Filters








169 Hits in 9.0 sec

A stochastic mixed finite element heterogeneous multiscale method for flow in porous media

Xiang Ma, Nicholas Zabaras
2011 Journal of Computational Physics  
This results in a set of low stochastic dimensional subproblems which are efficiently solved using the adaptive sparse grid collocation method (ASGC).  ...  Starting from a specified covariance function, the stochastic log-permeability is discretized in the stochastic space using a truncated Karhunen-Loève expansion with several random variables.  ...  The computing for this research was supported by the NSF through TeraGrid resources provided by NCSA under grant number TG-DMS090007 .  ... 
doi:10.1016/j.jcp.2011.03.001 fatcat:apqjkk54e5etfnj6rq7uvdsrqe

A Stochastic Mortar Mixed Finite Element Method for Flow in Porous Media with Multiple Rock Types

Benjamin Ganis, Ivan Yotov, Ming Zhong
2011 SIAM Journal on Scientific Computing  
The approximation uses stochastic collocation on either a tensor product or a sparse grid, coupled with a domain decomposition algorithm known as the multiscale mortar mixed finite element method.  ...  The latter method requires solving a coarse scale mortar interface problem via an iterative procedure.  ...  The authors would like to thank the Institute for Computational Engineering and Sciences at The University of Texas at Austin for the use of their computing resources.  ... 
doi:10.1137/100790689 fatcat:s72jqo2a3nfnrgztzzw2ziay4m

Kernel-based stochastic collocation for the random two-phase Navier-Stokes equations [article]

Michael Griebel, Christian Rieger, Peter Zaspel
2019 arXiv   pre-print
In this work, we apply stochastic collocation methods with radial kernel basis functions for an uncertainty quantification of the random incompressible two-phase Navier-Stokes equations.  ...  We are able to empirically show that the resulting kernel-based stochastic collocation is highly competitive in this setting and even outperforms some other standard methods.  ...  Furthermore, the errors of the RBF-based stochastic collocation method are always below the results of the sparse grid stochastic collocation method.  ... 
arXiv:1810.11270v3 fatcat:ghrjpvczwrc3jn3yyhizcvytby

Uncertainty Quantification and High Performance Computing (Dagstuhl Seminar 16372)

Vincent Heuveline, Michael Schick, Clayton Webster, Peter Zaspel, Marc Herbstritt
2017 Dagstuhl Reports  
However, there is a growing demand in methods to appropriately cope with uncertainties in those input parameters. This is addressed in the developing research field of uncertainty quantification.  ...  Simulations for a fixed, deterministic set of parameters are current state of the art.  ...  Special thanks go to the Schloss Dagstuhl team for its extremely friendly support during the preparation phase and for the warm welcome at Schloss Dagstuhl.  ... 
doi:10.4230/dagrep.6.9.59 dblp:journals/dagstuhl-reports/HeuvelineSWZ16 fatcat:y2k3hrzvvjct7bi7jci4rozx5i

Stochastic Modeling and Regularity of the Nonlinear Elliptic curl--curl Equation

Ulrich Römer, Sebastian Schöps, Thomas Weiland
2016 SIAM/ASA Journal on Uncertainty Quantification  
It is shown that, unlike to linear and several nonlinear elliptic problems, the solution is not analytic with respect to the random variables and an algebraic decay of the stochastic error is obtained.  ...  A stochastic non-linear curl-curl formulation is introduced and numerically approximated by a finite element and collocation method in the deterministic and stochastic variable, respectively.  ...  The authors would like to thank Stéphane Clénet for providing measurement data of B-H curves and Herbert De Gersem for valuable comments and discussions on the subject.  ... 
doi:10.1137/15m1026535 fatcat:cffx46ovn5hgvbs2xt2pv4hwky

A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty

D. P. Kouri, M. Heinkenschloss, D. Ridzal, B. G. van Bloemen Waanders
2013 SIAM Journal on Scientific Computing  
This paper introduces an efficient algorithm for solving such problems based on a combination of adaptive sparse-grid collocation for the discretization of the PDE in the stochastic space and a trust-region  ...  Numerical methods for solving PDEs with random data can be classified as projection-based methods and sample-based methods.  ...  Convergence results for sparse-grid stochastic collocation methods for PDEs with random input data can be found, for example, in [3, 45, 46, 47] .  ... 
doi:10.1137/120892362 fatcat:tztubukqu5aurcr5tyhwgpjltq

Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario

Markus Köppel, Fabian Franzelin, Ilja Kröker, Sergey Oladyshkin, Gabriele Santin, Dominik Wittwar, Andrea Barth, Bernard Haasdonk, Wolfgang Nowak, Dirk Pflüger, Christian Rohde
2018 Computational Geosciences  
A variety of methods is available to quantify uncertainties arising with\-in the modeling of flow and transport in carbon dioxide storage, but there is a lack of thorough comparisons.  ...  We consider recent versions of the following non-intrusive and intrusive uncertainty quantification methods: arbitary polynomial chaos, spatially adaptive sparse grids, kernel-based greedy interpolation  ...  Acknowledgements The authors would like to thank the German Research Foundation (DFG) for financial support of the project within the Cluster of Excellence in Simulation Technology (EXC 310/2) at the University  ... 
doi:10.1007/s10596-018-9785-x fatcat:tos3hfkpafdhde7x4ldiohws4q

A stochastic collocation method for the second order wave equation with a discontinuous random speed

Mohammad Motamed, Fabio Nobile, Raúl Tempone
2012 Numerische Mathematik  
In this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions.  ...  We provide a rigorous convergence analysis and demonstrate different types of convergence of the probability error with respect to the number of collocation points for full and sparse tensor product spaces  ...  collocation algorithm.  ... 
doi:10.1007/s00211-012-0493-5 fatcat:nn7ym3ecdzh3vlr5zkz7mzvuue

Algorithms for Propagating Uncertainty Across Heterogeneous Domains

H. Cho, X. Yang, D. Venturi, G. E. Karniadakis
2015 SIAM Journal on Scientific Computing  
problems with random reaction rates.  ...  The effectiveness of these new algorithms is demonstrated in numerical examples involving elliptic problems with random diffusion coefficients, stochastically advected scalar fields, and nonlinear advection-reaction  ...  Jared Knap of ARL for stimulating discussions and useful suggestions. This work was supported by ARO grant W911NF-14-1-0425 and ARL grant W911NF-12-2-0023.  ... 
doi:10.1137/140992060 fatcat:2lowqeho7rezxkojx2r6ls3yae

Adaptive ANOVA decomposition of stochastic incompressible and compressible flows

Xiu Yang, Minseok Choi, Guang Lin, George Em Karniadakis
2012 Journal of Computational Physics  
When applying the ANOVA method to stochastic simulation, we denote the highest dimension for the component functions we use in (2.2) with m and approximate f(x) with  ...  It was also shown in [21, 22] that ANOVA decomposition with m = 2 has a good accuracy if the anchor point is chosen as the mean with respect to the probability density function considered.  ...  In Section 3 we formulate the stochastic convection problem, present computational results, and compare the adaptive ANOVA method with the sparse grid and MC methods.  ... 
doi:10.1016/j.jcp.2011.10.028 fatcat:s2awdoto5rh7fpuajaogte6xbe

Stochastic collocation and mixed finite elements for flow in porous media

Benjamin Ganis, Hector Klie, Mary F. Wheeler, Tim Wildey, Ivan Yotov, Dongxiao Zhang
2008 Computer Methods in Applied Mechanics and Engineering  
The governing equations are based on Darcy's law with stochastic permeability.  ...  Mixed finite element approximations are used in the spatial domain and collocation at the zeros of tensor product Hermite polynomials is used in the stochastic dimensions.  ...  Moment/perturbation and finite element stochastic methods fall into the category of non-sampling methods. These methods are suitable for systems with relatively small random inputs and outputs.  ... 
doi:10.1016/j.cma.2008.03.025 fatcat:d7lbjr6ianbwldsmehrdf2lbjq

Uncertainty quantification in Discrete Fracture Network models: Stochastic fracture transmissivity

S. Berrone, C. Canuto, S. Pieraccini, S. Scialò
2015 Computers and Mathematics with Applications  
with Monte Carlo results show a clear gain in efficiency for the proposed method.  ...  The approximate computation of quantities of interest, such as mean value and variance for outgoing fluxes, is based on a stochastic collocation approach that uses suitable sparse grids in the range of  ...  Sparse grids Clever strategies for selecting the set of collocation points in Y N are fundamental for the efficiency, and even the feasibility, of a stochastic collocation method.  ... 
doi:10.1016/j.camwa.2015.05.013 fatcat:ji6p6v7zqffove6s4iussqetq4

Polynomial Chaos Expansion of Random Coefficients and the Solution of Stochastic Partial Differential Equations in the Tensor Train Format

Sergey Dolgov, Boris N. Khoromskij, Alexander Litvinenko, Hermann G. Matthies
2015 SIAM/ASA Journal on Uncertainty Quantification  
Other classical techniques to cope with high-dimensional problems are sparse grids [28, 10, 49] and (quasi) Monte Carlo methods [26, 62, 39] .  ...  We apply the tensor train (TT) decomposition to construct the tensor product polynomial chaos expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with the stochastic Galerkin  ...  We would like to thank Elmar Zander for his assistance in the usage of the stochastic Galerkin library sglib.  ... 
doi:10.1137/140972536 fatcat:kqguoefb6rdghmlu63oboiqt3u

Finite Volume Simulation Framework for Die Casting with Uncertainty Quantification [article]

Shantanu Shahane, Narayana Aluru, Placid Ferreira, Shiv G Kapoor, Surya Pratap Vanka
2018 arXiv   pre-print
The algebraic multigrid method, blended with a Krylov subspace solver is used to accelerate convergence.  ...  State of the art uncertainty quantification technique is included in the framework to incorporate the effects of stochastic variations in the input parameters.  ...  Implementing multiple region method for a practical complex geometry with irregular interfaces is quite difficult and computationally expensive.  ... 
arXiv:1810.08572v1 fatcat:dbx6eukoirhszneiw2piedg7du

Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network

Dongbin Xiu, Spencer J. Sherwin
2007 Journal of Computational Physics  
We demonstrate how the application of a high-order stochastic collocation method based on the generalized polynomial chaos expansion, combined with a discontinuous Galerkin spectral/hp element discretisation  ...  The uncertain parameters are modelled as random variables and the governing equations for the arterial network therefore become stochastic.  ...  Jordi Alastruey for his helpful comments on the paper and providing the data for the 37 arterial network.  ... 
doi:10.1016/j.jcp.2007.05.020 fatcat:vyetnkukebdalnk3xt4nv2qieq
« Previous Showing results 1 — 15 out of 169 results