scholarly journals Comparison of Monte Carlo Methods Efficiency to Solve Radiative Energy Transfer in High Fidelity Unsteady 3D Simulations

2017 ◽  
Author(s):  
Lorella Palluotto ◽  
Nicolas Dumont ◽  
Pedro Rodrigues ◽  
Chai Koren ◽  
Ronan Vicquelin ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Monte Carlo Methods ◽  
Computational Cost ◽  
Statistical Error ◽  
Radiative Energy ◽  
Maximum Temperature ◽  
Quasi Monte Carlo ◽  
High Scalability ◽  
Transfer Problems

The present work assesses different Monte Carlo methods in radiative heat transfer problems, in terms of accuracy and computational cost. Achieving a high scalability on numerous CPUs with the conventional forward Monte Carlo method is not straightforward. The Emission-based Reciprocity Monte Carlo Method (ERM) allows to treat each mesh point independently from the others with a local monitoring of the statistical error, becoming a perfect candidate for high-scalability. ERM is however penalized by a slow statistical convergence in cold absorbing regions. This limitation has been overcome by an Optimized ERM (OERM) using a frequency distribution function based on the emission distribution at the maximum temperature of the system. Another approach to enhance the convergence is the use of low-discrepancy sampling. The obtained Quasi-Monte Carlo method is combined with OERM. The efficiency of the considered Monte-Carlo methods are compared.

QUASI MONTE–CARLO EVALUATION OF SENSITIVITIES OF OPTIONS IN COMMODITY AND ENERGY MARKETS

2003 ◽  
Vol 06 (08) ◽  
pp. 865-884 ◽  
Author(s):  
FRED E. BENTH ◽  
LARS O. DAHL ◽  
KENNETH H. KARLSEN
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Monte Carlo Methods ◽  
Random Variable ◽  
Numerical Differentiation ◽  
Energy Markets ◽  
Forward Contracts ◽  
Quasi Monte Carlo ◽  
Adaptive Techniques ◽  
Monte Carlo Evaluation

In this paper we consider the evaluation of sensitivities of options on spots and forward contracts in commodity and energy markets. We derive different expressions for these sensitivities, based on techniques from the recently introduced Malliavin approach [8, 9]. The Malliavin approach provides representations of the sensitivities in terms of expectations of the payoff and a random variable only depending on the underlying dynamics. We apply Monte–Carlo methods to evaluate such expectations, and to compare with numerical differentiation. We propose to use a refined quasi Monte–Carlo method based on adaptive techniques to reduce variance. Our approach gives a significant improvement of convergence.

QUASI-MONTE CARLO METHODS IN COMPUTATIONAL FINANCE

COSMOS ◽  
2005 ◽  
Vol 01 (01) ◽  
pp. 113-125
Author(s):  
HARALD NIEDERREITER
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Monte Carlo Methods ◽  
Scientific Computing ◽  
Computational Finance ◽  
Quasi Monte Carlo ◽  
Random Samples ◽  
Mortgage Backed Securities

Quasi-Monte Carlo methods are deterministic versions of Monte Carlo methods, in the sense that the random samples used in the implementation of a Monte Carlo method are replaced by judiciously chosen deterministic points with good distribution properties. They outperform classical Monte Carlo methods in many problems of scientific computing. This paper discusses applications of quasi-Monte Carlo methods to computational finance, with a special emphasis on the problems of pricing mortgage-backed securities and options. The necessary background on Monte Carlo and quasi-Monte Carlo methods is also provided.

scholarly journals Multilevel Quasi-Monte Carlo methods for lognormal diffusion problems

2017 ◽  
Vol 86 (308) ◽  
pp. 2827-2860 ◽  
Author(s):  
Frances Y. Kuo ◽  
Robert Scheichl ◽  
Christoph Schwab ◽  
Ian H. Sloan ◽  
Elisabeth Ullmann
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Quasi Monte Carlo ◽  
Diffusion Problems

scholarly journals A quasi-Monte Carlo method for computing areas of point-sampled surfaces

2006 ◽  
Vol 38 (1) ◽  
pp. 55-68 ◽  
Author(s):  
Yu-Shen Liu ◽  
Jun-Hai Yong ◽  
Hui Zhang ◽  
Dong-Ming Yan ◽  
Jia-Guang Sun
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Quasi Monte Carlo

Reduction of Computing Time and Improvement of Convergence Stability of the Monte Carlo Method Applied to Radiative Heat Transfer With Variable Properties

1989 ◽  
Vol 111 (1) ◽  
pp. 135-140 ◽  
Author(s):  
M. Kobiyama
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Computing Time ◽  
Energy Difference ◽  
Radiative Properties ◽  
Radiative Energy ◽  
Control Element ◽  
The Monte Carlo Method ◽  
The Difference ◽  
Convergence Stability

A modified Monte Carlo method is suggested to reduce the computing time and improve the convergence stability of iterative calculations without losing other excellent features of the conventional Monte Carlo method. In this method, two kinds of radiative bundle are used: energy correcting bundles and property correcting bundles. The energy correcting bundles are used for correcting the radiative energy difference between two successive iterative cycles, and the property correcting bundles are used for correcting the radiative properties. The number of radiative energy bundles emitted from each control element is proportional to the difference in emissive energy between two successive iterative cycles.

MONTE CARLO METHODS IN FUZZY GAME THEORY

2007 ◽  
Vol 03 (02) ◽  
pp. 259-269 ◽  
Author(s):  
AREEG ABDALLA ◽  
JAMES BUCKLEY
Keyword(s):  
Game Theory ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Monte Carlo Methods ◽  
Mixed Strategy ◽  
Minimax Theorem ◽  
Approximate Solutions ◽  
Mixed Strategies ◽  
Fuzzy Game ◽  
Zero Sum

In this paper, we consider a two-person zero-sum game with fuzzy payoffs and fuzzy mixed strategies for both players. We define the fuzzy value of the game for both players [Formula: see text] and also define an optimal fuzzy mixed strategy for both players. We then employ our fuzzy Monte Carlo method to produce approximate solutions, to an example fuzzy game, for the fuzzy values [Formula: see text] for Player I and [Formula: see text] for Player II; and also approximate solutions for the optimal fuzzy mixed strategies for both players. We then look at [Formula: see text] and [Formula: see text] to see if there is a Minimax theorem [Formula: see text] for this fuzzy game.

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