A Novel, Noniterative Inverse Boundary Design Regularized Solution Technique Using the Backward Monte Carlo Method

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
M. Mosavati ◽  
F. Kowsary ◽  
B. Mosavati
Keyword(s):  
Inverse Problem ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Substantial Reduction ◽  
Standard Test ◽  
Dominant Mode ◽  
Computational Time ◽  
Solution Technique ◽  
Transfer Factors ◽  
Radiant Exchange

In this paper, the inverse radiation boundary problem is solved using a simplified backward Monte Carlo method (MCM) for cases in which radiation is the dominant mode of heat transfer (i.e., radiative equilibrium). For an N-surface enclosure, N2 radiative transfer factors are required to carry out the radiant exchange calculations. In this paper, it is shown that when the enclosure is comprised of some adiabatic surfaces (as is nearly always the case in radiative furnaces), this number can be reduced considerably. This reduction in the required number of distribution factors causes a clear simplification in the formulation of the inverse problem and a substantial reduction in the computational time. After presenting the formulation for the inverse problem, standard test cases are solved to demonstrate the efficiency and the accuracy of the proposed method.

Improved Monte Carlo Method for Total Radiant Exchange Areas in Cylindrical Enclosure

2021 ◽  
pp. 1-11
Author(s):  
Jiaqi Zhong ◽  
Guojun Li ◽  
Dingyong Li ◽  
Xiaodong Wang ◽  
Cunhai Wang
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Radiant Exchange

Nonlinear Transient Analysis of Large Rotordynamic Systems

1991 ◽  
Vol 58 (2) ◽  
pp. 596-598 ◽  
Author(s):  
T. N. Shiau ◽  
A. N. Jean
Keyword(s):  
Degrees Of Freedom ◽  
Substantial Reduction ◽  
Computational Time ◽  
Solution Technique ◽  
Flexible Rotor ◽  
Nonlinear Characteristics ◽  
Rotor Systems ◽  
Nonlinear Transient ◽  
Nonlinear Components ◽  
Flexible Rotor Systems

A solution technique based on implicit numerical integration combined with a condensation technique is presented to predict the transient response of large flexible rotor systems with nonlinear characteristics. The analysis directly tackles the nonlinear second-order differential equations which describe the system motion. The condensation technique can lead to a reduced model in which only the coordinates associated with nonlinear components of the system are considered. Thus, a substantial reduction of computation can be expected if the nonlinear components of system are sparse. A flexible rotor system is studied to illustrate the merits of the procedures. The results show that, if the system is of a small number of coordinates associated with nonlinear components compared to that of entire system degrees-of-freedom, the computational time can be considerably reduced using this technique.

Numerical solution of the multidimensional Gelfand–Levitan equation

2015 ◽  
Vol 23 (5) ◽  
Author(s):  
Sergey I. Kabanikhin ◽  
Karl K. Sabelfeld ◽  
Nikita S. Novikov ◽  
Maxim A. Shishlenin
Keyword(s):  
Inverse Problem ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Two Dimensional ◽  
Nonlinear Inverse Problem ◽  
Coefficient Inverse Problem ◽  
Specific Point ◽  
The Monte Carlo Method ◽  
Linear Integral ◽  
Linear Integral Equations

AbstractThe coefficient inverse problem for the two-dimensional wave equation is solved. We apply the Gelfand–Levitan approach to transform the nonlinear inverse problem to a family of linear integral equations. We consider the Monte Carlo method for solving the Gelfand–Levitan equation. We obtain the estimation of the solution of the Gelfand–Levitan equation in one specific point, due to the properties of the method. That allows the Monte Carlo method to be more effective in terms of span cost, compared with regular methods of solving linear system. Results of numerical simulations are presented.

A Combined P1 and Monte Carlo Model for Radiative Transfer in Multi-Dimensional Anisotropically Scattering Media

2010 ◽  
Author(s):  
Leonid Dombrovsky ◽  
Wojciech Lipin´ski
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Phase Function ◽  
Monte Carlo Model ◽  
Reference Method ◽  
Computational Time ◽  
Scattering Media ◽  
Combined Method ◽  
Scattering Phase ◽  
Scattering Phase Function

A combined two-step computational method incorporating (1) transport approximation of the scattering phase function, (2) P1 approximation and the finite element method for computing the radiation source function at the first step, and (3) the Monte Carlo method for computing radiative intensity at the second step, is developed. The accuracy of the combined method is examined for model problems involving two multi-dimensional configurations of an anisotropically scattering medium. A detailed analysis is performed for a medium with scattering phase function described by a family of the Henyey–Greenstein functions. The accuracy of the two-step method is assessed by comparing the distribution of the radiative flux leaving the medium to that obtained by a reference complete Monte Carlo method. This study confirms the main results of previous papers on the errors of the two-step solution method. The combined method leads to a significant reduction in computational time as compared to the reference method, by at least 1 order of magnitude. Finally, possible applications of the combined method are briefly discussed.

Reverse Monte Carlo Method for Transient Radiative Transfer in Participating Media

2003 ◽  
Author(s):  
Xiaodong Lu ◽  
Pei-Feng Hsu
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Radiative Transfer ◽  
Transport Process ◽  
Computational Time ◽  
Reverse Monte Carlo ◽  
Scattering Media ◽  
Participating Media ◽  
Reverse Monte Carlo Method ◽  
Mc Method

The Monte Carlo (MC) method has been widely used to solve radiative transfer problems due to its flexibility and simplicity in simulating the energy transport process in arbitrary geometries with complex boundary conditions. However, the major drawback of the conventional (or forward) Monte Carlo method is the long computational time for converged solution. Reverse or backward Monte Carlo (RMC) is considered as an alternative approach when solutions are only needed at certain locations and time. The reverse algorithm is similar to the conventional method, except that the energy bundle (photons ensemble) is tracked in a time-reversal manner. Its migration is recorded from the detector into the participating medium, rather than from the source to the detector as in the conventional MC. There is no need to keep track of the bundles that do not reach a particular detector. Thus, RMC method takes up much less computation time than the conventional MC method. On the other hand, RMC will generate less information about the transport process as only the information at the specified locations, e.g., detectors, is obtained. In the situation where detailed information of radiative transport across the media is needed the RMC may not be appropriate. RMC algorithm is most suitable for diagnostic applications where inverse analysis is required, e.g., optical imaging and remote sensing. In this study, the development of a reverse Monte Carlo method for transient radiative transfer is presented. The results of non-emitting, absorbing, and anisotropically scattering media subjected to an ultra short light pulse irradiation are compared with the forward Monte Carlo and discrete ordinates methods results.

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