Filters








5,485 Hits in 8.2 sec

Combination technique based k-th moment analysis of elliptic problems with random diffusion

Helmut Harbrecht, Michael Peters, Markus Siebenmorgen
2013 Journal of Computational Physics  
We consider the efficient deterministic solution of elliptic boundary value problems with random diffusion matrix.  ...  Assuming random perturbations with known k moments, we derive, to leading order in the random perturbation's amplitude, deterministic equations for k moments of the random solution.  ...  Section 2 is concerned with the modelling of elliptic boundary value problems with random diffusion.  ... 
doi:10.1016/j.jcp.2013.06.013 fatcat:hwjy25xocjhr5h5dp32n4gkzsa

A scalable framework for the solution of stochastic inverse problems using a sparse grid collocation approach

N. Zabaras, B. Ganapathysubramanian
2008 Journal of Computational Physics  
Various illustrative examples with multiple sources of uncertainty including inverse heat conduction problems in random heterogeneous media are provided to showcase the developed framework. Fig. 15.  ...  A novel stochastic sensitivity method is introduced based on multiple solutions to deterministic sensitivity problems.  ...  The computing was conducted using the resources of the Cornell Center for Advanced Computing.  ... 
doi:10.1016/j.jcp.2008.01.019 fatcat:gxzt3w267re3hgr3gd3yhlskui

A least-squares approximation of partial differential equations with high-dimensional random inputs

Alireza Doostan, Gianluca Iaccarino
2009 Journal of Computational Physics  
For the case of an elliptic SPDE, an a priori error analysis of the algorithm is derived.  ...  Stochastic collocation schemes, [27, 1, 20, 19 ] based on isotropic and anisotropic sparse grids reduce the problem of curse of dimensionality normally associated with conventional tensor-product schemes  ...  Acknowledgment This material is based upon work supported by the Department of Energy, National Nuclear Security Administration under Award Number NA28614.  ... 
doi:10.1016/j.jcp.2009.03.006 fatcat:tqkmookv3jbcfgjizwb7w47siy

A priori error analysis of a numerical stochastic homogenization method [article]

Julian Fischer, Dietmar Gallistl, Daniel Peterseim
2020 arXiv   pre-print
This paper provides an a priori error analysis of a localized orthogonal decomposition method (LOD) for the numerical stochastic homogenization of a model random diffusion problem.  ...  If the uniformly elliptic and bounded random coefficient field of the model problem is stationary and satisfies a quantitative decorrelation assumption in form of the spectral gap inequality, then the  ...  , random fields with moment bounds on E[|A| p ] + E[|A −1 | p ] for p ≫ 1 by using an adaptation of our strategy.  ... 
arXiv:1912.11646v2 fatcat:pyhraqpowndszjjhtp6xdarkoq

Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos

Dongbin Xiu, George Em Karniadakis
2002 Computer Methods in Applied Mechanics and Engineering  
In particular, we focus on the solution of the Poisson equation with random diffusivity, forcing and boundary conditions.  ...  The resulting set of deterministic equations for each random mode is solved iteratively by a block Gauss-Seidel iteration technique.  ...  Computations were performed at Brown's TCASCV and NCSA's (University of Illinois) facilities.  ... 
doi:10.1016/s0045-7825(02)00421-8 fatcat:zi3fo5fejbb2to67vqdehycg3q

Algorithms for Propagating Uncertainty Across Heterogeneous Domains

H. Cho, X. Yang, D. Venturi, G. E. Karniadakis
2015 SIAM Journal on Scientific Computing  
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  ...  problems with random reaction rates.  ...  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

Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics

Thomas Y. Hou, Wuan Luo, Boris Rozovskii, Hao-Min Zhou
2006 Journal of Computational Physics  
Simple formulas for statistical moments of the stochastic solution are presented. These formulas only involve the solutions of the propagator.  ...  The main advantage of the Wiener Chaos approach is that it allows for the separation of random and deterministic effects in a rigorous and effective manner.  ...  To address this problem, we have implemented a WCE based technique for computing moments of all orders.  ... 
doi:10.1016/j.jcp.2006.01.008 fatcat:iu7j54e7gbgkvdaiihpz5xgu5m

Multi-fidelity stochastic collocation method for computation of statistical moments

Xueyu Zhu, Erin M. Linebarger, Dongbin Xiu
2017 Journal of Computational Physics  
We present an efficient numerical algorithm to approximate the statistical moments of stochastic problems, in the presence of models with different fidelities.  ...  By combining the efficiency of low-fidelity models and the accuracy of high-fidelity models, our method exhibits fast convergence with a limited number of high-fidelity simulations.  ...  One dimensional stochastic elliptic equation. We now consider an elliptic equation with random diffusivity, a standard benchmark problem in stochastic computing.  ... 
doi:10.1016/j.jcp.2017.04.022 fatcat:l645p6q7wvc6feigxyxadf726e

Combination Technique Based Second Moment Analysis for Elliptic PDEs on Random Domains [chapter]

Helmut Harbrecht, Michael Peters
2016 Lecture Notes in Computational Science and Engineering  
In this article, we propose the sparse grid combination technique for the second moment analysis of elliptic partial differential equations on random domains.  ...  We make the ansatz Combination technique based second moment analysis In complete analogy to the non-tensor product case, we obtain the solution scheme (1) Solve ( This lemma tells us that, given Cov[δ  ...  This linearization technique has already been applied to random diffusion coefficients or even to elliptic equations on random domains in [18, 22, 23] .  ... 
doi:10.1007/978-3-319-28262-6_3 fatcat:qg4zrktrmfchxfqnzbm4efnm3y

RBF-based meshless methods for 2D elastostatic problems

Vitor Manuel Azevedo Leitão
2004 Engineering analysis with boundary elements  
The work presented here concerns the use of radial basis functions (RBFs) for the analysis of two dimensional elastostatic problems.  ...  The basic characteristic of the formulation is the definition of a global approximation for the variables of interest in each problem (the deflection for the plate bending problem and the stress function  ...  Acknowledgements The author is a member of ICIST (Instituto de Engenharia de Estruturas, Território e Construçáo do Instituto Superior Técnico) and acknowledges the financial support of FCT (Financiamento  ... 
doi:10.1016/j.enganabound.2003.06.003 fatcat:isgynzorirfuxeupo5j6ur5u4e

An asymptotically compatible probabilistic collocation method for randomly heterogeneous nonlocal problems [article]

Yiming Fan, Xiaochuan Tian, Xiu Yang, Xingjie Li, Clayton Webster, Yue Yu
2021 arXiv   pre-print
In particular, the random diffusivity coefficient is described by a finite-dimensional random variable or a truncated combination of random variables with the Karhunen-Loève decomposition, then a probabilistic  ...  On each sample, the deterministic nonlocal diffusion problem is discretized with an optimization-based meshfree quadrature rule.  ...  The results are then statistically analyzed based on all K samples to calculate leading moments of variables of interest.  ... 
arXiv:2107.01386v2 fatcat:rosrafxdmbf45g44aciibq6g2m

Transverse conductivity and longitudinal shear of elliptic fiber composite with imperfect interface

V.I. Kushch, V.S. Chernobai
2014 International Journal of Solids and Structures  
The paper addresses the problem of calculating the local fields and effective transport properties and longitudinal shear stiffness of elliptic fiber composite with imperfect interface.  ...  The developed method combines the superposition principle, the technique of complex potentials and certain new results in the theory of special functions.  ...  Our analysis employs the technique of complex potentials (e.g., Muskhelishvili, 1953) .  ... 
doi:10.1016/j.ijsolstr.2014.03.024 fatcat:wwmq4uuzljfafdzgbf5zqc5szq

Surface processing methods for point sets using finite elements

Ulrich Clarenz, Martin Rumpf, Alexandru Telea
2004 Computers & graphics  
The definition of tangent planes relies on moment-based computation with proven scaling and stability properties.  ...  Our framework efficiently and effectively brings well-known PDE-based processing techniques to the field of point-based surfaces.  ...  When combined with advanced rendering techniques such as splatting [1, 2] , point based surfaces can be superior to triangle meshes in terms of rendering quality and data storage flexibility.  ... 
doi:10.1016/j.cag.2004.08.013 fatcat:sys7rsjxi5bnjh5lynehbn2x3m

A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data

Ivo Babuška, Fabio Nobile, Raúl Tempone
2010 SIAM Review  
Anal. 42(2004)] and allows one to treat easily a wider range of situations, such as: input data that depend non-linearly on the random variables, diffusivity coefficients with unbounded second moments  ...  In this paper we propose and analyze a Stochastic-Collocation method to solve elliptic Partial Differential Equations with random coefficients and forcing terms (input data of the model).  ...  or exponential ones. • deals with no difficulty with a diffusivity coefficient a with unbounded second moment.  ... 
doi:10.1137/100786356 fatcat:fdxdhxwppvaxdkvmh7jei5e64m

Aperiodic Photonics of Elliptic Curves

Luca Dal Dal Negro, Yuyao Chen, Fabrizio Sgrignuoli
2019 Crystals  
Our theoretical analysis combines the interdisciplinary methods of point patterns spatial statistics with the rigorous Green's matrix solution of the multiple wave scattering problem for electric and magnetic  ...  environments beyond the limitations of traditional random media.  ...  Abbreviations The following abbreviations are used in this manuscript: EC Elliptic curve structure UR Uniform random structure UR e Ensemble averaged uniform random structures EC DL Elliptic curve discrete  ... 
doi:10.3390/cryst9090482 fatcat:kftf5zrmlnaqrjo3m47bbr2aji
« Previous Showing results 1 — 15 out of 5,485 results