Sign in
Author

Conference

Journal

Organization

Year

DOI
Look for results that meet for the following criteria:
since
equal to
before
between
and
Search in all fields of study
Limit my searches in the following fields of study
Agriculture Science
Arts & Humanities
Biology
Chemistry
Computer Science
Economics & Business
Engineering
Environmental Sciences
Geosciences
Material Science
Mathematics
Medicine
Physics
Social Science
Multidisciplinary
Keywords
(15)
Automatic Detection
Collocation Method
Correlation Function
Fluid Mechanics
Heterogeneous Media
High Dimensional Model Representation
High Dimensionality
Monte Carlo
Reduced Order Model
Sparse Grids
Statistical Analysis
Stochastic Model
Stochastic Partial Differential Equation
Higher Order
Input Output
Subscribe
Academic
Publications
An adaptive highdimensional stochastic model representation technique for the solution of stochastic partial differential equations
An adaptive highdimensional stochastic model representation technique for the solution of stochastic partial differential equations,10.1016/j.jcp.201
Edit
An adaptive highdimensional stochastic model representation technique for the solution of stochastic partial differential equations
(
Citations: 3
)
BibTex

RIS

RefWorks
Download
Xiang Ma
,
Nicholas Zabaras
A computational methodology is developed to address the solution of highdimensional stochastic problems. It utilizes highdimensional model representation (HDMR) technique in the stochastic space to represent the model output as a finite hierarchical correlated function expansion in terms of the stochastic inputs starting from lowerorder to higherorder component functions. HDMR is efficient at capturing the highdimensional input–output relationship such that the behavior for many physical systems can be modeled to good accuracy only by the first few lowerorder terms. An adaptive version of HDMR is also developed to automatically detect the important dimensions and construct higherorder terms using only the important dimensions. The newly developed adaptive sparse grid collocation (ASGC) method is incorporated into HDMR to solve the resulting subproblems. By integrating HDMR and ASGC, it is computationally possible to construct a lowdimensional stochastic reducedorder model of the highdimensional stochastic problem and easily perform various statistic analysis on the output. Several numerical examples involving elementary mathematical functions and
fluid mechanics
problems are considered to illustrate the proposed method. The cases examined show that the method provides accurate results for stochastic dimensionality as high as 500 even with largeinput variability. The efficiency of the proposed method is examined by comparing with
Monte Carlo
(MC) simulation.
Journal:
Journal of Computational Physics  J COMPUT PHYS
, vol. 229, no. 10, pp. 38843915, 2010
DOI:
10.1016/j.jcp.2010.01.033
Cumulative
Annual
View Publication
The following links allow you to view full publications. These links are maintained by other sources not affiliated with Microsoft Academic Search.
(
www.sciencedirect.com
)
(
www.osti.gov
)
(
adsabs.harvard.edu
)
(
mpdc.mae.cornell.edu
)
(
linkinghub.elsevier.com
)
More »
Citation Context
(1)
...The HDMR expansion is built iteratively by including only the “most significant” component functions to minimize the computational cost of building the surrogate model [
5
]...
...On the other hand, one can apply the MC method to an approximation of ( ) V x , namely its surrogate model, a compact polynomial representation of ( ) V x . In this case, the difficulty lies in obtaining an accurate but cheap to evaluate surrogate model of ( ) V x . This can be achieved using the iterative HDMR method proposed in [
5
]...
...Representation (1) can be constructed using the cutHDMR method [
5
], which expresses the component functions in terms of observable values on lines, planes, and hyperplanes (i.e...
...iD ∈ but S i ∉ u , are set to their corresponding mean values (see [4,
5
] for details)...
...[
5
]. This limits the direct application of cutHDMR in realistic largescale...
...EMC/EMI problems for large dof N . This high cost can be reduced considerably by integrating an iterative scheme to the hierarchical cutHDMR method, which automatically selects random variables that significantly contribute to () V x and iteratively includes these variables’ higherorder component functions in the cutHDMR expansion [
5
]...
...Iterative cutHDMR Construction: The iterative cutHDMR scheme [
5
] first constructs the firstorder component functions by setting 1 S = . Then, it computes...
Abdulkadir C. Yucel
,
et al.
Efficient stochastic EMC/EMI analysis using HDMRgenerated surrogate m...
References
(43)
Stochastic Finite Elements: A Spectral Approach
(
Citations: 1000
)
P. Spanos
Published in 1991.
Modeling diffusion in random heterogeneous media: Datadriven models, stochastic collocation and the variational multiscale method
(
Citations: 16
)
Baskar Ganapathysubramanian
,
Nicholas Zabaras
Journal:
Journal of Computational Physics  J COMPUT PHYS
, vol. 226, no. 1, pp. 326353, 2007
A nonlinear dimension reduction methodology for generating datadriven stochastic input models
(
Citations: 6
)
Baskar Ganapathysubramanian
,
Nicholas Zabaras
Published in 2007.
Stochastic Methods for Flow in Porous Media: Coping With Uncertainties
(
Citations: 129
)
D Zhang
Published in 2001.
An efficient, highorder perturbation approach for flow in random porous media via Karhunen–Loève and polynomial expansions
(
Citations: 68
)
Dongxiao Zhang
,
Zhiming Lu
Journal:
Journal of Computational Physics  J COMPUT PHYS
, vol. 194, no. 2, pp. 773794, 2004
Sort by:
Citations
(3)
Efficient stochastic EMC/EMI analysis using HDMRgenerated surrogate models
Abdulkadir C. Yucel
,
Hakan Bagci
,
Eric Michielssen
Conference:
General Assembly and Scientific Symposium  URSI
, 2011
Development of Closed Loop Control Schemes for Constant Speed Operation of a Thyristorized Commutatorless Series Motor Drive
(
Citations: 1
)
Kaushik Mukherjee
,
Sabyasachi SenGupta
,
T. K. Bhattacharya
,
A. K. Chattopadhyay
Conference:
International Conference on Power Electronics and Drive Systems  PEDS
, 2005
Design of a MEMSbased resonant force sensor for compliant, passive microgripping
(
Citations: 2
)
Issam Bait Bahadur
,
James Mills
,
Yu Sun
Published in 2005.