On Monte Carlo Hybrid Methods for Linear Algebra

2016 ◽  
Author(s):  
Diego Davila ◽  
Vassil Alexandrov ◽  
Oscar A. Esquivel-Flores
Keyword(s):  
Monte Carlo ◽  
Linear Algebra ◽  
Hybrid Methods

The Monte Carlo Method in Radiative Heat Transfer

1998 ◽  
Vol 120 (3) ◽  
pp. 547-560 ◽  
Author(s):  
J. R. Howell
Keyword(s):  
Heat Transfer ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Hybrid Methods ◽  
Participating Media ◽  
Practical Applications ◽  
Monte Carlo Techniques ◽  
The Monte Carlo Method

The use of the Monte Carlo method in radiative heat transfer is reviewed. The review covers surface-surface, enclosure, and participating media problems. Discussion is included of research on the fundamentals of the method and on applications to surface-surface interchange in enclosures, exchange between surfaces with roughness characteristics, determination of configuration factors, inverse design, transfer through packed beds and fiber layers, participating media, scattering, hybrid methods, spectrally dependent problems including media with line structure, effects of using parallel algorithms, practical applications, and extensions of the method. Conclusions are presented on needed future work and the place of Monte Carlo techniques in radiative heat transfer computations.

scholarly journals Large Sample Properties of the Adaptive Gaussian Mixture Filter

2017 ◽  
Vol 145 (7) ◽  
pp. 2533-2553 ◽  
Author(s):  
Andreas S. Stordal ◽  
Hans A. Karlsen
Keyword(s):  
Monte Carlo ◽  
Particle Filter ◽  
Sample Size ◽  
Sequential Monte Carlo ◽  
Hybrid Methods ◽  
Gaussian Mixture ◽  
Error Norm ◽  
Filter Performance ◽  
Special Cases ◽  
Gaussian Mixture Filters

In high-dimensional dynamic systems, standard Monte Carlo techniques that asymptotically reproduce the posterior distribution are computationally too expensive. Alternative sampling strategies are usually applied and among these the ensemble Kalman filter (EnKF) is perhaps the most popular. However, the EnKF suffers from severe bias if the model under consideration is far from linear. Another class of sequential Monte Carlo methods is kernel-based Gaussian mixture filters, which reduce the bias but maintain the robustness of the EnKF. Although many hybrid methods have been introduced in recent years, not many have been analyzed theoretically. Here it is shown that the recently proposed adaptive Gaussian mixture filter can be formulated in a rigorous Bayesian framework and that the algorithm can be generalized to a broader class of interpolated kernel filters. Two parameters—the bandwidth of the kernel and a weight interpolation factor—determine the filter performance. The new formulation of the filter includes particle filters, EnKF, and kernel-based Gaussian mixture filters as special cases. Techniques from particle filter literature are used to calculate the asymptotic bias of the filter as a function of the parameters and to derive a central limit theorem. The asymptotic theory is then used to determine the parameters as a function of the sample size in a robust way such that the error norm vanishes asymptotically, whereas the normalized error is sample independent and bounded. The parameter choice is tested on the Lorenz 63 model, where it is shown that the error is smaller or equal to the EnKF and the optimal particle filter for a varying sample size.

Molecular dynamics, Monte Carlo and their hybrid methods: applications to thin film growth dynamics

1998 ◽  
Vol 334 (1-2) ◽  
pp. 209-213
Author(s):  
Jun-ichiro Takano ◽  
Osamu Takai ◽  
Yoshiaki Kogure ◽  
Masao Doyama
Keyword(s):  
Thin Film ◽  
Molecular Dynamics ◽  
Monte Carlo ◽  
Film Growth ◽  
Hybrid Methods ◽  
Growth Dynamics ◽  
Thin Film Growth

scholarly journals Monte Carlo Numerical Treatment of Large Linear Algebra Problems

2007 ◽  
pp. 747-754 ◽  
Author(s):  
Ivan Dimov ◽  
Vassil Alexandrov ◽  
Rumyana Papancheva ◽  
Christian Weihrauch
Keyword(s):  
Monte Carlo ◽  
Linear Algebra ◽  
Numerical Treatment
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