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Litvinenko, Alexander (24)

Tempone, Raul (8)Genton, Marc G. (6)Matthies, Hermann G. (6)Sun, Ying (6)View MoreDepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division (18)Applied Mathematics and Computational Science Program (7)Extreme Computing Research Center (4)Center for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ) (3)Statistics Program (3)View MoreSubjecthierarchical matrices (5)Bayesian (4)Matern covariance (3)Uncertainty Quantification (3)HLIB (2)View MoreType
Poster (24)

Year (Issue Date)2019 (1)2018 (1)2017 (4)2016 (3)2015 (9)View MoreItem AvailabilityOpen Access (24)

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Risk assessment of salt contamination of groundwater under uncertain aquifer properties

Litvinenko, Alexander; Keyes, David E.; Logashenko, Dmitry; Tempone, Raul; Wittum, Gabriel (2017-10-01) [Poster]

One of the central topics in hydrogeology and environmental science is the investigation of salinity-driven groundwater flow in heterogeneous porous media. Our goals are to model and to predict pollution of water resources.
We simulate a density driven groundwater flow with uncertain porosity and permeability. This strongly non-linear model describes the unstable transport of salt water with building ‘fingers’-shaped patterns. The computation requires
a very fine unstructured mesh and, therefore, high computational resources.
We run the highly-parallel multigrid solver, based on ug4, on supercomputer Shaheen II. A MPI-based parallelization is done in the geometrical as well as in the stochastic spaces. Every scenario is computed on 32 cores and
requires a mesh with ~8M grid points and 1500 or more time steps. 200 scenarios are computed concurrently. The total number of cores in parallel computation is 200x32=6400. The main goal of this work is to estimate propagation of uncertainties through the model, to investigate sensitivity of the solution to the input uncertain parameters. Additionally, we demonstrate how the multigrid ug4-based solver can be applied as a black-box in the uncertainty quantification framework.

Uncertainty Quantification in Numerical Aerodynamics

Litvinenko, Alexander; Matthies, Hermann G.; Liu, Dishi; Schillings, Claudia; Schulz, Volker (2017-05-16) [Poster]

We consider uncertainty quantification problem in aerodynamic simulations. We identify input uncertainties, classify them, suggest an appropriate statistical model and, finally, estimate propagation of these uncertainties into the solution (pressure, velocity and density fields as well as the lift and drag coefficients). The deterministic problem under consideration is a compressible transonic Reynolds-averaged Navier-Strokes flow around an airfoil with random/uncertain data. Input uncertainties include: uncertain angle of attack, the Mach number, random perturbations in the airfoil geometry, mesh, shock location, turbulence model and parameters of this turbulence model.
This problem requires efficient numerical/statistical methods since it is computationally expensive, especially for the uncertainties caused by random geometry variations which involve a large number of variables.
In numerical section we compares five methods, including quasi-Monte Carlo quadrature, polynomial chaos with coefficients determined by sparse quadrature and gradient-enhanced version of Kriging, radial basis functions and point collocation polynomial chaos, in their efficiency in estimating statistics of aerodynamic performance upon random perturbation to the airfoil geometry [D.Liu et al '17]. For modeling we used the TAU code, developed in DLR, Germany.

Non-linear Bayesian update of PCE coefficients

Litvinenko, Alexander; Matthies, Hermann G.; Pajonk, Oliver; Rosic, Bojana; Zander, Elmar (2013-12-22) [Poster]

Develop a non-linear approximation of Bayesian Update. This formula is applied directly to PCE coefficients.

Scalable Hierarchical Algorithms for stochastic PDEs and Uncertainty Quantification

Litvinenko, Alexander; Chavez Chavez, Gustavo Ivan; Keyes, David E.; Ltaief, Hatem; Yokota, Rio (2015-01-05) [Poster]

H-matrices and Fast Multipole (FMM) are powerful methods to approximate linear operators coming from partial differential and integral equations as well as speed up computational cost from quadratic or cubic to log-linear (O(n log n)), where n number of degrees of freedom in the discretization. The storage is reduced to the log-linear as well. This hierarchical structure is a good starting point for parallel algorithms. Parallelization on shared and distributed memory systems was pioneered by R. Kriemann, 2005. Since 2005, the area of parallel architectures and software is developing very fast. Progress in GPUs and Many-Core Systems (e.g. XeonPhi with 64 cores) motivated us to extend work started in [1,2,7,8].

Hierarchical matrix approximation of large covariance matrices

Litvinenko, Alexander; Genton, Marc G.; Sun, Ying (2015-11-30) [Poster]

We approximate large non-structured Matérn covariance matrices of size n×n in the H-matrix format with a log-linear computational cost and storage O(kn log n), where rank k ≪ n is a small integer. Applications are: spatial statistics, machine learning and image analysis, kriging and optimal design.

Hierarchical matrix approximation of large covariance matrices

Litvinenko, Alexander; Genton, Marc G.; Sun, Ying; Tempone, Raul (2015-01-05) [Poster]

We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(nlogn). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and op- timal design.

Computation of Electromagnetic Fields Scattered From Dielectric Objects of Uncertain Shapes Using MLMC Center for Uncertainty

Litvinenko, Alexander; Haji Ali, Abdul Lateef; Uysal, Ismail Enes; Ulku, Huseyin Arda; Oppelstrup, Jesper; Tempone, Raul; Bagci, Hakan (2015-01-05) [Poster]

Simulators capable of computing scattered fields from objects of uncertain shapes are highly useful in electromagnetics and photonics, where device designs are typically subject to fabrication tolerances. Knowledge of statistical variations in scattered fields is useful in ensuring error-free functioning of devices. Oftentimes such simulators use a Monte Carlo (MC) scheme to sample the random domain, where the variables parameterize the uncertainties in the geometry. At each sample, which corresponds to a realization of the geometry, a deterministic electromagnetic solver is executed to compute the scattered fields. However, to obtain accurate statistics of the scattered fields, the number of MC samples has to be large. This significantly increases the total execution time. In this work, to address this challenge, the Multilevel MC (MLMC) scheme is used together with a (deterministic) surface integral equation solver. The MLMC achieves a higher efficiency by “balancing” the statistical errors due to sampling of the random domain and the numerical errors due to discretization of the geometry at each of these samples. Error balancing results in a smaller number of samples requiring coarser discretizations. Consequently, total execution time is significantly shortened.

Kriging accelerated by orders of magnitude: combining low-rank with FFT techniques

Litvinenko, Alexander; Nowak, Wolfgang (2014-01-08) [Poster]

Kriging algorithms based on FFT, the separability of certain covariance functions and low-rank representations of covariance functions have been investigated. The current study combines these ideas, and so combines the individual speedup factors of all ideas. For separable covariance functions, the results are exact, and non-separable covariance functions can be approximated through sums of separable components. Speedup factor is 1e+8, problem sizes 1.5e+13 and 2e+15 estimation points for Kriging and spatial design.

Likelihood Approximation With Parallel Hierarchical Matrices For Large Spatial Datasets

Litvinenko, Alexander (2018-04-10) [Poster]

Use H-matrices to approximate large covariance matrices in spatial statistics

Computation of Electromagnetic Fields Scattered From Objects With Uncertain Shapes Using Multilevel Monte Carlo Method

Litvinenko, Alexander; Yucel, Abdulkadir; Bagci, Hakan; Oppelstrup, Jesper; Tempone, Raul; Michielssen, Eric (2019-02-14) [Poster]

Computational tools for characterizing electromagnetic scattering from objects with uncertain shapes are needed in various applications ranging from remote sensing at microwave frequencies to Raman spectroscopy at optical frequencies. Often, such computational tools use the Monte Carlo (MC) method to sample a parametric space describing geometric uncertainties. For each sample, which corresponds to a realization of the geometry, a deterministic electromagnetic solver computes the scattered fields. However, for an accurate statistical characterization the number of MC samples has to be large. In this work, to address this challenge, the continuation multilevel Monte Carlo (CMLMC) method is used together with a surface integral equation solver. The CMLMC method optimally balances statistical errors due to sampling of the parametric space, and numerical errors due to the discretization of the geometry using a hierarchy of discretizations, from coarse to fine. The number of realizations of finer discretizations can be kept low, with most samples computed on coarser discretizations to minimize computational cost. Consequently, the total execution time is significantly reduced, in comparison to the standard MC scheme.

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