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Litvinenko, Alexander (9)

Tempone, Raul (4)Genton, Marc G. (3)Sun, Ying (3)Bagci, Hakan (2)View MoreDepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division (5)Applied Mathematics and Computational Science Program (3)Center for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ) (2)ECRC, KAUST (2)Environmental Statistics Group, KAUST (2)View MoreSubjecthierarchical matrices (3)approximate covariance (1)data compression (1)electromagnetics and photonics (1)geostatistical optimal design (1)View MoreTypePoster (9)Year (Issue Date)
2015 (9)

Item AvailabilityOpen Access (9)

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

Litvinenko, Alexander; Haji Ali, Abdul Lateef; Uysal, Ismail Enes; Ulku, Huseyin Arda; Tempone, Raul; Bagci, Hakan; Oppelstrup, Jesper (2015-01-07) [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 [1]) 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.

Scalable Hierarchical Algorithms for stochastic PDEs and UQ

Litvinenko, Alexander; Chavez Chavez, Gustavo Ivan; Keyes, David E.; Ltaief, Hatem; Yokota, Rio (2015-01-07) [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 Kriemann [1,2]. 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].

Response Surface in Tensor Train Format for Uncertainty Quantification

Litvinenko, Alexander; Dolgov, Sergey; Khoromskij, Boris; Matthies, Hermann G. (2015-01-07) [Poster]

Minimum mean square error estimation and approximation of the Bayesian update

Litvinenko, Alexander; Matthies, Hermann G.; Zander, Elmar (2015-01-07) [Poster]

Given: a physical system modeled by a PDE or ODE with uncertain coefficient q(w), a measurement operator Y (u(q); q), where u(q; w) uncertain solution. Aim: to identify q(w). The mapping from parameters to observations is usually not invertible, hence this inverse identification problem is generally ill-posed. To identify q(w) we derived non-linear Bayesian update from the variational problem associated with conditional expectation. To reduce cost of the Bayesian update we offer a functional approximation, e.g. polynomial chaos expansion (PCE). New: We derive linear, quadratic etc approximation of full Bayesian update.

Hierarchical matrix approximation of large covariance matrices

Litvinenko, Alexander; Genton, Marc G.; Sun, Ying; Tempone, Raul (2015-01-07) [Poster]

We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(n log n). 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 optimal design

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.

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.

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.

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