Yousefi, Hassan, Seyed Shahram Ghorashi, and Timon Rabczuk. "Directly Simulation of Second Order Hyperbolic Systems in Second Order Form via the Regularization Concept." Communications in Computational Physics 20, no. 1 (2016): 86–135. http://dx.doi.org/10.4208/cicp.101214.011015a.

Full text
Abstract:
AbstractWe present an efficient and robust method for stress wave propagation problems (second order hyperbolic systems) having discontinuities directly in their second order form. Due to the numerical dispersion around discontinuities and lack of the inherent dissipation in hyperbolic systems, proper simulation of such problems are challenging. The proposed idea is to denoise spurious oscillations by a post-processing stage from solutions obtained from higher-order grid-based methods (e.g., high-order collocation or finite-difference schemes). The denoising is done so that the solutions remai
APA, Harvard, Vancouver, ISO, and other styles
50

Rehme, Michael, Stephen Roberts, and Dirk Pflüger. "Uncertainty quantification for the Hokkaido Nansei-Oki tsunami using B-splines on adaptive sparse grids." ANZIAM Journal 62 (June 29, 2021): C30—C44. http://dx.doi.org/10.21914/anziamj.v62.16121.

Full text
Abstract:
Modeling uncertainties in the input parameters of computer simulations is an established way to account for inevitably limited knowledge. To overcome long run-times and high demand for computational resources, a surrogate model can replace the original simulation. We use spatially adaptive sparse grids for the creation of this surrogate model. Sparse grids are a discretization scheme designed to mitigate the curse of dimensionality, and spatial adaptivity further decreases the necessary number of expensive simulations. We combine this with B-spline basis functions which provide gradients and a
APA, Harvard, Vancouver, ISO, and other styles
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography